Using Dual-Polarization Interferograms to Correct Atmospheric ... - MDPI

remote sensing Article

Using Dual-Polarization Interferograms to Correct Atmospheric Effects for InSAR Topographic Mapping Zhiwei Liu 1 , Haiqiang Fu 1, *, Jianjun Zhu 1 , Cui Zhou 2 and Tingying Zuo 1 1 2

*

The School of Geosciences and Info-Physics, Central South University, Changsha 410083, China; [email protected] (Z.L.); [email protected] (J.Z.); [email protected] (T.Z.) The School of Key Laboratory for Digital Dongting Lake Basin of Hunan Province & College of Science, Central South University of Forestry and Technology, Changsha 410018, China; [email protected] Correspondence: [email protected]

Received: 28 June 2018; Accepted: 16 August 2018; Published: 20 August 2018







Abstract: Atmospheric effect represents one of the major error sources for interferometric synthetic aperture radar (InSAR), particularly for the repeat-pass InSAR data. In order to further improve the practicability of InSAR technology, it is essential to study how to estimate and eliminate the undesired impact of atmospheric effects. In this paper, we propose the multi-resolution weighted correlation analysis (MRWCA) method between the dual-polarization InSAR data to estimate and correct atmospheric effects for InSAR topographic mapping. The study is based on the a priori knowledge that atmospheric effects is independent of the polarization. To find the identical atmospheric phase (ATP) signals of interferograms in different polarizations, we need to remove the other same or similar phase components. Using two different topographic data, differential interferometry was firstly performed so that the obtained differential interferograms (D-Infs) have different topographic error phases. A polynomial fitting method is then used to remove the orbit error phases. Thus, the ATP signals are the only identical components in the final obtained D-Infs. By using a forward wavelet transform, we break down the obtained D-Infs into building blocks based on their frequency properties. We then applied weighted correlation analysis to estimate the wavelet coefficients attributed to the atmospheric effects. Thus, the ATP signals can be obtained by the refined wavelet coefficients during inverse wavelet transform (IWT). Lastly, we tested the proposed method by the L-band Advanced Land Observing Satellite (ALOS)-1 PALSAR dual-polarization SAR data pairs covering the San Francisco (USA) and Moron (Mongolia) regions. By using Ice, Cloud, and land Elevation Satellite (ICESat) data as the reference data, we evaluated the vertical accuracy of the InSAR digital elevation models (DEMs) with and without atmospheric effects correction, which shows that, for the San Francisco test site, the corrected interferogram could provide a DEM with a root-mean-square error (RMSE) of 7.79 m, which is an improvement of 40.5% with respect to the DEM without atmospheric effects correction. For the Moron test site, the corrected interferogram could provide a DEM with an RMSE of 10.74 m, which is an improvement of 30.2% with respect to the DEM without atmospheric effects correction. Keywords: Interferometric synthetic aperture radar (InSAR); atmospheric effects; multi-resolution analysis; correlation analysis; dual-polarization

1. Introduction Interferometric synthetic aperture radar (InSAR) is a powerful technology for Earth observations, which is noted for its all-weather and day-and-night working capability, wide spatial coverage, and fine resolution [1]. In particular, the repeat-pass interferometric mode has been widely employed to acquire InSAR data [2]. For repeat-pass synthetic aperture radar (SAR) interferograms, different image Remote Sens. 2018, 10, 1310; doi:10.3390/rs10081310

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acquisition times lead to different atmospheric delays for different SAR images, which result in significant atmospheric error in the interferometric phases. As an inevitable error source, the presence of atmospheric effects is a major problem in repeat-pass InSAR topographic mapping measurement [3]. In recent years, to estimate and correct atmospheric effects, three main types of methods have been proposed [4–10]: (1) Correlation analysis between interferometric phases and elevation [4,5]: Correlation analysis can be applied to remove the atmospheric phase (ATP) signals strongly correlated with topography. However, it is difficult to achieve satisfactory results with the interferograms acquired over plain areas. (2) Calibration with external data (e.g., GPS data [6], or Moderate Resolution Imaging Spectroradiometer (MODIS) [7] and Medium Resolution Imaging Spectrometer (MERIS) water vapor data [8]): This method based on external data has attracted increasing attention in recent years since the accuracy and resolution of the water vapor data are improved. However, we need to solve the problems of the inconsistent resolution and nonsynchronous acquisition times between the external data and SAR images. (3) Spatio-temporal analysis by multi-baseline InSAR data [9,10]: spatio-temporal analysis can be used to mitigate the atmospheric effects without relying on the relationship between the ATP signals and the topography or auxiliary data. However, to perform reliable spatio-temporal analysis, we need a large volume of repeat-pass SAR data covering the same area. Owing to the requirements for external auxiliary data or large volume of SAR data, it is difficult to use the above-mentioned methods to correct the atmospheric effects for accurate InSAR topographic mapping. As the ATP signals are independent of the polarization, multi-polarization SAR images contain the same atmospheric delay [11]. As a result, this provides a new idea for us to detect and remove the identical ATP components by use of multi-polarization interferograms. To achieve this goal, we propose the multi-resolution weighted correlation analysis (MRWCA) method between dual-polarization interferograms to estimate and remove the atmospheric effects for InSAR digital elevation model (DEM) generation. The main advantage of the MRWCA method is that it can remove the ATP signals for single-baseline InSAR data without depending on any a prior knowledge or external water vapor data. This paper is organized as follows. We begin by describing the phase components of differential interferograms (D-Infs) and the MRWCA method in Section 2. We then test the proposed method with real SAR data acquired over different topographic conditions in Section 3. In Section 4, we discuss the characteristics of the MRWCA method and some conclusions are drawn in the last section. 2. Methodology When two interferograms acquired in different polarizations are available, it provides us with the possibility to estimate the common ATP signals by correlation analysis. Before performing this, it is necessary to analyze their phase components and any other similar or identical phase components should be removed. 2.1. Phase in the Differential Interferograms The phase component of an interferogram is composed of flat-earth phase, topographic phase, ATP and noise phase (NP) [12]. In such a case, it is difficult to identify the ATP signals directly from the interferogram. In order to detect the ATP signals in the dual-polarization interferograms, differential interferometry is adopted to generate D-Infs whose phases are decomposed as:

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p

p

p

p

p

p

p

p

p

p

1 1 1 φdi1f f = φεtopo + φatm + φorbit + φnoise + φde1 f + φiono

(1)

2 2 2 φdi2f f = φεtopo + φatm + φorbit + φnoise + φde2 f + φiono

p

where ‘p1’ and ‘p2’ are the two selected polarizations (e.g., HH, HV, VV [13]). φεtopo is the topographic error phase (TEP), which is caused by the height error of auxiliary DEM used to simulate the topographic phase. φatm is the ATP, and φorbit is the orbit error phase caused by the uncertainty p in the orbit parameters. φnoise is the NP that is mainly attributed to thermal noise and de-correlation p p effect. φde f and φiono are the ground deformation and ionosphere phases, respectively, and are not considered in our study. Among the four phase components, except the ATP, the orbit error phase is also polarization-independent, which should be removed [14]. The orbit error phase is usually shown as a systematic phase trend and can be removed by a polynomial model incorporating elevation information [10,15]. In addition, since the SAR signals in different polarizations are sensitive to different scattering mechanisms, they are characterized by different phase centers and NP signals. In particular, p1 p2 the different phase centers will result in different TEPs φεtopo and φεtopo . However, if common external p

1 DEM is used to simulate the topographic phase for the dual-polarization interferograms, TEPs φεtopo

p2 φεtopo

and will be similar because they have the phase components caused by the identical ground elevation errors. In order to solve this problem, two different external DEMs are used to simulate the topographic phases for the two interferograms, respectively. Thus, the only common component in the two obtained D-Infs is the ATP φatm . 2.2. Estimation of the Atmospheric Effects Although previous studies have demonstrated that the TEP and the NP signals are composed by short-wavelength components, while the wavelengths of the ATP signals can range from tens of meters to tens of kilometers [5]. As a result, it is difficult to directly separate the ATP and non-ATP (TEP and NP) signals from the D-Inf only by filtering components characterized by different wavelengths. However, for the phase components characterized by different wavelengths, which are composed by different ATP and non-ATP signals. In such a case, it provides us the possibility to detect the common ATP signals mixed with different non-ATP signals. To achieve this goal, multi-resolution analysis performed by wavelet can be considered. To begin with, in the wavelet domain, a D-Inf can be expressed as multiple components characterized by different wavelengths. Consequently, we can investigate the spatial distribution of the D-Inf at different decomposition scales. In this paper, we introduce the multi-resolution analysis [16] p to the two D-Infs. Assuming φdii f f ( x, y) to be a 2D image with a size of m × n, the two D-Infs can be decomposed in the wavelet domain as follows [16]: p

m −1 n −1

φdi1f f ( x, y) = ∑ ∑ p2 di f f ( x, y )

k x ky m −1 n −1

= ∑ ∑ kx

ky

p1 v

p2 v

Jk x k y Φ Jk x k y ( x, y ) +

J −1 m −1 n −1 3

∑ ∑ ∑ ∑ p1 wεjk x ky ψεjk x ky ( x, y)

j k x ky ε J −1 m −1 n −1 3

(2)

p2 ε ε Jk x k y Φ Jk x k y ( x, y ) + ∑ ∑ ∑ ∑ w jk x k y ψ jk x k y ( x, y ) j

kx

ky

ε

where Φ and Ψ are the smoothing and the mother wavelet functions, respectively; p1 w and p2 w are the wavelet coefficients; J is the number of decomposition scales, and ε = 1, 2, 3 represents the horizontal (H), vertical (V), and diagonal (D) detail information, respectively. The high-frequency components of the two D-Infs, which contain the common ATP signals, have the same or similar values. To evaluate this similarity, we calculate the linear relationship between the wavelet coefficients in different polarizations for each scale j as follows: p1

wεj = f p2 wεj + c j

(3)

