Benefit of Using Multiple Baselines and Multiple Aspects for SAR ...

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Benefit of Using Multiple Baselines and Multiple Aspects for SAR Interferometry of Urban Areas Michael Schmitt, Student Member, IEEE, Johannes L. Schönberger, and Uwe Stilla, Senior Member, IEEE

Abstract—In this paper, extensive real-data experiments for the investigation of the benefit of exploiting multiple aspects and multiple baselines for the reconstruction of urban surface models by synthetic aperture radar interferometry are documented. These experiments are carried out within a recently proposed reconstruction framework that allows the fusion of almost arbitrary configurations of multi-aspect multi-baseline InSAR data. The results based on airborne decimeter-resolution millimeterwave imagery prove and quantify that multiple baselines help to solve the phase ambiguity problem, while multiple aspects reduce the parts of the scene affected by radar shadowing. In addition, the inherent redundancy provides a significant improvement in the achievable reconstruction accuracy, which is evaluated relative to the reconstruction error common for conventional single-aspect single-baseline SAR interferometry. Index Terms—Maximum-likelihood estimation, multi-aspect, multi-baseline, synthetic aperture radar interferometry (InSAR), synthetic aperture radar (SAR), urban areas.

I. INTRODUCTION HILE synthetic aperture radar interferometry (InSAR) has been used operationally for terrain reconstruction for years [1]–[3], the reconstruction of digital surface models (DSMs) of urban areas from InSAR data is still a challenging task [4], [5]. This is caused by the well-known layover and shadowing effects, which lead to a mixture of phase measurements and a lack of exploitable phase observations, respectively, if elevated objects are imaged. Besides, the nontrivial phase unwrapping operation needed for resolving ambiguous phase measurements usually fails at large phase jumps as they appear, e.g., at building edges [6]. Therefore, many sophisticated processing strategies have been proposed during the last decade. Many of them are based on multi-baseline [7]–[11] or multi-aspect techniques [12]–[15]. It has to be mentioned, however, that most of the hitherto proposed multi-baseline approaches rely on repeat-pass data acquired by spaceborne platforms. This introduces a couple of drawbacks: First, the capability of timely data delivery unique to weather-independent SAR sensors is lost, if imagery is collected over relatively long periods of time. Second, multitemporal SAR data suffer from decorrelation of moving objects (e.g., cars) and vegetated areas (e.g., trees), which frequently

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Manuscript received October 24, 2013; revised February 19, 2014; accepted March 08, 2014. This work was supported by the German Research Foundation (DFG project STI 545/4-1). The authors are with the Department of Photogrammetry and Remote Sensing, Technische Universitaet Muenchen (TUM), Munich 80333, Germany (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSTARS.2014.2311505

appear in urban regions. Third, state-of-the-art satellite missions only allow for the fusion of ascending and descending acquisitions (i.e., two opposing aspects), which only partly helps to achieve a comprehensive analysis of the scene of interest. Therefore, this paper focuses on the concept of multiaspect multi-baseline SAR interferometry (MAMBInSAR) in a maximum-likelihood (ML)-based estimation framework with a special emphasis on the exploitation of airborne single-pass InSAR data. With this sensor configuration, highly coherent data from almost arbitrary aspect angles can be acquired in very short time, thus providing the full advantages and flexibilities of radar remote sensing. In this context, the proposed work can be seen as an extension and generalization of existing ML approaches in SAR interferometry. The basic concept for low-resolution twoimage interferograms of rural areas was first introduced by [16]. A theoretical investigation of ML SAR interferometry in the phase unwrapping context was presented in [17], while [18] was among the first manuscripts demonstrating the exploitation of multibaseline data of natural terrain by a ML framework. Finally, [19] extended the well-established persistent scatterer technique to the distributed scatterer case, also employing the ML principle. The most sophisticated approach so far was described in [20], allowing for the fusion of arbitrary single-baseline interferograms acquired over mountainous landscapes. In contrast, the main purpose of the presented article is to show the benefit gained by fusing SAR measurements from multiple baselines and multiple aspect angles simultaneously. Therefore, many possible different acquisition configurations are investigated based on the MAMBInSAR algorithm first proposed in [21]. The remainder of the text is organized as follows: Section II describes the ML-based framework for MAMBInSAR; Section III introduces the airborne SAR system and the test area that is used for the experiments; and Section IV shows the experimental results that are further discussed in Section V. II. ML-BASED MULTI-ASPECT MULTI-BASELINE SAR INTERFEROMETRY

Recently, in [21], a ML-based approach for multi-aspect multibaseline SAR interferometry was introduced. The general idea of this algorithm is inspired by [20], which, however, is limited to the fusion of individual single-baseline interferograms with different master images each. In contrast, our more general estimation framework also enables to consider correlated interferograms as they are frequently delivered by airborne single-pass multibaseline sensors. Furthermore, the focus has shifted from medium-resolution SAR data of mountainous terrain to decimeterresolution InSAR imagery of densely built-up urban areas.