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where f is the slope and ranges from 0 to 1, which is called the correlation coefficient since it indicates the similarity of the ATP signals within the two polarimetric interferograms; and c j represents a constant bias term. The larger the slope, the more similar the ATP components. In this paper, least squares (LS) estimation is used to calculate the slope f and constant bias c j . Although f can determine the ratio of the ATP signals in the obtained D-Infs, it only expresses the global correlation relationship. In such a case, the correlation coefficient f has low sensitivity to the ATP variation since the ATP ratios are different for each pixel. To solve this problem, the perpendicular distance from the wavelet coefficient point to the fitting line is then used to formulate a weighted indicator [17] and the correlation coefficient f is refined by: ! 2 d f i0 = λi f where λi = exp − 2 i (4) dmax where di is the perpendicular distance from the ith wavelet coefficient point to the fitting line, and dmax is the maximum distance. λi is the weighted indicator that indicates that when a wavelet coefficient point has a lager perpendicular distance to the fitting line, it makes a smaller contribution to the global correlation coefficient f and has less ATP signals. Thus, the wavelet coefficients atm wεj of the ATP signals can be obtained as follows: atm ε wˆ ij = f i0 p wijε + c j (5) Following the refined wavelet coefficients, the ATP signals can be reconstructed by IWT. Finally, the corrected D-Infs can be obtained by removing the ATP signals from the original D-Infs. Another problem should be considered is that how to identify an appropriate number of decomposition scales for the wavelet decomposition to better separate the high-frequency and low-frequency components. This problem can be solved either by visually or based on a priori information. However, owing to the difficulties for either visually or the acquisition of priori information of ATP signals, it is difficult to use the above-mentioned methods to determine an appropriate number of scales for the wavelet decomposition. Thus, in our study a relatively straightforward method was selected, which assumes the ATP signals have a variety of wavelengths from pixel size to broader scales as large as the whole interferogram and was described in [5]. To better understand the MRWCA method, its workflow is presented in Figure 1, which can be divided into the D-InSAR processing, wavelet transform, weight correlation analysis and the estimation of ATP phases. Firstly, two independent external DEMs are adopted to simulate the topographic phases for different polarimetric interferograms so that the obtained D-Infs contain different TEP signals. We then use two-dimensional discrete wavelet transform (2D-DWT) to decompose the D-Infs into different phase components characterized by different wavelengths. However, before doing this, we need to adopt suitable strategy to remove other similar or identical phase components (e.g., orbit error phases). After this, the correlations between the two D-Infs are calculated, which are mainly attributed to the identical ATP signals. Lastly, we can estimate the ATP signals in the D-Infs by IWT and obtain the corrected D-Infs.

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Figure 1. 1. The ofthe themulti-resolution multi-resolution weighted weighted correlation correlation analysis analysis (MRWCA) Figure The workflow workflow of (MRWCA) method. method.

3. Experiments and Analysis 3. Experiments and Analysis To demonstrate the validity of the proposed approach, we applied it to two interferometric To demonstrate the validity of the proposed approach, we applied it to two interferometric pairs pairs of L-band Advanced Land Observing Satellite (ALOS)-1 PALSAR images covering the San of L-band Advanced Land Observing Satellite (ALOS)-1 PALSAR images covering the San Francisco Francisco (USA) and Moron (Mongolia) regions. The first test area is near the Pacific Ocean, while (USA) and Moron (Mongolia) regions. The first test area is near the Pacific Ocean, while the second test the second test site is located in inland, and they are characterized by different weather and site is located in inland, and they are characterized by different weather and topographic conditions. topographic conditions. This results in different atmospheric distributions, allowing us to This results in different atmospheric distributions, allowing us to investigate the effectiveness of the investigate the effectiveness of the proposed method under different conditions. The images were proposed method under different conditions. The images were acquired in fine-beam dual-polarization acquired in fine-beam dual-polarization (FBD) mode, and the spatial resolution is azimuth × range = (FBD) mode, and the spatial resolution is azimuth × range = 3.1 m × 9.4 m. Moreover, since the two 3.1 m × 9.4 m. Moreover, since the two test sites are at high geographic latitudes, the total electron test sites are at high geographic latitudes, the total electron content (TEC) is relatively low [18], and the content (TEC) is relatively low [18], and the ionospheric effects can be ignored. ionospheric effects can be ignored. For the accuracy assessment for the InSAR DEM, due to the lack of a high-accuracy DEM, the For the Laser accuracy assessment for(GLAS)/ the InSAR the Elevation lack of a Satellite high-accuracy DEM, Geoscience Altimeter System Ice, DEM, Cloud,due andto land (ICESat) L2 the Geoscience Laser Altimeter System (GLAS)/ Ice, Cloud, and land Elevation Satellite (ICESat) Global Land Surface Altimetry Data Version 34 (GLAH 14) [19] are used as the reference data. The L2 Global Land Surface Altimetry Data Version 34 (GLAH 14) [19] used diameter. as the reference data. GLAS instrument produced laser spots on the Earth’s surface withare a 70-m Its vertical The GLAS instrument produced laser spots on the Earth’s surface with a 70-m diameter. Its vertical accuracy is better than 1 m [20]. accuracy is better than 1 m [20]. 3.1 San Francisco Test Site 3.1. San Francisco Test Site The first test site is located in San Francisco (USA). The dual-polarization (HH and HV The first test site is located in San Francisco (USA). The dual-polarization (HH and HV polarizations) pair of L-band ALOS-1 PALSAR images have a 46-day interval, and the coverage is polarizations) L-band ALOS-1 PALSAR a 46-day interval, andand thefeatures coverage roughly 80 kmpair × 75 of km, as shown in Figure 2. Theimages test sitehave is close to the Pacific Ocean a ishigh roughly km ×content. 75 km, as shown in Figure 2. The test site is close to the Pacific Ocean and features water80vapor a high water vapor content.

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Figure footprint of the ALOS-1 PALSAR images over the Francisco region and spatial Figure 2. 2. The The of of thethe ALOS-1 PALSAR images overover the San San regionregion and the the spatial Figure 2. Thefootprint footprint ALOS-1 PALSAR images the Francisco San Francisco and the coverage of the Ice, Cloud, and land Elevation Satellite/Geoscience Laser Altimeter System coverage of the Ice, Cloud, and land Elevation Satellite/Geoscience Laser Altimeter System spatial coverage of the Ice, Cloud, and land Elevation Satellite/Geoscience Laser Altimeter System (ICESat/GLAS) over the study area. (ICESat/GLAS) data data (ICESat/GLAS) data over over the the study study area. area.

Figure Figure 3a 3a displays displays the the 30-m 30-m resolution resolution DEM DEM of of the the test test site site acquired acquired by by the the Shuttle Shuttle Radar Radar Figure 3a displays the 30-m resolution DEM of the varies test site acquired by the Shuttle Radar Topography Mission (SRTM) [21], in which the elevation between 10 m and 1440 m above Topography Mission (SRTM) [21], in which the elevation varies between 10 m and 1440 m above Topography Mission (SRTM) [21], in which the elevation varies between 10 m and 1440 m above mean mean sea sea level. level. Moreover, Moreover, another another 30-m 30-m DEM DEM measured measured by by the the Advanced Advanced Spaceborne Spaceborne Thermal Thermal mean sea level. Moreover, another 30-m DEM measured by the Advanced Spaceborne Thermal Emission Emission and and Reflection Reflection Radiometer Radiometer (ASTER) (ASTER) [22] [22] was was also also collected collected and and is is shown shown in in Figure Figure 3b. 3b. The The Emission and Reflection Radiometer (ASTER) [22] was also collected andthey is shown in Figure 3b. elevation errors of the two DEMs are different and independent, because were measured elevation errors of the two DEMs are different and independent, because they were measured by by The elevation errors of the two DEMs areby different anderror independent, The because they were measured by two two different different techniques techniques characterized characterized by different different error sources. sources. The difference difference map map of of the the two two two different techniques characterized by differentmean error sources. The difference map of the two DEMs DEMs DEMs is is shown shown in in Figure Figure 3c, 3c, which which has has aa global global mean of of 0.07 0.07 m m with with aa standard standard deviation deviation (STD) (STD) of of is shown in Figure 3c, which has a global mean of 0.07 m with a standard deviation (STD) of 7.07 m. 7.07 7.07 m. m.

Figure 3. Mission digital elevation model (SRTM DEM); (b) Advanced Figure 3. 3. (a) (a) Shuttle Shuttle Radar Radar Topography Topography Mission Mission digital digital elevation elevation model model (SRTM (SRTM DEM); DEM); (b) (b) Advanced Advanced Figure (a) Shuttle Topography Spaceborne Thermal Emission and Reflection Radiometer (ASTER) DEM; (c) Difference map Spaceborne Thermal ThermalEmission Emission Reflection Radiometer (ASTER) DEM; (c) Difference map Spaceborne andand Reflection Radiometer (ASTER) DEM; (c) Difference map between between the SRTM DEM and the ASTER DEM. the SRTMthe DEM andDEM the ASTER DEM. between SRTM and the ASTER DEM.