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A. Statistical Properties of Multi-Baseline InSAR Observations Generally, the method is based on the assumption that the measurement vector C containing the single look complex (SLC) values of a pixel in a stack of coregistered SAR images agrees with Goodman’s model [22] and thus follows a zero-mean circular complex Gaussian distribution with the probability density function

which is fully characterized by its complex covariance matrix

In this context, denotes the dimensionality of the distribution, i.e., the number of antennas that receive observations stored in . describes the intensity of acquisition and stands for the complex coherence between acquisitions and . Although this assumption is only fulfilled in low or medium resolution data of natural scenes showing primarily distributed targets with fully developed speckle [23], we still consider the Gaussian model the best asymptotic approximation that offers favorable conveniences for the estimation process [24], [25]. Since is usually not known, it has to be estimated using a set of sample pixels from an area of homogeneous backscattering. However, especially in high-resolution SAR images of heterogeneous backscattering, such as urban areas, the homogeneity of pixels taken from a simple rectangular window is unlikely. Therefore, an adaptive pixel selection procedure has to be used as, e.g., proposed by [26]–[28]. An estimate of the sample covariance matrix can then be calculated by

where is the number of sample pixels. Before this estimation, any deterministic phase components have to be removed [29]. B. Height Reconstruction The starting situation of the height reconstruction is a predefined surface grid in some world coordinate system (e.g., Universal Transverse Mercator), whose grid elements are sized such that they fit both the available sensor resolution and the desired spacing of the final height map. With just little prior knowledge about the height extension of the investigated scene, a number of height hypotheses can be created corresponding to the height resolution of the SAR interferometer. In this way, a column of hypothetical three-dimentional points is constructed, which are projected into the

Fig. 1. Simulated peak of the adapted likelihood function if (a) the covariance matrix and (b) the coherence matrix is used in the estimation.

SAR data by directly solving the range and the inverted Doppler equation

is the slant range distance between the hypothetical object point and the master antenna position at time . denotes the velocity of the master antenna, which is assumed to be constant. symbolizes the slave antenna position analogue to . Finally, denotes the time corresponding to the acqusition of the first azimuth bin. Although (5) is designed for linearized flight trajectories, the extension to nonlinear geometries is straight forward. After the location of the 3-D point is found in the image, the sample covariance matrix of the corresponding SLC observations can be obtained by bilinear interpolation of the sample covariance matrices of the neighboring pixels. In addition to that, a hypothetical complex observation vector for every height hypothesis is simulated by

where

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Fig. 2. Slice through the probabilistic volume model created by calculating the joint likelihood function for every voxel. The green line shows LiDAR reference data.

is the signal phase resulting from the path between transmitter, target and receiver, and indexes the slave antennas while the master antenna is assumed to double-act as both emitting and receiving horn. Of course, contains only phase information, while the complex covariance matrix also contains backscattering intensities. Therefore, we propose to normalize such that the so-called coherence matrix

available. It has to be noted, however, that under certain conditions, the sample covariance matrix might be singular. This can be caused by using less samples for the estimation than antennas ( < ) or by a single dominant scattering contribucan be used instead tion. In this case, e.g., the pseudoinverse of in (9). Another fact to be mentioned is that the framework was explicitly developed for the simultaneous fusion of multi-modal InSAR data. If, however, only data from a single aspect are available, standard multi-baseline solutions (such as proposed in [17]) that carry out the estimation in slant range geometry should preferably be used for sake of computational cost and processing speed.

is formed, which does not contain any information about the backscattering intensities anymore. The benefit of this operation is shown in Fig. 1. Eventually, this leads to the adapted likelihood function

C. Consideration of the Layover Effect

which only exploits complex coherence information. Evaluating (9) by a simple grid search for all height hypotheses , the ML estimate of the desired height in a grid cell is found as

This estimator can be applied to an arbitrary configuration of multi-baseline InSAR data acquired from arbitrary aspect angles. Since the acquisitions from different viewing angles can be considered as independent variables, their joint likelihood function is found to be [30]

The final estimator then becomes

Although the MAMBInSAR framework provides a flexible formulation for multi-aspect multi-baseline InSAR data fusion, the layover effect, which is always an obstacle for urban area remote sensing by synthetic aperture radar, is not considered explicitly. This is caused by the fact that only vertical height columns in object space are used during height reconstruction, instead of resolution cells in slant range geometry. However, calculating (11) for every voxel in the voxel space created by the hypotheses columns above each grid cell leads to the creation of a probabilistic volume model. An exemplary slice through this volume model is displayed in Fig. 2. In this slice, the smearing of the probability profile at the building walls strikes the attention, indicating that a probabilistic fusion of MAMBInSAR data is implicitly affected by layover. In any case, a deeper analysis of these probabilistic volume models has to be a direction of future research efforts. Besides a potential exploitation of the probabilistic volume model, another possible solution came to the authors attention recently. In [31], a principal component analysis-based approach for the reduction of multi-baseline covariance matrices to their dominant scattering contribution was proposed. In this way, it may be ensured that each resolution cell of the multi-baseline InSAR data, each represented by its corresponding covariance matrix, contains only one scatterer. After this a priori layover separation, the MAMBInSAR reconstruction can possibly be carried out without being affected by any geometrical distortions anymore. D. Reliability Measures

This estimator allows a maximum amount of flexibility and can be applied to any kind of interferometric SAR data, no matter how many baselines per aspect or how many aspects are

Although a fusion of multi-aspect multi-baseline InSAR data by this method can be expected to lead to a significant reduction of surface model parts affected by radar shadowing [32], still some patches will remain to be impinged by this effect. This leads

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TABLE I TEST DATA PARAMETERS

Fig. 3. Comparison of different reliability measures: (a) Logarithmic likelihood function maxima. (b) Entropy-based measure. (c) Determinant-based measure proposed in this paper.

to surface grid cells in which the estimated height values are pure noise. Therefore, it is advisable to detect these unreliable height estimations and exclude them from the resulting surface model. In principle, several reliability measures are possible. One could, e.g., just threshold the peak of the likelihood function for each height estimation. However, the likelihood values are dependent on the number of aspects and baselines, which means they are not limited to a fixed range as, e.g., probabilities or coherence values would be. Therefore, the likelihood peak values cannot be employed as a universal reliability measure with a constant threshold. Due to this fact, in [21], an entropy-based reliability measure was introduced, which provides results similar to the well-known coherence magnitude that is usually employed in conventional two-antenna SAR interferometry. In this article, we propose another reliability measure, which exploits the properties of the magnitude of the correlation matrix , which contains the entire coherence information of a multibaseline InSAR stack, whereas each element of it is limited to the range . The correlations between each SLC image in the stack and itself are 1 and are expressed by the main diagonal elements. In analogy, the off-diagonal elements describe the correlation between the individual images: the larger the respective value is, the more coherent and therefore reliable are the corresponding phase measurements. While the case, where all image acquisitions are fully coherent and therefore 100% statistically dependent, leads to a coherence magnitude matrix filled with ones, the worst-case, where all acquisitions are fully incoherent, yields an identity matrix.

Fig. 4. Optical image of the test area composed from four orthophotos provided by the Bavarian Administration for Surveying (LVG).

For a single aspect, this relationship can be mapped to a scalar value by the determinant of the magnitude coherence matrix that corresponds to the resolution cell for which the ML estimate was found:

If the height estimate is achieved from multiple aspects, this value must be calculated for each coherence matrix of each aspect separately. The final reliability measure is then derived by averaging the individual reliability values. A global threshold can now be applied in order to exclude estimates, which are considered to be unreliable, if the following criterion is met: >

Since the threshold is independent of the number of aspects or the number of baselines per aspect, it can be applied globally for every surface grid cell in the entire scene. A comparison of the likelihood function peak values, the entropy measure, and the newly proposed determinant-based measure can be seen in Fig. 3.

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TABLE II MULTI-ASPECT CONFIGURATION

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Although the measures show different scalings and therefore need different thresholds, their general messages are similar. III. TEST SYSTEM AND DATA All experiments are based on data acquired by the German experimental millimeterwave SAR sensor MEMPHIS in 2011. MEMPHIS is an acronym for Millimeterwave Experimental Multifrequency Polarimetric High Resolution Interferometric System and was developed by the Research Institute for High-Frequency Physics and Radar Techniques of the FGAN, now Fraunhofer FHR [33]. Since MEMPHIS is still an experimental system, it is commonly mounted on a C-160 Transall and flown at low altitudes of about 300 to 1000 m above ground level with a mean viewing angle of about . Although it can be operated in different modes, for our reflections only the interferometric 35 GHz (Ka band) configuration with four receiving antennas is considered. Detailed test data parameters are listed in Table I.

Fig. 5. Height reconstruction results for the individual MEMPHIS baselines of aspect 18: (a) 5.5 cm; (b) 11 cm; (c) 16.5 cm; (d) 22 cm; and (e) 27.5 cm. The large relative error (f) of the case shown in (e) is due to ambiguity problems. The heights are given above the reference ellipsoid surface.