(1) Generation of differential interferograms: used to (1) Generation Generation of of differential differential interferograms: interferograms: The The dual-polarization dual-polarization SAR SAR images images were were used used to to (1) The dual-polarization SAR images were constitute two polarimetric interferograms with a perpendicular baseline [12] of 300 m and constitutetwo twopolarimetric polarimetric interferograms a perpendicular baseline ofand 300a m and aa constitute interferograms withwith a perpendicular baseline [12] of [12] 300 m temporal temporal baseline of 46 days. The acquisition time interval was only 46 days, so we could exclude temporalofbaseline 46 days. The acquisition timewas interval was onlyso46we days, so exclude we could baseline 46 days.ofThe acquisition time interval only 46 days, could theexclude phase the phase caused by topography change in this test site. We firstly adopted two-pass differential the phase caused by topography change in this test site. We firstly adopted two-pass differential caused by topography change in this test site. We firstly adopted two-pass differential interferometry interferometry to polarimetric interferometry to produce produce the the polarimetric D-Infs. D-Infs. to produce the polarimetric D-Infs. The interferograms were multi-looked with pixels in the azimuth direction and 22 pixels in The interferograms were multi-looked with1010 10 pixels azimuth direction pixels in The interferograms were multi-looked with pixels in in thethe azimuth direction andand 2 pixels in the the range direction to obtain aa final resolution of 30 m ×× 30 m. The two DEMs (ASTER DEM and the range direction to obtain final resolution of 30 m 30 m. The two DEMs (ASTER DEM and range direction to obtain a final resolution of 30 m × 30 m. The two DEMs (ASTER DEM and SRTM SRTM DEM) were then used to the topographic phase and SRTMwere DEM) were used the to remove remove the phase topographic phase for for the the HH-polarization HH-polarization and DEM) then usedthen to remove topographic for the HH-polarization and HV-polarization HV-polarization interferograms, respectively. Moreover, to suppress noise, the interferograms were HV-polarization interferograms, respectively. Moreover, to suppress noise, the interferograms were interferograms, respectively. Moreover, to suppress noise, the interferograms were filtered with the filtered the Goldstein filter [23], and the minimum cost flow (MCF) method [24] filtered with with the improved improved Goldstein filter and then then theflow minimum flow[24] (MCF) improved Goldstein filter [23], and then the[23], minimum cost (MCF) cost method wasmethod applied[24] for was applied for the unwrapping process to those pixels that presented coherence of at least 0.3 [25]. was applied for the unwrapping process to those pixels that presented coherence of at least 0.3while [25]. the unwrapping process to those pixels that presented coherence of at least 0.3 [25]. However, However, while interferogram is affected because of which will result However, while the the interferogram is seriously seriously affected becausewhich of decorrelation, decorrelation, which result in in the interferogram is seriously affected because of decorrelation, will result in somewill uncertainty some uncertainty problems in noise filtering and phase unwrapping [26,27]. To solve these some uncertainty problems in noise filtering and phase unwrapping [26,27]. To solve these problems, problems, we we should should consider consider the the improved improved methods methods for for D-InSAR D-InSAR processing processing in in the the future future work. work. Then, Then, to to evaluate evaluate the the wavelet wavelet transform, transform, the the data data should should be be continuous continuous on on aa regular regular grid, grid, so so the the

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problems in noise filtering and phase unwrapping [26,27]. To solve these problems, we should consider Remote 77 of Remote Sens. Sens. 2018, 2018,10, 10,xx FOR FORPEER PEERREVIEW REVIEW of 18 18 the improved methods for D-InSAR processing in the future work. Then, to evaluate the wavelet transform, the data should be continuous on a regular grid, sointerpolation. the voids with the low-coherence pixels voids voids with with the the low-coherence low-coherence pixels pixels were were filled filled using using linear linear interpolation. Then, Then, after after the the removal removal of of were filled using linear interpolation. Then, after the removal of the orbit error phases by a polynomial the the orbit orbit error error phases phases by by aa polynomial polynomial model model incorporating incorporating elevation elevation information information [10,15], [10,15], the the model incorporating elevation information [10,15], the obtained D-Infs were superimposed on the obtained obtained D-Infs D-Infs were were superimposed superimposed on on the the SRTM SRTM DEM DEM and and are are shown shown in in Figure Figure 4a,b. 4a,b. ItIt is is clear clear that that SRTM DEM and are shown inobvious Figure 4a,b. It is clear the obtained obvious positive the D-Infs contain positive and negative signals, which are by the obtained obtained D-Infs contain obvious positive and that negative signals,D-Infs whichcontain are contributed contributed by the the and negative signals, which are contributed by the identical ATPHV signals. In addition, the difference map identical ATP signals. In the map and D-Infs shown in identical ATP signals. In addition, addition, the difference difference map of of the the HV and HH HH D-Infs is is shown in Figure Figure of HV the andsame HH D-Infs shownhave in Figure Since the same signalsmap haveisbeen counteracted, 4c. Since ATP signals been counteracted, the difference up 4c.the Since the same ATP is signals have been 4c. counteracted, theATP difference map is made made up of of the the the difference map is made up of the topography-relevant phase signals caused by the difference of topography-relevant topography-relevant phase phase signals signals caused caused by by the the difference difference of of the the external external elevation elevation data data and and the the the external elevation data and the difference of the polarimetric phase centers. difference difference of of the the polarimetric polarimetric phase phase centers. centers.

Figure map between the HV and HH D-Infs. Figure 4. 4. Original Original (a) (a) HH HH and and (b) (b) HV HV D-Infs; D-Infs; (c) (c) the the difference differencemap mapbetween betweenthe theHV HVand andHH HHD-Infs. D-Infs. Figure 4. Original (a) HH and (b) HV D-Infs; (c) the difference

(2) Estimation the ATP: To begin with, we decomposed the obtained (2) Estimation Estimation and and correction correction of of the the ATP: ATP: To To begin begin with, with, we we decomposed decomposed the the obtained obtained (2) and correction of dual-polarization D-Infs into different scales. Before doing this, we needed to choose an optimal dual-polarization D-Infs D-Infs into into different different scales. scales. Before Before doing doing this, this, we we needed needed to to choose choose an an optimal optimal dual-polarization J wavelet decomposition scale , which could ensure the separation of the ATP signals and the other J wavelet decomposition scale , which could ensure the separation of the ATP signals and the other wavelet decomposition scale J, which could ensure the separation of the ATP signals and the other non-ATP signals. In this study, the optimal decomposition scale was set to 11, for which we refer the non-ATP signals. In this study, the optimal decomposition scale was set to 11, for which we refer the non-ATP signals. In this study, the optimal decomposition scale was set to 11, for which we refer the reader to [5]. We could then establish the linear relationship between the wavelet coefficients for readertoto[5]. [5].We Wecould could then establish linear relationship between the wavelet coefficients for reader then establish thethe linear relationship between the wavelet coefficients for each each level of decomposition with Equation (3). To better understand the correlation analysis, the red each level of decomposition with Equation (3). To better understand the correlation analysis, the red level of decomposition with Equation (3). To better understand the correlation analysis, the red solid solid lines in 5 show plots of coefficients in direction. It is solidin lines in Figure Figure show scatter scatter of the the wavelet wavelet coefficients in the the horizontal horizontal direction. is lines Figure 5 show5scatter plots ofplots the wavelet coefficients in the horizontal direction. It is clearItto clear to see that the correlation of the wavelet coefficients increases with the decomposition scale. clear to the see correlation that the correlation of thecoefficients wavelet coefficients increases with the decomposition see that of the wavelet increases with the decomposition scale. The scale. high The high correlation indicates that the wavelet coefficients are almost all contributed by same The high correlation indicates that the wavelet coefficients are almost all contributed by the the same correlation indicates that the wavelet coefficients are almost all contributed by the same ATP signals. ATP signals. In the scatter plots have trends the vertical ATP signals.the In addition, addition, thehave scatter plotstrends have similar similar trends in in thediagonal vertical and and diagonal diagonal directions. directions. In addition, scatter plots similar in the vertical and directions.

5. Scatter plots (HV vs. HH) the wavelet coefficients direction indicates Figure the wavelet coefficients in in horizontal direction (a–k(a–k indicates the Figure5. 5.Scatter Scatterplots plots(HV (HVvs. vs.HH) HH)ofof of the wavelet coefficients in horizontal horizontal direction (a–k indicates the wavelet decomposition scales ranging from 1 to 11). wavelet decomposition scales ranging from 1 to 11). the wavelet decomposition scales ranging from 1 to 11).

We We can can see see that that the the correlation correlation between between the the coefficients coefficients expresses expresses the the global global trend; trend; however, however, the the ratios ratios of of atmosphere atmosphere composition composition are are different different for for each each pixel, pixel, so so the the values values of of the the ATP ATP ratio ratio should should also also have have some some differences. differences. In In this this study, study, we we append append an an appropriate appropriate weighting weighting indicator indicator to to refine refine the correlation coefficients, which can be used to extract the ATP signals accurately. Thus, the correlation coefficients, which can be used to extract the ATP signals accurately. Thus, the the

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We can see that the correlation between the coefficients expresses the global trend; however, the ratios of atmosphere composition are different for each pixel, so the values of the ATP ratio should also have some differences. In this study, we append an appropriate weighting indicator to refine the correlation Remote Sens. 2018, 10, x FOR PEER REVIEW 8 of 18 Remote Sens. 2018, 10, xcan FORbe PEER REVIEW of 18 coefficients, which used to extract the ATP signals accurately. Thus, the wavelet coefficients of8 ATP signals can be calculated by Equation (5), and the ATP signals can be obtained by computing the IWT wavelet coefficients of ATP signals can be calculated by Equation (5), and the ATP signals can be wavelet of ATP signals canthe berefined calculated by Equation (5), and the ATP signals can be using thecoefficients refined wavelet coefficients. obtained by computing the IWT using wavelet coefficients. obtained by computing the using the refined waveletinin coefficients. The corrected and are Figure Clearly, most of The final final corrected HH HHIWT andHV HVD-Infs D-Infs arepresented presented Figure6a,b, 6a,b,respectively. respectively. Clearly, most The final corrected HH and HV D-Infs are presented in Figure 6a,b, respectively. Clearly, most the positive and negative signals MRWCA method. method. of the positive and negative signalsininFigure Figure4a,b 4a,bare areremoved removedby bythe the use use of of the the MRWCA of the positive and negative signals in Figure 4a,b are removed by the use of the MRWCA method. Figure 6c shows the difference map of the corrected HV and HH D-Infs. Figure 6c shows the difference map of the corrected HV and HH D-Infs. Figure 6c shows the difference map of the corrected HV and HH D-Infs.

Figure 6. 6. (a) (a)HH HHand and D-Infs corrected byMRWCA the MRWCA method. The difference map Figure (b)(b) HVHV D-Infs corrected by the method. (c) The (c) difference map between Figure 6.the (a)corrected HH and HV (b) and HV HH D-Infs corrected by the MRWCA method. (c) The difference map between D-Infs. the corrected HV and HH D-Infs. between the corrected HV and HH D-Infs.

(3) Assessment of the derived DEMs: After mitigating the ATP signals, the corrected HH (3) Assessment of the derived DEMs: After mitigating mitigating the ATP ATP signals, signals, the the corrected HH (3) Assessment of the derivedthe DEMs: HH interferogram was used to generate DEM After since it has higherthe phase quality, which corrected is of benefit to interferogram was was used used to to generate generate the the DEM DEM since since it it has has higher higher phase phase quality, quality, which which is is of of benefit benefit to interferogram to extract DEM. To verify the effectiveness of the proposed method, we evaluated the vertical accuracy extract DEM. verify the effectiveness of the method, we evaluated thethe vertical accuracy of extract DEM. To To verify thewere effectiveness theproposed proposed method, we evaluated vertical accuracy of the InSAR DEMs that generatedofwithout atmospheric effects correction, with atmospheric thethe InSAR DEMs thatthat werewere generated without atmospheric effectseffects correction, with atmospheric effects of DEMs generated without atmospheric correction, with atmospheric effects InSAR correction using Shirzaei’s atmospheric correction method [5], and with atmospheric effects correction using Shirzaei’s atmospheric correction method [5], and with atmospheric effects correction effects correction using Shirzaei’s atmospheric [5], and with atmospheric effects correction using the MRWCA method, as showncorrection in Figuremethod 7. using the MRWCA asmethod, shown inasFigure correction using themethod, MRWCA shown7.in Figure 7.

Figure7. Interferometric synthetic aperture radar (InSAR) DEM (a) without atmospheric correction, Figure7. Interferometric synthetic aperture radar (a) atmospheric correction, Figure Interferometric synthetic aperture radar (InSAR) (InSAR) DEMMRWCA (a) without without atmospheric correction, (b) with7.Shirzaei’s atmospheric correction method, and (c) DEM with atmospheric correction. (b) with Shirzaei’s atmospheric correction method, and (c) with MRWCA atmospheric correction. (b) with Shirzaei’s atmospheric correction method, and (c) with MRWCA atmospheric correction.

Firstly, owing to the lack of actual ground measurement elevation data, while the ASTER DEM Firstly, owing to the lack of actual ground measurement elevation data, while theDEM ASTER DEM was used as owing input data forlack theof HH-polarization interferogram,elevation we selected the SRTM covering Firstly, to the actual ground measurement data, while the ASTER DEM was used as input data for interferogram, weanalysis. selected thecalculated SRTM DEM the experimental as the the HH-polarization validation data for the qualitative thecovering vertical was used as inputregion data for the HH-polarization interferogram, we selectedWe the SRTM DEM covering the experimental region as the validation datathe for the qualitative We obtained calculated theelevation vertical difference of the InSAR-derived DEMs with SRTManalysis. DEM, and the the experimental region as the validation data forvalidation the qualitative analysis. We calculated the vertical difference of the InSAR-derived DEMs with the validation SRTM DEM, and obtained the elevation difference of distribution, as shownDEMs in Figure 8. From FigureSRTM 8, weDEM, can see elevation difference the InSAR-derived with the validation andthe obtained thedifference elevation difference distribution, as shown in Figure 8. From Figure 8, we can see the elevation difference without atmospheric larger than 8,that thethe atmosphere correction difference distribution,correction as shownisinsignificantly Figure 8. From Figure we after can see elevation difference without atmospheric correction is significantly largeratmospheric than that after the atmosphere process. atmospheric In addition, correction the InSARisDEM with Shirzaei’s correction method alsocorrection contains without significantly larger than that after the atmosphere correction process. process. In addition, the InSAR DEM with Shirzaei’s atmospheric correction method also contains large errors the when compared withShirzaei’s the resultatmospheric of the MRWCA method, whichalso cancontains be attributed to the In addition, InSAR DEM with correction method large errors large errors when compared the evaluate result of the the ATP MRWCA method, which can bewith attributed to the fact that Shirzaei’s method iswith used signals thatcan are correlated topography. when compared with the result oftothe MRWCA method, which be attributed to the fact that fact that Shirzaei’s method is used evaluate thetopography-dependent ATP signals that are correlated with topography. However, the MRWCA method cantoremove both ATPtopography. signals (TD-ATP) and Shirzaei’s method is used to evaluate the ATP signals that are correlated with However, However, the MRWCA method can remove both topography-dependent ATP signals (TD-ATP) and the turbulent ATP (T-ATP) signals [12], without depending on the relationship between ATP signals the ATP (T-ATP) signals [12], without depending on the relationship between ATP signals andturbulent topography. and topography.

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the MRWCA method can remove both topography-dependent ATP signals (TD-ATP) and the turbulent Remote Sens. 2018, 10, x FOR PEER REVIEW 9 of 18 ATP signals [12], without depending on the relationship between ATP signals and topography. Remote(T-ATP) Sens. 2018, 10, x FOR PEER REVIEW 9 of 18

Figure 8. The elevation difference distribution (a) without atmospheric correction; (b) with Shirzaei’s Figure 8. 8. The The elevation elevation difference difference distribution distribution (a) (a) without without atmospheric atmospheric correction; correction; (b) (b) with with Shirzaei’s Shirzaei’s Figure atmospheric correction method; and (c) with MRWCA atmospheric correction. atmospheric correction method; and (c) with MRWCA atmospheric correction. atmospheric correction method; and (c) with MRWCA atmospheric correction.

In order to further verify the accuracy, we used ICESat altimetry data as a reference for the In order to further verify the accuracy, we used ICESat altimetry data as a reference for the In order analysis. to furtherThe verify theinstrument accuracy, we used ICESat altimetry as asurface reference the quantitative GLAS produces laser spots on thedata Earth’s withfor a 70-m quantitative analysis. The GLAS instrument produces laser spots on the Earth’s surface with a 70-m quantitative analysis. The GLAS instrument produces laser spots on the Earth’s surface with a 70-m diameter in each footprint location of ICESat, so we calculated an average value of the DEMs within diameter in each footprint location of ICESat, so we calculated an average value of the DEMs within diameter each footprint location between of ICESat,the so ICESat we calculated an average value of theToDEMs within 70 m to in evaluate the difference and InSAR-derived DEMs. quantify the 70 m to evaluate the difference between the ICESat and InSAR-derived DEMs. To quantify the 70difference, m to evaluate the difference between the ICESat and InSAR-derived DEMs. To quantify the Figure 9 shows the histograms of the differences. Quantitatively, we evaluate the difference, Figure 9 shows the histograms of the differences. Quantitatively, we evaluate the difference, Figure 9accuracy shows the histograms of the differences. Quantitatively, we evaluate the the absolute absolute vertical of the InSAR-derived DEMs in Figure 7, which shows that after use of absolute vertical accuracy of the InSAR-derived DEMs in Figure 7, which shows that after the use of vertical accuracy of the InSAR-derived DEMsthe in Figure which showsfrom that after use10.16 of Shirzaei’s Shirzaei’s atmospheric correction method, RMSE 7, has decreased 13.10the m to m, while Shirzaei’s atmospheric correction method, the RMSE has decreased from 13.10 m to 10.16 m, while atmospheric correction method, hasMRWCA decreasedcorrection from 13.10method. m to 10.16 m, while the RMSE has the RMSE has decreased to 7.79the mRMSE with the the RMSE has decreased to 7.79 m with the MRWCA correction method. decreased to 7.79 m with the MRWCA correction method.

Figure 9.Histograms Histograms ofthe the elevationdifferences differences betweenthe the ICESatdata data andthe the InSAR-derived Figure Figure 9. 9. Histograms of of the elevation elevation differences between between the ICESat ICESat data and and the InSAR-derived InSAR-derived DEMs generated without atmospheric correction, with Shirzaei’s atmospheric correction and DEMs generated without atmospheric correction, with Shirzaei’s atmospheric correction and MRWCA DEMs generated without atmospheric correction, with Shirzaei’s atmospheric correction and MRWCA atmospheric correction, respectively. atmospheric correction,correction, respectively. MRWCA atmospheric respectively.

3.2Moron MoronTest TestSite Site 3.2. 3.2 Moron Test Site Thesecond secondtest testarea areacovers covers approximately8080km km ×75 75 km of the Moron area, located in the The covers approximately approximately km × × 75 km of the Moron area, located in the northwestern part of Mongolia. This area has a landform of mountainswith withsteep steepslopes, slopes,where wherethe the northwestern part of Mongolia. This area has a landform of mountains elevation changes substantially, and features complex terrain conditions. Two L-bandPALSAR ALOS-1 elevation andand features complex terrainterrain conditions. Two L-band elevation changes changessubstantially, substantially, features complex conditions. Two ALOS-1 L-band ALOS-1 PALSAR images acquired in dual-polarization (HH and HV) were collected, as shown in Figure 10. images acquired dual-polarization (HH and HV) collected, shown in PALSAR images in acquired in dual-polarization (HHwere and HV) were as collected, as Figure shown 10. in Figure 10.