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Our study area is located in the neighborhood of the main campus of Technische Universität München (TUM) located in the center of Munich, Germany (target coordinates: , ), showing mainly dense building blocks, but also some larger buildings surrounded by patches of concrete or lawn, respectively, and many urban trees (see Fig. 4). The reference altitude (corresponding to the relatively flat terrain surface) was defined to be 560.7 m above the GRS80 ellipsoid, whereas the building heights extend up to about 40 m. Therefore, the height search interval was set to be with a height spacing of 5 cm. The spacing of a surface grid element is . The input data of the experiments consisted of five coregistered multi-baseline InSAR stacks acquired from 70 , 160 , 250 , and 340 . The flying altitude of the four basic multi-aspect tracks was approximately 710 m above ground level, while the additional fifth track (heading angle: 340 ) was flown at about 770 m. See Table II for more details. After flat earth correction and calibration of the phase measurements using a corner reflector placed in the scene, the complex sample covariance matrices have been calculated for every pixel in every stack by adaptive multilooking as a preprocessing step [28]. The reference data for the evaluation was derived from a helicopter-borne multi-aspect LiDAR point cloud as described in [34] and [35]. In order to compare the relative errors between the different reconstruction results, the LiDAR point cloud was converted to a 2.5-D height map using a k-d tree implementation [36]. The resulting dataset was then used as reference for the error calculation. It is important to note that during the comparison, only nondiscarded, reliable grid elements were considered with a determinant-based reliability value exceeding the threshold . All grid elements with a reliability value below this threshold were considered shadow pixels. Although the methodical framework used in this paper can basically be applied to any kind of interferometric SAR data, millimeterwave SAR provides some peculiar advantages. Generally, it can be considered to follow the Gaussian scattering assumption even in urban areas due to its high sensitivity to surface roughness. Apart from that, it is particularly promising for remote sensing of trees and canopies as its short waves penetrate vegetation less than the more common longer radar wavelengths [37]. IV. EXPERIMENTS AND RESULTS The main focus of this paper is to evaluate the benefit of utilizing multiple baselines and multiple aspects within the described reconstruction framework. For this reason, experiments with various configurations are carried out and evluated with respect to the relative improvements that are achievable by adding baselines or aspects to conventional SAR interferometry (i.e., the single-aspect single-baseline case). These evaluations characterized by three values: 1) Relative error: After discarding all nonreliable pixels, the root-mean-square error (RMSE) with respect to the LiDAR reference data is calculated and normalized to the singleaspect single-baseline reference case for all cases.

Fig. 6. Adapted likelihood functions of based on a different number of antennas for a simulated scatterer located at a height of 100 m.

2) Shadow grid cells: The relative share of shadowed grid cells is calculated by dividing the number of nonreliable grid cells by the overall number of grid cells. 3) Ambiguities: The relative share of ambiguously reconstructed grid cells is calculated by dividing the number of all reliable grid cells with an error greater than 20 m by the overall number of grid cells. A. A Single Aspect but Multiple Baselines The first set of experiments is designed to prove the benefit of utilizing more than a single interferometric baseline for interferometric height reconstruction. As already described by [38] and [39], the resolution of phase ambiguities is an essential goal of multi-baseline and multi-frequency SAR interferometry, especially for highly sloped and discontinuous height profiles. In addition to that, a certain amount of noise reduction can be expected due to the exploitation of redundant phase measurements for every height value to be reconstructed.

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Fig. 7. Height reconstruction results for multi-baseline interferometry of aspect 18 based on the same master antenna: (a) two antennas; (b) three antennas; (c) four antennas; and (d) shows the relative improvement. The heights are given above the reference ellipsoid surface.

Fig. 5 shows the height maps derived from the individual baselines that can be created from the receiving antennas of the MEMPHIS system as a reference. While the four shorter baselines, of which the results are shown in Fig. 5(a)–(d), are able to resolve the full height extension of the scene without making use of any phase unwrapping procedure, the longest baseline shows some ambiguities in the bottom right part of the scene. This corresponds with the relative error [compare Fig. 5(f)], which becomes lower inversely proportional to the baseline length, if the larger error caused by the ambiguities is ignored. Another observable effect is the share of discarded grid elements, which is larger for longer baselines than for shorter ones. This is caused by an overestimation of the phase observations’ reliabilities in the short baseline cases. An explanation of the ambiguity problem and the solution by introducing multi-baseline interferometry can be drawn from Fig. 6. If multiple peaks fall into the search interval employed for the ML estimator, noise can lead to the choice of one of the wrong peaks, which leads to a wrongly reconstructed height value. If, however, the ambiguity height is larger than the search interval or if more than just two antennas are used to form more than a single baseline, the ambiguity problem is solved since just one peak remains to be detectable. The fact that only few or none ambiguities appear for the shorter baselines shown in Fig. 5 is therefore caused by an intelligent choice of the height search interval. In case the reference height were not well-known or the search interval were chosen too large, also for them, many ambiguous height reconstructions would occur. Fig. 7 shows the results for the multi-baseline case by adding more antennas to the constant master antenna. While already in

Fig. 8. Exemplary coherence maps for different baselines referring to the same master antenna of aspect 15: (a) 11 cm baseline; (b) 22 cm baseline; and (c) 27.5 cm baseline.

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Fig. 9. Height reconstruction results for different combinations of multi-aspect single-baseline data. (a) Single aspect 15 as a reference. (b) Orthogonal aspects 15 and 17. (c) Opposing aspects 15 and 16. (d) Aspects 15–17. (e) Full multi-aspect configuration (15–18). (f) Full multi-aspect configuration plus additional aspect acquired from different altitude (14–18). The heights are given above the reference ellipsoid surface.