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Figure footprint of ALOS-1 the ALOS-1 PALSAR images over the Moron the coverage spatial Figure 10. 10. TheThe footprint of the PALSAR images over the Moron regionregion and theand spatial coverage ofThe the ICESat/GLAS data over thePALSAR study area. Figure 10. footprint of the ALOS-1 images over the Moron region and the spatial of the ICESat/GLAS data over the study area. coverage of the ICESat/GLAS data over the study area. Figure 10. The DEMs footprint of the PALSAR over the Moron andresolution the spatial of 30 The reference were theALOS-1 SRTM DEM andimages the ASTER DEM withregion a spatial coverage of the ICESat/GLAS data over the study area. The reference DEMs were the SRTM DEM and the ASTER DEM with a spatial resolution of 30 m, m, which are shown in Figure 11a,b. The elevation in this area varies from 1220 m to 2560 m above

The reference DEMs were the SRTM DEM and the ASTER DEM with a spatial resolution of 30 which are shown inThe Figure 11a,b.11a,b. The elevation inDEMs this varies from 12201220 m towhich m above mean mean sea level. difference map of the two is shown in Figure 11c, has a global m, which are shown in Figure The elevation in area this area varies from m2560 to 2560 m above TheThe reference DEMs were the SRTM DEM and the ASTER DEM11c, with a spatial resolution of 30 of seamean level. difference map of the two DEMs is shown in Figure which has a global mean mean of 0.05 m with a standard deviation (STD) of 10.71 m. sea level. The difference map of the two DEMs is shown in Figure 11c, which has a global m,mwhich are shown in Figure 11a,b. elevation in this area varies from 1220 m to 2560 m above 0.05 a standard (STD)The of 10.71 meanwith of 0.05 m with adeviation standard deviation (STD)m. of 10.71 m. mean sea level. The difference map of the two DEMs is shown in Figure 11c, which has a global mean of 0.05 m with a standard deviation (STD) of 10.71 m.

Figure 11. (a) SRTM DEM. (b) ASTER DEM. (c) Difference map between the SRTM DEM and the ASTER DEM. Figure SRTMDEM. DEM.(b) (b)ASTER ASTER DEM. DEM. (c) (c) Difference Difference map and thethe Figure 11.11. (a)(a)SRTM mapbetween betweenthe theSRTM SRTMDEM DEM and ASTER DEM. ASTER DEM. Figure 11. (a) SRTM DEM. (b) ASTER DEM. (c) Difference map between the SRTM DEMwere and the (1) Generation of differential interferograms: The dual-polarization SAR images used to ASTER DEM. constitute two polarimetric interferograms with a perpendicular baseline [12] of 190 m and a

(1) Generation of differential interferograms: The dual-polarization SAR images were used to (1) Generation of46 differential interferograms: dual-polarization SAR were temporal baseline of days. interferograms We then appliedwith the same two-pass differential strategy constitute two polarimetric a The perpendicular baselineinterferometry [12] images of 190 m andused a (1) Generation of differential interferograms: The dual-polarization SAR images were used to a to temporal constitute two interferograms with a perpendicular baseline [12] of 190 m and to obtain baseline the twopolarimetric polarimetric D-Infs, which were superimposed on the SRTM DEM and are shown of 46 days. We then applied the same two-pass differential interferometry strategy constitute two polarimetric interferograms with a perpendicular baseline [12] of 190 m and a in obtain Figure 12a,b. Inpolarimetric addition, the difference shown in Figure 12c.SRTM Clearly, the and obvious phase temporal baseline 46 days. We then applied theissame two-pass differential interferometry strategy to the twoof D-Infs, whichmap were superimposed on the DEM are shown temporal baseline of 46 days. We then applied the same two-pass differential interferometry strategy signals in 12a,b. Figure have disappeared, confirms the HHDEM and to obtain the two polarimetric D-Infs, whichwhich were superimposed onoriginal the and are shown in Figure In12a,b addition, the difference map is shown that in Figure 12c.SRTM Clearly, theHV-polarization obvious phase in to obtain the two polarimetric D-Infs, which were superimposed on the SRTM DEM and are shown D-Infs contain common ATP signals. Moreover, the time interval of the InSAR wasphase 46 days, so Figure 12a,b. In addition, the difference mapwhich is shown in Figure 12c. Clearly, thepairs obvious signals signals in Figure 12a,b have disappeared, confirms that the original HH and HV-polarization in Figure 12a,b. In addition, thedeformation, difference map is shown incould Figure 12c. Clearly, to thebeobvious phase we could also exclude surface so the D-Infs be considered composed of D-Infs contain common ATP signals. Moreover, thethat timethe interval of the pairs was 46 days, so in Figure 12a,b have disappeared, which confirms original HHInSAR and HV-polarization D-Infs signals in Figure 12a,b have disappeared, which confirms that the original HH and HV-polarization ATP signals, TEP signals, and NP signals. we could also ATP exclude surface deformation, so the D-Infs be considered to composed of contain signals. the time interval of could the InSAR was 46 be days, we could D-Infscommon contain common ATPMoreover, signals. Moreover, the time interval of thepairs InSAR pairs was 46sodays, so ATP signals, TEP signals, and NP signals. also surface deformation, so the D-Infs be considered to be composed of ATP signals, weexclude could also exclude surface deformation, so could the D-Infs could be considered to be composed of TEP signals, and NP signals. ATP signals, TEP signals, and NP signals.

Figure 12. Original (a) HH and (b) HV D-Infs. (c) The difference map between the HV and HH D-Infs. 12. Original (a) HH and (b) HV D-Infs. (c) The difference map between the HV and HH Figure D-Infs. Figure Original D-Infs. (c) The difference between the and HV HH and D-Infs. HH Figure 12.12. Original (a) (a) HHHH andand (b) (b) HV HV D-Infs. (c) The difference mapmap between the HV D-Infs.

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Estimation and correction of the ATP: ATP: To To begin begin with, with, we we also also decompose decompose the the obtained obtained (2) Estimation (2) Estimation and correction of the ATP: To begin with, we also decompose the obtained this testtest site,site, the the optimal decomposition scalescale was dual-polarization D-Infs D-Infs into intodifferent differentscales. scales.For For this optimal decomposition dual-polarization D-Infs into different scales. For this test site, the optimal decomposition scale was set as We We could then establish wavelet was set11. as 11. could then establishthe thelinear linearrelationship relationshipbetween between the the high-frequency wavelet set as 11. We could then establish the linear relationship between the high-frequency wavelet each level level of of decomposition decomposition with Equation (3). The red solid lines in Figure 13 show coefficients for each coefficients for each level of decomposition with Equation (3). The red solid lines in Figure 13 show wavelet coefficients in the vertical vertical direction, where it can be seen that that the the scatter scatter scatter plots of the wavelet scatter plots of the wavelet coefficients in the vertical direction, where it can be seen that the scatter plots have have similar similar trends trends in in the the horizontal horizontal and anddiagonal diagonaldirections. directions. plots plots have similar trends in the horizontal and diagonal directions.

Figure 13. 13. Scatter plots (HV vs. HH) of the wavelet coefficients in the vertical direction direction (a–k (a–k indicates indicates Figure Figure 13. Scatter plots (HV vs. HH) of the wavelet coefficients in the vertical direction (a–k indicates the the wavelet wavelet decomposition decomposition scales scales ranging ranging from from 11 to to 11). 11). the wavelet decomposition scales ranging from 1 to 11).

The final final corrected corrected HH HH and and HV HV D-Infs D-Infs are are presented presented in in Figure Figure 14a,b, 14a,b, respectively. respectively. It It is clear clear that that The The final corrected HH and HV D-Infs are presented in Figure 14a,b, respectively. It is is clear that most of the positive and negative signals are mitigated by the use of the MRWCA method. Figure most of byby thethe useuse of the MRWCA method. Figure 14c most of the the positive positiveand andnegative negativesignals signalsare aremitigated mitigated of the MRWCA method. Figure 14c shows the difference map of the corrected HV and HH D-Infs. shows the difference mapmap of the HV and HH HH D-Infs. 14c shows the difference of corrected the corrected HV and D-Infs.

Figure 14. (a) HH and (b) HV D-Infs corrected by the MRWCA method. (c) The difference map Figure 14. (a) HH (b) HV D-Infs D-Infs corrected corrected by by the the MRWCA MRWCA method. method. (c) Figure 14. HH and andHV (b)and HV (c) The The difference difference map map between the(a) corrected HH D-Infs. between the corrected HV and HH D-Infs. between the corrected HV and HH D-Infs.

(3) Assessment of the derived DEMs: Lastly, after eliminating the effects of ATP signals, the (3) Assessment of the derived DEMs: Lastly, after eliminating the effects of ATP signals, the corrected HH interferogram wasDEMs: used Lastly, to generate the InSAR We evaluated thecorrected vertical (3) Assessment of the derived after eliminating theDEMs. effects of ATP signals, the corrected HH interferogram was used to generate the InSAR DEMs. We evaluated the vertical accuracy of the InSAR DEMs extractedthe without effects correction, with atmospheric HH interferogram was used to generate InSARatmospheric DEMs. We evaluated the vertical accuracy of the accuracy of the InSAR DEMs extracted without atmospheric effects correction, with atmospheric effects DEMs correction using Shirzaei’s correction method [5], and atmospheric effects correction InSAR extracted without atmospheric effects correction, withwith atmospheric effects correction using effects correction using Shirzaei’s correction method [5], and with atmospheric effects correction using the MRWCA in Figure 15. Shirzaei’s correctionmethod, method as [5],shown and with atmospheric effects correction using the MRWCA method, using the MRWCA method, as shown in Figure 15. as shown in Figure 15.

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Figure 15. 15. InSAR DEM (a) without atmospheric correction; (b) with Shirzaei’s atmospheric Figure (a) without atmospheric correction; (b) with(b) Shirzaei’s atmospheric correction Figure 15.InSAR InSARDEM DEM (a) without atmospheric correction; with Shirzaei’s atmospheric correction method; and (c) with MRWCA atmospheric correction. method; and (c) with MRWCA atmospheric correction. Figure 15. InSAR DEM (a) without atmospheric correction; (b) with Shirzaei’s atmospheric correction method; and (c) with MRWCA atmospheric correction. correction method; and (c) with MRWCA atmospheric correction.

We also used the SRTM DEM as the validation data for the qualitative analysis. We calculated We also used the SRTM DEM as the validation data for the qualitative analysis. We calculated the vertical difference of the InSAR-derived DEMs with the validation SRTM DEM, and obtained the We difference also used the SRTM DEM as the validation data the qualitative Weobtained calculated the vertical of the InSAR-derived DEMs with thefor validation SRTManalysis. DEM, and the elevation difference distribution, as shown in Figure 16. We can also see that the elevation difference the vertical difference of the InSAR-derived the can validation SRTM DEM, and obtained the We elevation difference distribution, as shown in DEMs Figurewith 16. We also see that the elevation difference without atmospheric correction is significantly larger16. than that after thethat correction process, and the elevation difference distribution, as shown in Figure We can also see the elevation difference atmospheric correction correction is significantly significantly larger larger than than that after the correction process, and the without atmospheric MRWCA correction method showsisthe best elevation without atmospheric correction significantly largeraccuracy. than that after the correction process, and the MRWCA correction method shows the best elevation accuracy. accuracy. MRWCA correction method shows the best elevation accuracy.