the three-antenna (two-baseline) case all ambiguities are fully removed, also some relative accuracy improvement is observable, although not really a significant one. This is caused by the overall high coherence level of the small baselines of the MEMPHIS system. With this configuration, almost no baseline decorrelation occurs. The coherence maps of three baselines of aspect 15 are shown exemplarily in Fig. 8. Two main features are obvious: 1) the large number of shadow-affected (i.e., lowcoherence) pixels and 2) the overall high coherence level in nonshadow areas, including vegetation. However, it can be expected that multi-baseline data introduces more significant improvements for longer baselines that are closer to the critical baseline of the interferometer [17]. B. A Single Baseline but Multiple Aspects The second group of experiments is intended to show the benefits introduced by fusing single-baseline interferometric

data from multiple aspects, which is expected to be especially valuable for reducing the number of height grid elements affected by radar shadowing. Fig. 9 shows the reconstructed height maps for different combinations of aspects, each created from the longest available baseline. In addition, Fig. 10 contains the bar plots showing the relative error, the number of shadow pixels and the number of ambiguous grid elements. From these results, several insights can be drawn. First, the number of shadowed grid elements leading to erroneous or discarded height values can be significantly reduced by inclusion of complementary aspects. While orthogonal viewing angles already show a certain amount of improvement, it is—as probably expected—better to employ opposing views. The best results, however, can be achieved by a full multi-aspect configuration. A similar outcome is achieved concerning the ambiguously reconstructed grid cells. Even with respect to this problem, multi-aspect InSAR data can help to reduce ambiguity effects. Interestingly, however, the addition of data from a track with the same viewing angle but a different

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of all four receiving antennas of the MEMPHIS system and with a configuration analogue to the one used in Section IV-B are displayed in Fig. 11. The bar plots showing the relative accuracy improvement and the amount of shadow reduction are found in Fig. 12; in contrast to the single-baseline results, however, no plot for ambiguity reduction is included as the multi-baseline interferometer is not exposed to ambiguity problems anyway (see Section IV-A for details). Comparably to the multi-aspect single-baseline case, the results show a strong reduction of shadow-affected pixels, especially for multi-aspect configurations consisting of both orthogonal and opposing views. In addition to that, the relative improvement with respect to the single-aspect multi-baseline case is stronger than in the cases before, namely in the range of about 30% for a full multi-aspect configuration. Again, the addition of an aspect with an already used viewing angle but different flying altitude does not add any useful information in this estimation framework. Finally, the more effective reduction in the number of shadow pixels is caused by an improved estimation of the reliability measure for multi-baseline data. A comparison of the relative accuracy improvement with respect to the conventional single-aspect single-baseline InSAR case for different configurations investigated in this paper is shown in Fig. 13. For each, the most favorable setup has been chosen. It can easily be seen that the utilization of additional data from multiple baselines or multiple aspects provides a means to reduce the overall reconstruction error due to redundant measurements, whereas full multi-aspect multi-baseline SAR interferometry shows the strongest improvement. In this case, the reconstruction error can be expected to be about 35% less than in the standard case. V. DISCUSSION

Fig. 10. Bar plots summarizing (a) the relative improvement with respect to the single-aspect single-baseline reference case; (b) the number of shadowaffected grid elements; and (c) the number of ambiguous height reconstruction values.

height as an already used track do not bring any further improvements in both cases. Also concerning the improvement in the reconstruction error, each additional aspect helps to achieve an improvement, although the most beneficial strategy is to fuse two aspects of opposing viewing angles. Again, the utilization of a fifth aspect with redundant heading angle but different flying altitude is counterproductive. C. Multiple Aspects and Multiple Baselines The final experiments were set up in order to show the effect of utilizing the full benefit of multi-aspect multi-baseline SAR interferometry. The corresponding results based on exploitation

The results achieved in the experiments for this paper prove several hypotheses: 1) Multi-baseline SAR interferometry greatly reduces the phase ambiguity problem even for a small number of additional receiving antennas. The accuracy gain between the investigated two-antenna and four-antenna cases, however, was below 10%. 2) The fusion of multiple aspects also helps to resolve ambiguities, if not as efficiently as multi-baseline data does. In addition, multi-aspect data helps to reduce the overall reconstruction error for about 30%, whereas the fusion of orthogonal aspects is not as useful as the fusion of opposing aspects. The greatest benefit of multi-aspect SAR interferometry, however, is the reduction in surface parts that cannot be reconstructed due to shadowing. While the combination of two complementary aspects (no matter if orthogonal or from opposing viewing angles) already reduces the amount of shadow pixels for about 20%, a full multi-aspect configuration consisting of four complementary aspects reduces the shadow effect for almost 50%. 3) The most powerful setup for the task of urban surface model reconstruction is MAMBInSAR, fusing all kinds of multi-modal InSAR data simultaneously. In this case, all ambiguity problems within a reasonable height interval

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Fig. 11. Height reconstruction results for different combinations of multi-aspect multi-baseline data. (a) Single aspect 15 as a reference. (b) Orthogonal aspects 15 and 17. (c) Opposing aspects 15 and 16. (d) Aspects 15–17. (e) Full multi-aspect configuration (15–18). (f) Full multi-aspect configuration plus additional aspect acquired from different altitude (14–18). The heights are given above the reference ellipsoid surface.