Figure 16. The elevation difference distribution (a) without atmospheric correction; (b) with Figure 16.The Theelevation elevation difference distribution (a) atmospheric correction; (b) with with Figure 16. The elevation difference distribution (a) without without atmospheric correction; Figure 16. difference distribution (a) with without atmospheric correction; (b) with (b) Shirzaei’s Shirzaei’s atmospheric correction method; and (c) MRWCA atmospheric correction. Shirzaei’s atmospheric correction method; and (c) with MRWCA atmospheric correction. Shirzaei’s atmospheric correction method; and (c) with MRWCA atmospheric correction. atmospheric correction method; and (c) with MRWCA atmospheric correction.

We then used the ICESat altimetry data as the reference for the quantitative analysis, and the then used ICESat altimetrydata dataasasthe thereference reference for for the the quantitative quantitative analysis, We We then used thethe ICESat altimetry analysis,and andthe the We then used the ICESat the altimetry data as the reference forICESat the quantitative analysis, and elevation differences between InSAR-derived DEMs and the data were wereanalyzed. analyzed. The elevation differences between the InSAR-derived DEMs and the ICESat data The elevation differences between the InSAR-derived DEMs and the ICESat data were analyzed. The the elevation between the InSAR-derived DEMs and the ICESat data werethe analyzed. histograms of differences the differences are displayed ininFigure 17. Quantitatively, we evaluate vertical histograms of the differences displayedin Figure17. 17. Quantitatively, Quantitatively, we histograms of the differences areare displayed Figure we evaluate evaluate the thevertical vertical The histograms of the differences are displayed in Figure 17. Quantitatively, we evaluate the vertical accuracy of the InSAR-derived DEMs ininFigure 15, which shows that after the the useofofShirzaei’s Shirzaei’s accuracy of the InSAR-derived DEMsin Figure15, 15,which which shows shows that that after after accuracy of the InSAR-derived DEMs Figure the use use of Shirzaei’s accuracy of the InSAR-derived DEMs in Figure 15, which shows that after the use of Shirzaei’s atmospheric correction method, the RMSE has decreased from 15.40 m to 12 m, and after MRWCA atmospheric correction method, RMSEhas hasdecreased decreasedfrom from 15.40 15.40 m m to to 12 atmospheric correction method, thethe RMSE 12 m, m, and and after afterMRWCA MRWCA atmospheric correction method, the RMSE has decreased from 15.40 m to 12 m, and after MRWCA correction, the RMSE has decreased to 10.74 m. atmospheric correction, RMSE has decreasedtoto10.74 10.74m. m. atmospheric correction, thethe RMSE has decreased atmospheric correction, the RMSE has decreased to 10.74 m.

Figure Histograms elevation differencesbetween betweenthe theInSAR-derived InSAR-derived DEMs Figure 17. 17. Histograms of of thethe elevation differences DEMsand andthe theICESat ICESat Figure 17.generated Histograms of theATP elevation differences betweenatmospheric the InSAR-derived DEMs and the ICESat data, without correction, with Shirzaei’s correction method, and with data, generated without ATPelevation correction, with Shirzaei’s correction method, and with Figure 17. Histograms of the differences betweenatmospheric the InSAR-derived DEMs and the ICESat data, generated without correction. ATP correction, with Shirzaei’s atmospheric correction method, and with MRWCA atmospheric MRWCA atmospheric correction. data, generated without ATP correction, with Shirzaei’s atmospheric correction method, and with MRWCA atmospheric correction. MRWCA atmospheric correction.

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4. Discussion 4.1. Summary of the MRWCA Method This paper has presented an effective atmosphere correction method for InSAR topographic mapping, which integrates wavelet multi-resolution analysis and weighted correlation analysis. The main idea of the MRWCA method is based on a priori knowledge that the dual-polarization interferograms have identical ATP signals. To detect the same ATP signals, we firstly apply two-pass differential interferometry technology to generate D-Infs and remove any other similar or identical phase components, the only common component in the two obtained D-Infs is the ATP signals. Thus, the obtained wavelet coefficients have the same or similar values over a range of scales, which represents the key rationale of correlation analysis. Following the decomposition of different polarimetric D-Infs, the global correlation coefficient between the corresponding wavelet coefficients are most likely to be the ratio of the ATP signals in the obtained D-Infs. To improve the sensitivity of the global correlation coefficient to the ATP variations, a weighted indicator is formulated to refine the global correlation coefficient. In most applications of wavelet transforms, the choice of wavelet family is critical. However, in this paper, this choice is rather straightforward. We choose a wavelet that can separate the non-ATP signals (e.g., TEP and NP) from the D-Inf [28]. In other words, the selected wavelet should be able to better separate the ATP and non-ATP signals into different phase components characterized by different wavelengths, which will reduce the effects of confounding signals (e.g. non-ATP signals) and improve the robustness of the correlation analysis. One should note that continuous wavelets may have better capacity to support the correlation analysis since they have higher spectral resolution, which will be investigated in the future works. 4.2. Self-Consistency Checking between Differences Maps before and after MRWCA Method Correction In order to quantitatively check the phase quality after MRWCA method correction, the correlation of the differences between the HV and HH D-Infs before and after atmospheric effects correction were investigated, the associated joint distributions were shown in Figure 18a,b. We can see that, in the San Francisco experiment, the corrected and original difference maps, as shown in Figures 6c and 4c, have a correlation coefficient of 0.94 and an RMSE of 0.07 rad. In the Moron test site, a correlation coefficient of 0.84 with an RMSE of 0.05 rad was obtained, as presented in Figure 18b. In both of the cases, the high correlations and the small RMSEs indicate that the MRWCA method can correct ATP signals, without significantly reducing the phase quality. With the consideration of phase-to-height conversion parameters associated with the two interferometric pairs, these phase losses cannot be the major factor mitigating the DEM quality. However, for both of the cases, the corresponding correlation coefficients less than 1 indicate that some of the non-ATP signals are regarded as ATP signals by the MRWCA method. This can be explained by two possible reasons: (1) the global correlation analysis cannot accurately describe the correlations of some pixels which attributed to ATP signals. As a result, the ATP signals can be over- or under-estimated. (2) If the phase centers of different polarimetric interferograms are similar, some of the non-ATP signals can also be regarded as the ATP signals.

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Figure18. 18.Joint Joint distribution of differences the differences differences of the the HV and HH HH D-Infs before and after after Figure distribution of the of the of HV andHV HH and D-Infs before and before after atmospheric Figure 18. Joint distribution of the D-Infs and effects correction (a) San Francisco test site; (b) Moron test site. atmospheric effects correction (a) San Francisco test site; (b) Moron test site. atmospheric effects correction (a) San Francisco test site; (b) Moron test site.

4.3.Effects Effectsof ofDifferent DifferentDecomposition DecompositionScales Scaleson onATP ATPCorrection Correction 4.3. Effects of Different Decomposition 4.3. Scales on ATP Correction Tobetter betterunderstand understand the effect of decomposition decomposition scale on ATP ATP correction, as an example, example, we To the effect of of decomposition scale on ATP correction, as anas example, we chose To better understand the effect scale on correction, an we chose four different decomposition scales (3, 6, 9, 11) for ATP correction for Moron test site as shown four different decomposition scales (3, 6, 9, 11) for ATP correction for Moron test site as shown in chose four different decomposition scales (3, 6, 9, 11) for ATP correction for Moron test site as shown in Figure 19. Figure 19.19. in Figure

Figure19. 19.The Theelevation elevationdifference differencemaps mapsbetween betweenInSAR InSAR DEMsand and SRTMDEM. DEM.(a–d) (a–d)indicates indicatesthe the Figure Figure 19. The elevation difference maps between InSAR DEMs DEMs and SRTM SRTM DEM. (a–d) indicates the waveletdecomposition decompositionscale scalewith with3, 3,6, 6, 9and and11 11(the (theselection selectionof ofthis thispaper), paper),respectively. respectively. wavelet wavelet decomposition scale with 3, 6, 99 and 11 (the selection of this paper), respectively.