are solved and with respect to conventional SAR interferometry, the amount of shadow pixels is reduced for about 70%, while the reconstruction accuracy is improved for about 35%. 4) If already a full multi-aspect configuration with four complementary aspects is used, the addition of a fifth aspect acquired from an already utilized viewing angle but from a different flying altitude does not add any further benefit. These insights show that sophisticated flight planning and mission design can be used to greatly enhance the potential quality and quantity of any reconstruction results in complex scenes such as urban areas. It also shows the benefit introduced by the high flexibility of airborne sensor technology, which is not limited to ascending and descending orbits such as most earth observation satellites. To this end, only airborne remote sensing can provide multi-aspect multi-baseline data without temporal decorrelation and strongly varying aspect angles. However, flight time is quite expensive; it is therefore useful to know

about the benefit of different multi-aspect configurations such that efficient prior planning can help to reduce the campaign costs significantly. In addition, the findings of this article can help to inspire the mission design of future multi-satellite missions [40]. VI. CONCLUSION In this paper, extensive experiments aiming at proving the benefit of multi-aspect multi-baseline InSAR data for the reconstruction of urban surface models are shown. Based on airborne decimeter-resolution millimeterwave imagery, these experiments were carried out in a recently developed ML estimation framework enabling the fusion of almost arbitrary configurations of interferometric SAR observations. It has been shown that multi-baseline data help to reduce the ambiguity problem wellknown to SAR interferometry, whereas multi-aspect data significantly decrease the nonreconstructable parts of the scene affected by radar shadow. In addition to that, the exploitation of

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Technology FHR) as well as C. Magnard and Dr. E. Meier (Remote Sensing Laboratories at the University of Zurich) for providing the MEMPHIS test data.

REFERENCES

Fig. 12. Bar plots summarizing (a) the relative improvement with respect to the single-aspect multi-baseline reference case and (b) the number of shadowaffected grid elements.

Fig. 13. Error reduction with respect to the conventional single-aspect singlebaseline SAR interferometry case. SA: single-aspect; SB: single-baseline; MA: multi-aspect; and MB: multi-baseline.

redundant measurements yields a significant improvement in the achievable accuracy; in comparison with conventional single-aspect single-baseline interferometry, the utilization of a multi-aspect multi-baseline configuration shows a 35% smaller reconstruction error. ACKNOWLEDGMENT The authors would like to thank T. Brehm and Dr. S. Stanko (Fraunhofer Institute for High Frequency Physics and Radar

[1] L. Graham, “Synthetic interferometer radar for topographic mapping,” Proc. IEEE, vol. 62, no. 6, pp. 763–768, Jun. 1974. [2] R. Bamler and P. Hartl, “Synthetic aperture radar interferometry,” Inverse Probl., vol. 14, no. 4, pp. R1–R54, 1998. [3] P. A. Rosen, S. Hensley, I. R. Joughin, F. K. Li, S. N. Madsen, E. Rodriguez et al., “Synthetic aperture radar interferometry,” Proc. IEEE, vol. 88, no. 3, pp. 333–382, Mar. 2000. [4] U. Stilla, U. Soergel, and U. Thoennessen, “Potential and limits of InSAR data for building reconstruction in built-up areas,” ISPRS J. Photogramm. Remote Sens., vol. 58, no. 1–2, pp. 113–123, 2003. [5] M. Schmitt, C. Magnard, S. Stanko, C. Ackermann, and U. Stilla, “Advanced high resolution SAR interferometry of urban areas with airborne millimeterwave radar,” Photogramm. Fernerkundung Geoinf., vol. 2013, no. 6, pp. 603–617, 2013. [6] A. Schubert, “Stereo-Assisted Interferometric SAR,” Ph.D. thesis, Remote Sens. Lab., Univ. Zurich, 2004. [7] A. Ferretti, C. Prati, and F. Rocca, “Permanent scatterers in SAR interferometry,” IEEE Trans. Geosci. Remote Sens., vol. 39, no. 1, pp. 8–20, Jan. 2001. [8] A. Budillon, A. Evangelista, and G. Schirinzi, “Three-dimensional SAR focusing from multipass signals using compressive sampling,” IEEE Trans. Geosci. Remote Sens., vol. 49, no. 1, pp. 488–499, Jan. 2011. [9] D. Reale, G. Fornaro, A. Pauciullo, X. Zhu, and R. Bamler, “Tomographic imaging and monitoring of buildings with very high resolution SAR data,” IEEE Geosci. Remote Sens. Lett., vol. 8, no. 4, pp. 661–665, Jul. 2011. [10] Y. Wang, X. X. Zhu, and R. Bamler, “Retrieval of phase history parameters from distributed scatterers in urban areas using very high resolution SAR data,” ISPRS J. Photogramm. Remote Sens., vol. 73, pp. 89–99, 2012. [11] A. Shabou, F. Baselice, and G. Ferraioli, “Urban digital elevation model reconstruction using very high resolution multichannel InSAR data,” IEEE Trans. Geosci. Remote Sens., vol. 50, no. 11, pp. 4748–4758, Nov. 2012. [12] A. Thiele, E. Cadario, K. Schulz, U. Thoennessen, and U. Soergel, “Building recognition from multi-aspect high-resolution InSAR data in urban areas,” IEEE Trans. Geosci. Remote Sens., vol. 45, no. 11, pp. 3583–3593, Nov. 2007. [13] F. Xu and Y.-Q. Jin, “Automatic reconstruction of building objects from multiaspect meter-resolution SAR images,” IEEE Trans. Geosci. Remote Sens., vol. 45, no. 7, pp. 2336–2353, Jul. 2007. [14] M. Schmitt and U. Stilla, “Fusion of airborne multi-aspect InSAR data by simultaneous backward geocoding,” in Proc. Joint Urban Remote Sens. Event, Munich, Germany, 2011, pp. 53–56. [15] S. Gernhardt, X. Cong, M. Eineder, S. Hinz, and R. Bamler, “Geometrical fusion of multitrack PS point clouds,” IEEE Geosci. Remote Sens. Lett., vol. 9, no. 1, pp. 38–42, Jan. 2012. [16] M. Seymour and I. Cumming, “Maximum likelihood estimation for SAR interferometry,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., 1994, pp. 2272–2275. [17] F. Lombardini, “Optimum absolute phase retrieval in three-element SAR interferometer,” Electron. Lett., vol. 34, no. 15, pp. 1522–1524, 1998. [18] G. Fornaro, A. M. Guarnieri, A. Pauciullo, and F. De Zan, “Maximum likelihood multi-baseline SAR interferometry,” IEE Proc. Radar Sonar Navig., vol. 153, no. 3, pp. 279–288, Jun. 2006. [19] A. Ferretti, A. Fumagalli, F. Novali, C. Prati, F. Rocca, and A. Rucci, “A new algorithm for processing interferometric data-stacks: SqueeSAR,” IEEE Trans. Geosci. Remote Sens., vol. 49, no. 9, pp. 3460–3470, Sep. 2011. [20] M. Eineder and N. Adam, “A maximum-likelihood estimator to simultaneously unwrap, geocode, and fuse SAR interferograms from different viewing geometries into one digital elevation model,” IEEE Trans. Geosci. Remote Sens., vol. 43, no. 1, pp. 24–36, Jan. 2005. [21] M. Schmitt and U. Stilla, “Maximum-likelihood estimation for multi-aspect multi-baseline SAR interferometry of urban areas,” ISPRS J. Photogramm. Remote Sens., vol. 87, pp. 68–77, 2014.

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[22] J. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, vol. 9, Topics in Applied Physics, J. Dainty, A. Ennos, M. Franon, J. Goodman, T. McKechnie, G. Parry, and J. Goodman, Eds. Berlin, Germany: Springer-Verlag, 1975, pp. 9–75. [23] D. Just and R. Bamler, “Phase statistics of interferograms with applications to synthetic aperture radar,” Appl. Opt., vol. 33, no. 20, pp. 4361–4368, 1994. [24] F. De Zan, “Optimizing SAR interferometry for decorrelating scatterers,” Ph.D. dissertation, Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy, 2008. [25] F. Baselice, A. Budillon, G. Ferraioli, and V. Pascazio, “Layover solution in SAR imaging: A statistical approach,” IEEE Geosci. Remote Sens. Lett., vol. 6, no. 3, pp. 577–581, Jul. 2009. [26] G. Vasile, E. Trouv, M. Ciuc, and V. Buzuloiu, “General adaptiveneighborhood technique for improving synthetic aperture radar interferometric coherence estimation,” J. Opt. Soc. Amer. A Opt. Image Sci. Vis., vol. 21, no. 8, pp. 1455–1464, 2004. [27] A. Parizzi and R. Brcic, “Adaptive InSAR stack multilooking exploiting amplitude statistics: A comparison between different techniques and practical results,” IEEE Geosci. Remote Sens. Lett., vol. 8, no. 3, pp. 441–445, May 2011. [28] M. Schmitt and U. Stilla, “Adaptive multilooking of airborne single-pass multi-baseline InSAR stacks,” IEEE Trans. Geosci. Remote Sens., vol. 52, no. 1, pp. 305–312, Jan. 2014. [29] H. Zebker and K. Chen, “Accurate estimation of correlation in InSAR observations,” IEEE Geosci. Remote Sens. Lett., vol. 2, no. 2, pp. 124–127, Apr. 2005. [30] K.-R. Koch, in Introduction to Bayesian Statistics, 2nd ed. Berlin, Germany: Springer-Verlag, 2007. [31] G. Fornaro, A. Pauciullo, D. Reale, and S. Verde, “SAR coherence tomography: A new approach for coherent analysis of urban areas,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., 2013, pp. 73–76. [32] M. Schmitt, C. Magnard, T. Brehm, and U. Stilla, “Towards airborne single pass decimeter resolution SAR interferometry over urban areas,” in Photogrammetric Image Analysis, vol. 6952, Lecture Notes in Computer Science, U. Stilla, F. Rottensteiner, H. Mayer, B. Jutzi, and M. Butenuth, Eds. Berlin, Germany: Springer-Verlag, 2011, pp. 197–208. [33] H. Schimpf, H. Essen, S. Boehmsdorff, and T. Brehm, “MEMPHIS—A fully polarimetric experimental radar,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., Toronto, Canada, 2002, pp. 1714–1716. [34] M. Hebel and U. Stilla, “Automatic registration of laser point clouds of urban areas,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci., vol. 36, no. Part 3/W49A, pp. 13–18, 2007. [35] M. Hebel and U. Stilla, “Simultaneous calibration of ALS systems and alignment of multiview lidar scans of urban areas,” IEEE Trans. Geosci. Remote Sens., vol. 50, no. 6, pp. 2364–2379, Jun. 2012. [36] J. Schönberger, “Fusion of multi-aspect multi-baseline InSAR data for urban surface model reconstruction,” Bachelor’s thesis, Dept. Photogramm. Remote Sens., Technische Universitaet Muenchen (TUM), München, Germany, 2013. [37] M. Schmitt, A. Brück, J. Schönberger, and U. Stilla, “Potential of airborne single-pass millimeterwave InSAR data for individual tree recognition,” in Proc. 33rd Wissenschaftlich-Technische Jahrestagung der DGPF, Freiburg, Germany, 2013, pp. 427–436. [38] G. Corsini, M. Diani, F. Lombardini, and G. Pinelli, “Simulated analysis and optimization of a three-antenna airborne InSAR system for topographic mapping,” IEEE Trans. Geosci. Remote Sens., vol. 37, no. 5, pp. 2518–2529, Sep. 1999. [39] V. Pascazio and G. Schirinzi, “Multifrequency InSAR height reconstruction through maximum likelihood estimation of local planes parameters,” IEEE Trans. Image Process., vol. 11, no. 12, pp. 1478–1489, Dec. 2002. [40] G. Krieger and A. Moreira, “Multistatic SAR satellite formations: Potentials and challenges,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., Seoul, Korea, 2005, pp. 2680–2684.