We firstly firstly used used the the SRTM SRTM DEM DEM as as the the validation validation data data for for the the qualitative qualitative analysis, analysis, the the elevation elevation We We firstly used themaps SRTMbetween DEM asInSAR the validation data for the qualitative analysis, the19. elevation difference distribution DEMs and SRTM DEM are shown in Figure Clearly, difference distribution maps between InSAR DEMs and SRTM DEM are shown in Figure 19. Clearly, difference distribution maps between InSAR DEMs and SRTM DEM are shown in Figure 19. althoughaapart partof ofATP ATPsignals signalscan canbe beremoved removedby byusing usingthe thesmall smalldecomposition decompositionscales, scales,the theresidual residual although Clearly, although a part of ATP signals can be removed by using the small decomposition scales, error attributed attributed to to ATP ATP signals signals are are still still significant. significant. In In order order to to investigate investigate the the corrected corrected effects effects more more error the residual error attributed to ATP signals are still significant. Inanalysis, order tothe investigate the corrected clearly, the ICESat altimetry data was used for the quantitative corresponding RMSEs clearly, the ICESat altimetry data was used for the quantitative analysis, the corresponding RMSEs effects more clearly, the ICESat altimetry data wasmused for them, quantitative analysis, the corresponding ofelevation elevation difference are15 15m, m, 14.84m, m, 12.43 and10.74 10.74 respectively. of difference are 14.84 12.43 m and m, respectively. RMSEs of elevation difference are 15 m, 14.84 m, 12.43 m and 10.74 m, respectively. Basedon onthe theabove aboveanalysis, analysis,we wecan canfind findthat, that,the thesmaller smallerdecomposition decompositionscales scalescan canonly onlycorrect correct Based Based on the above analysis, we can find that, the smaller decomposition scales can test only site correct the ATP signals with short wavelength, however, the ATP signals of the Moron are the ATP signals with short wavelength, however, the ATP signals of the Moron test site are the ATP signals with short wavelength, however, the ATP signals of the Moron test site are dominated dominated by by longer longer wavelength wavelength that that can can be be confirmed confirmed by by Figure Figure 13. 13. Therefore, Therefore, itit isis necessary necessary to to dominated by longer wavelength number that can of be decomposition confirmed by Figure 13. the Therefore, itdecomposition is necessary towhich select can an select an appropriate scales for wavelet select an appropriate number of decomposition scales for the wavelet decomposition which can appropriate number of decomposition scaleswith for the wavelet decomposition which canD-Inf. separate almost separatealmost almost all the the ATPsignals signalsmixed mixed different non-ATP signalsfrom fromthe the separate all ATP with different non-ATP signals D-Inf. all the ATP signals mixed with different non-ATP signals from the D-Inf. 4.4.Comparison Comparisonwith withthe the Existing ExistingMethod Method 4.4. We extracted extracted the the ATP ATP maps maps that that are are shown shown in in Figure Figure 20a,d 20a,d for for the the two two experiment experimentregions. regions.For For We the two HH D-Infs, the ATP signals make up 63.6% and 44.8% of the total D-Infs signals. For the San the two HH D-Infs, the ATP signals make up 63.6% and 44.8% of the total D-Infs signals. For the San Francisco test testsite, site, the the corrected corrected interferogram interferogram could could provide provide aa DEM DEM with with aa RMSE RMSE of of 7.79 7.79 m m (Figure (Figure Francisco

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4.4. Comparison with the Existing Method We extracted the ATP maps that are shown in Figure 20a,d for the two experiment regions. For the two HH ATP signals make up 63.6% and 44.8% of the total D-Infs signals. For the San Remote Sens.D-Infs, 2018, 10,the x FOR PEER REVIEW 15 of 18 Francisco test site, the corrected interferogram could provide a DEM with a RMSE of 7.79 m (Figure 9), which is an improvement of of 40.5% with 9), which is an improvement 40.5% withrespect respecttotothe theDEM DEMbefore beforeatmospheric atmospheric effects correction; for the Moron test site, the corrected interferogram could provide a DEM with an RMSE RMSE of 10.74 10.74 m, m, which is an improvement improvement of 30.2% 30.2% with respect to to the the DEM DEM without without atmospheric atmospheric effects correction (Figure 17), which demonstrates the MRWCA method is effective in detecting the ATP signals with different ATP ATP content content conditions. conditions. From the ATP maps (Figure 20a,d), we canwe alsocan findalso that find the San theextracted extracted ATP maps (Figure 20a,d), thatFrancisco the Sanexperiment Francisco has serious atmospheric effects, which are attributed to this test site because it is close to the Pacific experiment has serious atmospheric effects, which are attributed to this test site because it is close to Ocean and Ocean featuresand a high watera vapor content. Thecontent. effect ofThe ATPeffect signals divided into the Pacific features high water vapor of can ATPbesignals can be TD-ATP divided and [12]. theAlthough polynomial incorporating elevation information can remove into T-ATP TD-ATP andAlthough T-ATP [12]. themodel polynomial model incorporating elevation information the TD-ATP signals in the orbit error removing [10,15], only the ATP signals linearly correlated can remove the TD-ATP signals in the orbit error removing [10,15], only the ATP signals linearly with topography can be dealcan estimated. In order toIn solve this wavelet correlated with topography be deal estimated. order to problem, solve thisShirzaei problem,proposed Shirzaei aproposed decomposition based methodbased to remove the TD-ATP signals [5].TD-ATP With Shirzaei’s a wavelet decomposition method to remove the signalsatmospheric [5]. With correction Shirzaei’s method, the extracted TD-ATP maps are shown in Figure 20b,e. The residual ATP signals can atmospheric correction method, the extracted TD-ATP maps are shown in Figure 20b,e. The residual thus regarded as the signals, shownsignals, in Figure 20c,f. Quantitatively, 47.2% and ATP be signals can thus be T-ATP regarded as theasT-ATP as shown in Figure 20c,f.only Quantitatively, 55.7% of the total ATP signals could be detected by Shirzaei’s method in these two experiments. only 47.2% and 55.7% of the total ATP signals could be detected by Shirzaei’s method in these two However, the However, MRWCA method can remove both the TD-ATP signals. experiments. the MRWCA method canof remove both ofand theT-ATP TD-ATP and T-ATP signals.

Figure 20. 20. (a) (a)ATP ATPmap, map,(b) (b)TD-ATP TD-ATP map, and T-ATP for San Francisco test (d) site.ATP (d) map, ATP Figure map, and (c) (c) T-ATP mapmap for San Francisco test site. map, (e) TD-ATP map, and (f) T-ATP map for Moron Test site. (e) TD-ATP map, and (f) T-ATP map for Moron Test site.

4.5. Potential and Limits Limits of of MRWCA MRWCA Method in Atmospheric Atmospheric Correction Correction 4.5. Potential and Method in Using the theproposed proposed method, does not on depend on any or assumption or external Using method, whichwhich does not depend any assumption external meteorological meteorological data, we only need single-baseline SAR dual-polarization SAR dataexternal and two different data, we only need single-baseline dual-polarization data and two different DEMs, thus external DEMs, thus it is relatively easier to collect and process these data. So we believe this study it is relatively easier to collect and process these data. So we believe this study will provide an effective will provide an effective method to correct effects by SAR usingdata single-baseline SAR data method to correct the atmospheric effects the by atmospheric using single-baseline (e.g., Sentinel-1 [29], (e.g., Sentinel-1 [29], ALOS-2 [30], and future Tandem-L [31]), which contain multi-polarization SAR ALOS-2 [30], and future Tandem-L [31]), which contain multi-polarization SAR data, have high data, have high and aperiod. short revisit result, canMRWCA use the MRWCA to resolution, and resolution, a short revisit As aperiod. result, As wea can usewethe method method to correct correct ATP for signals for DEM InSARgeneration DEM generation andhigh invert high resolution water data. vaporIndata. this ATP signals InSAR and invert resolution water vapor this In study, study, the selected interferometric pairs had not underwent a significant ionospheric effect, which the selected interferometric pairs had not underwent a significant ionospheric effect, which can be can be divided into a Faraday angle and ionospheric delay. Although the ionosphere induced Faraday angle is polarization-dependent [32], the ionospheric delay is identical for all polarizations [33]. In such a case, we can also remove the ionospheric phase from the D-Inf by the MRWCA method and have no impact on DEM inversion. But when the D-Infs contain large proportion ionosphere components, which will make the polarimetric D-Infs more similar, in particular for

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divided into a Faraday angle and ionospheric delay. Although the ionosphere induced Faraday angle is polarization-dependent [32], the ionospheric delay is identical for all polarizations [33]. In such a case, we can also remove the ionospheric phase from the D-Inf by the MRWCA method and have no impact on DEM inversion. But when the D-Infs contain large proportion ionosphere components, which will make the polarimetric D-Infs more similar, in particular for interferograms acquired at low-frequency, and make it difficult to estimate the ionospheric and atmospheric phases without losing the TEP signals by the correlation analysis. To solve this problem, before performing the MRWCA method, the ionospheric phases should be removed by the proper methods [34,35]. However, after correcting the ionospheric effect, the interferograms still contain residual ionospheric phases [36,37], and the effect of residual ionospheric phases on the correlation analysis is dependent on how much of the ionospheric phase is left. In addition, the effect of residual ionospheric phases on the correlation analysis still needs to be further investigated. The major limit of this method is that the unwrapped phase is required. If the unwrapping step fails due to very low coherence, this can affect the application of the proposed approach. In this study, although the phase unwrapping method can affect the atmospheric phase removal, it is not the major limited factor. Thus, we have not done further research about the effect of phase unwrapping on the atmospheric phase removal. Moreover, the proposed approach is not to distinguish the atmospheric effects and the ground surface deformation signals which are similar or same in the interferograms acquired in different polarizations. Therefore, if the deformation signals are identical in different polarimetric D-Infs, the MRWCA method can remove the deformation signals during the ATP removal and have no impact on DEM production. However, when the polarimetric D-Infs have similar deformation signals, some of the deformation signals will be miss-interpreted as TEP signals, which will be converted into the wrong topographic information. 5. Conclusions In this paper, a novel approach to correct the atmospheric effects in a repeat-pass interferogram has been presented, which combines wavelet multi-resolution analysis and weighted correlation analysis to identify the same ATP signals from dual-polarization InSAR interferograms. We successfully tested the method on two test sites over San Francisco (USA) and Moron (Mongolia), which have different topographic characteristics and different water vapor distributions. The results demonstrate that the atmospheric effects can be effectively eliminated. The estimated DEMs have improvements of 40.5% and 30.2% in term of RMSE for the two test sites, respectively. In addition, compared with the existing method [5], the proposed method cannot only deal with the TD-ATP signals, but also the T-ATP signals. The proposed method does not depend on any assumption or external meteorological data and we only need single-baseline dual-polarization SAR data and two different external DEMs, which allow us to extract the DEM with large-scale and high-resolution. In our future work, we will further test the application scope of the method by selecting SAR data acquired from different topographic conditions. In addition, we will investigate how to use full-polarization data, which contain more scattering information being helpful to conduct the correlation analysis, to identify more accurate ATP signals. Furthermore, how to use these ATP signals to estimate high resolution water vapor data may also help us to better understand the atmosphere. Lastly, in this study, the effects of the ground deformation and ionospheric delay have been neglected, how to reduce these effects on DEM extraction needs to be further investigated. Author Contributions: Z.L.: Conceptualization; Data curation; Investigation; Methodology; Validation; Visualization; Writing-original draft. H.F.: Conceptualization; Supervision; Investigation; Validation; Writing—review and editing. J.Z.: Conceptualization; Funding acquisition; Investigation; Validation. C.Z.: Conceptualization; Investigation; Validation. T.Z.: Conceptualization; Investigation; Validation. Funding: This paper was supported by the Key Research and Development Project in Hunan Province of China under Grant 2016SK2029. In addition, this paper was also supported by the National Natural Science Foundation of China under Grant 41531068, Grant 41674009, and Grant 41604012.