Michael Schmitt (S’08) was born in Munich, Germany, in 1984. He received the Dipl.-Ing. (Univ.) degree in Geodesy and Geoinformation from the Technische Universitaet Muenchen (TUM), Munich, Germany, in 2009. He is currently working toward the Ph.D. degree in airborne SAR interferometry using multi-baseline and multi-aspect millimetre wave data at the Department of Photogrammetry and Remote Sensing, TUM, where he has been a full-time research assistant since May 2009. Besides SAR interferometry, his main interests are (statistical) signal processing and parameter estimation theory applied to sensor data fusion and the extraction of information from imagery.

Johannes L. Schönberger was born in Munich, Germany, in 1991. He received the B.Sc. degree in geodesy and geoinformation from the Technische Universitaet Muenchen (TUM), Munich, Germany, in 2013. He is currently working toward the M.Sc. degree in geodesy and geoinformation, TUM, and at the University of North Carolina at Chapel Hill, Chapel Hill, NC, USA. Besides SAR, his research interests include image processing, parameter estimation theory, and computer vision.

Uwe Stilla (M’04–SM’09) was born in Cologne, Germany, in 1957. In 1980, he received the Dipl.Ing. in electrical engineering from Gesamthochschule Paderborn, Paderborn, Germany, and in 1987, additionally, he received Dipl.-Ing. in biomedical engineering from the University of Karlsruhe, Karlsruhe, Germany. In 1993, he received the Ph.D. degree in engineering in the field of pattern recognition from the University of Karlsruhe. From 1990 to 2004, he was with the Institute of Optronics and Pattern Recognition (FGAN-FOM), a German research establishment for defence-related studies. Since 2004, he is a Professor at Technische Universitaet Muenchen (TUM), Munich, Germany, the Head of the Department of Photogrammetry and Remote Sensing, TUM, and currently the Director of the Institute of Photogrammetry and Cartography, Zagreb, Croatia. He is the Vice Dean of the Faculty of Civil Engineering and Surveying and Dean of Student Affairs of the Bachelor’s and Master Program “Geodesy and Geoinformation” and the international Master Programs “Earth Oriented Space Science and Technology (ESPACE)” and “Cartography.” Dr. Stilla is the Chair of the ISPRS working group III/VII “Pattern Analysis in Remote Sensing,” Principal Investigator of the International Graduate School of Science and Engineering (IGSSE), Vice President of the German Society of Photogrammetry, Remote Sensing and Geoinformation (DGPF), Member of the Scientific Board of German Commission of Geodesy (DGK), and Member of Commission for Geodesy and Glaciology (KEG) of the Bavarian Academy of Science and Humanities. He has been the Organizer and Chair of the conferences “Photogrammetric Image Analysis (PIA),” “City Models, Roads and Traffic (CMRT),” “GRSS/ISPRS Joint Urban Remote Sensing Event (JURSE 2011),” “Earth Observation and Global Changes (EOGC 2011),” and the “IEEE-GRSS REMOTE SENSING SUMMER SCHOOL (RSSS12).” His research interests include image analysis in the field of photogrammetry and remote sensing. He published more than 300 contributions.