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Acknowledgments: The ALOS data are provided by Japan Aerospace Exploration Agency (JAXA) (PI No. 3098). Conflicts of Interest: The authors declare no conflict of interest.

References 1.

2. 3. 4.

5. 6. 7.

8.

9.

10. 11.

12. 13. 14. 15. 16. 17. 18. 19.

20. 21.

Hu, J.; Li, Z.W.; Zhu, J.J.; Ding, X.L.; Wang, C.C.; Feng, G.C.; Sun, Q. Measuring three-dimensional surface displacements from combined InSAR and GPS data based on BFGS method. Chin. J. Geophys. 2013, 56, 117–126. Zebker, H.A.; Werner, C.L.; Rosen, P.A.; Hensley, S. Accuracy of topographic maps derived from ERS-1 interferometric radar. IEEE Trans. Geosci. Remote Sens. 1994, 32, 823–836. [CrossRef] Ferretti, A.; Prati, C.; Rocca, F. Multibaseline InSAR DEM reconstruction: The wavelet approach. IEEE Trans. Geosci. Remote Sens. 1999, 37, 705–715. [CrossRef] Liao, M.S.; Jiang, H.J.; Wang, Y.; Wang, T.; Zhang, L. Improved topographic mapping through high-resolution SAR interferometry with atmospheric effect removal. ISPRS J. Photogramm. Remote Sens. 2013, 80, 72–79. [CrossRef] Shirzaei, M.; Bürgmann, R. Topography correlated atmospheric delay correction in radar interferometry using wavelet transforms. Geophys. Res. Lett. 2012, 39, 1305–1310. [CrossRef] Li, Z.H.; Fielding, E.J.; Cross, P.; Muller, J.-P. Interferometric synthetic aperture radar atmospheric correction: GPS topography-dependent turbulence model. J. Geophys. Res. Solid Earth 2006, 111, B02404. [CrossRef] Li, Z.H.; Muller, J.-P.; Cross, P.; Fielding, E.J. Interferometric synthetic aperture radar (InSAR) atmospheric correction: GPS, moderate resolution imaging spectroradiometer (MODIS), and InSAR integration. J. Geophys. Res. Solid Earth 2005, 110, B03410. [CrossRef] Li, Z.H.; Fielding, E.J.; Cross, P.; Muller, J.-P. Interferometric synthetic aperture radar atmospheric correction: Medium resolution imaging spectrometer and advanced synthetic aperture radar integration. Geophys. Res. Lett. 2006, 33, 272–288. [CrossRef] Rosen, P.A.; Hensley, S.; Zebker, H.A.; Webb, F.H.; Fielding, E.J. Surface deformation and coherence measurements of Kilauea Volcano, Hawaii, from SIR-C radar interferometry. J. Geophys. Res.: Planets 1996, 101, 23109–23125. [CrossRef] Ferretti, A.; Prati, C.; Rocca, F. Permanent scatterers in SAR interferometry. IEEE Trans. Geosci. Remote Sens. 2001, 39, 8–20. [CrossRef] Ishitsuka, K.; Matsuoka, T.; Tamura, M. Persistent Scatterer Selection Incorporating Polarimetric SAR Interferograms Based on Maximum Likelihood Theory. IEEE Trans. Geosci. Remote Sens. 2016, 55, 38–50. [CrossRef] Hanssen, R.F. Radar Interferometry Data Interpretation and Error Analysis; Kluwer: Norwell, MA, USA, 2001. Cloude, S.R.; Papathanassiou, K.P. Polarimetric SAR interferometry. IEEE Trans. Geosci. Remote Sens. 1998, 36, 1551–1565. [CrossRef] Shanker, P.; Zebker, H. Persistent scatterer selection using maximum likelihood estimation. Geophys. Res. Lett. 2007, 34, 315–324. [CrossRef] Xu, B.; Li, Z.W.; Wang, Q.J.; Jiang, M.; Zhu, J.J.; Ding, X.L. A Refined Strategy for Removing Composite Errors of SAR Interferogram. IEEE Geosci. Remote Sens. Lett. 2013, 11, 143–147. [CrossRef] Mallat, S.G. A theory for multiresolution signal decomposition: The wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell. 1989, 11, 674–693. [CrossRef] Levin, D. The approximation power of moving least-squares. Math. Comp. 1998, 67, 1517–1531. [CrossRef] Shim, J.S. Analysis of Total Electron Content (TEC) Variations in the Low- and Middle-Latitude Ionosphere. Ph.D. Thesis, Utah State University, Logan, UT, USA, 2009. Satgé, F.; Bonnet, M.-P.; Timouk, F.; Calmant, S.; Pillco, R.; Molina, J.; Lavado-Casimiro, W.; Arsen, A.; Crétaux, J.; Garnier, J. Accuracy assessment of SRTM v4 and ASTER GDEM v2 over the Altiplano watershed using ICESat/GLAS data. Int. J. Remote Sens. 2015, 36, 465–488. [CrossRef] Zhang, G.Q.; Xie, H.; Kang, S.; Yi, D.; Ackley, S.F. Monitoring lake level changes on the Tibetan plateau using ICESat altimetry data (2003–2009). Remote Sens. Environ. 2011, 115, 1733–1742. [CrossRef] Bhang, K.; Schwartz, F.W.; Braun, A. Verification of the vertical error in C-band SRTM DEM using ICESat and Landsat-7, Otter Tail County, MN. IEEE Trans. Geosci. Remote Sens. 2007, 45, 36–44. [CrossRef]

Remote Sens. 2018, 10, 1310

22. 23. 24. 25.

26. 27. 28. 29.

30.

31.

32. 33. 34. 35. 36.

37.

18 of 18

Hirano, A.; Welch, R.; Lang, H. Mapping from ASTER stereo image data: DEM validation and accuracy assessment. ISPRS J. Photogramm. 2003, 57, 356–370. [CrossRef] Li, Z.W.; Ding, X.L.; Huang, C.; Zhu, J.J.; Chen, Y.L. Improved filtering parameter determination for the Goldstein radar interferogram filter. ISPRS J. Photogramm. 2008, 63, 621–634. [CrossRef] Chen, C.W.; Zebker, H.A. Two-dimensional phase unwrapping with use of statistical models for cost function in nonlinear optimization. J. Opt. Soc. Am. A 2001, 18, 338–351. [CrossRef] Costantini, M.; Rosen, P.A. A generalized phase unwrapping approach for sparse data. In Proceedings of the 1999 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Hamburg, Germany, 28 June–2 July 1999. Marghany, M. DInSAR technique for three-dimensional coastal spit simulation from radarsat-1 fine mode data. Acta Geophysica 2013, 61, 478–493. [CrossRef] Imperatore, P.; Pepe, A. Topological characterization and advanced noise filtering techniques for phase unwrapping of interferometric data-stacks. Remote Sens. Environ. 2016. [CrossRef] Shirzaei, M. A Wavelet-Based Multitemporal DInSAR Algorithm for Monitoring Ground Surface Motion. IEEE Geosci. Remote Sens. Lett. 2013, 10, 456–460. [CrossRef] Neelmeijer, J.; Schöne, T.; Dill, R.; Klemann, V.; Motagh, M. Ground Deformations around the Toktogul Reservoir, Kyrgyzstan, from Envisat ASAR and Sentinel-1 Data—A Case Study about the Impact of Atmospheric Corrections on InSAR Time Series. Remote Sens. 2018, 10, 462. [CrossRef] Beiranvand Pour, A.; Hashim, M. Application of PALSAR-2 remote sensing data for landslide hazard mapping in Kelantan river basin, Peninsular Malaysia. Int. Arch. Photogramm. Remote Sens. Spat. Inf. 2016, 37, 012067. Moreira, A.; Krieger, G.; Hajnsek, I.; Papathanassiou, K. Tandem-L: A highly innovative bistatic SAR mission for global observation of dynamic processes on the earth’s surface. IEEE Geosci. Remote Sens. Mag. 2015, 3, 8–23. [CrossRef] Freeman, A. Calibration of linearly polarized polarimetric SAR data subject to Faraday rotation. IEEE Trans. Geosci. Remote Sens. 2004, 42, 1617–1624. [CrossRef] Dubois-Fernandez, P.C.; Souyris, J.C.; Angelliaume, S.; Garestier, F. The Compact Polarimetry Alternative for Spaceborne SAR at Low Frequency. IEEE Trans. Geosci. Remote Sens. 2008, 46, 3208–3222. [CrossRef] Jung, H.S.; Lee, D.T.; Lu, Z.; Won, J.S. Ionospheric correction of SAR interferograms by multiple-aperture interferometry. IEEE Trans. Geosci. Remote Sens. 2013, 51, 3191–3199. [CrossRef] Rosen, P.A.; Hensley, S.; Chen, C. Measurement and mitigation of the ionosphere in L-band Interferometric SAR data. In Proceedings of the IEEE Radar Conference, Washington, DC, USA, 10–14 May 2010. [CrossRef] Gomba, G.; Parizzi, A.; Zan, F.D.; Eineder, M.; Bamler, R. Toward Operational Compensation of Ionospheric Effects in SAR Interferograms: The Split-Spectrum Method. IEEE Trans. Geosci. Remote Sens. 2016, 54, 1446–1461. [CrossRef] Fattahi, H.; Simons, M.; Agram, P. InSAR time-series estimation of the ionospheric phase delay: An extension of the split range-spectrum technique. IEEE Trans. Geosci. Remote Sens. 2017, 55, 1–13. [CrossRef] © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).