INFORMATION MINING VIA COHERENCE ESTIMATION FROM MULTI-LOOK INCOHERENT SAR IMAGERY Bruno Aiazzi(1) , Luciano Alparone(2) , Stefano Baronti(1) Massimo Bianchini(2) , Andrea Garzelli(3) , Massimo Selva(1) (1)
IFAC–CNR: Institute of Applied Physics “Nello Carrara”, Italian National Research Council Via Panciatichi, 64, 50127 Firenze (Italy), {B.Aiazzi S.Baronti M.Selva}@ifac.cnr.it (2) DET-UniFI: Department of Electronics and Telecommunications, University of Firenze Via Santa Marta, 3, 50139 Firenze (Italy), {Alparone Bianchini}@lci.det.unifi.it (3) DII-UniSI: Department of Information Engineering, University of Siena Via Roma, 56, 53100 Siena (Italy),
[email protected]
ABSTRACT In this work, an application of “browsing by coherence” is presented. An interferometric pair of single-look complex (SLC) ERS-1/2 Tandem images is multi-look processed and the resulting real-valued images are further compressed through a hierarchical method to yield quick-looks that may be browsed at different spatial resolutions, i.e. number of looks. Pairs of quick-look icons are utilized to estimate coherence by means of a new method based on measurements of temporal correlation of speckle. The outcome maps are compared with spatially degraded versions of the coherence map calculated from the original SLC data. Experiments are aimed at showing that the method yields steady results varying with the number of looks of icons that are browsed. 1
INTRODUCTION
Multi-temporal analysis of Synthetic Aperture Radar (SAR) imagery has nowadays become one of the most relevant tasks to perform environmental monitoring. Unlike optical observations, multi-temporal SAR data may yield a further source of information, besides radar backscatters, by analyzing how the temporal coherence characteristics vary throughout the scene. Originally introduced for SAR interferometry applications [1], coherence analysis has been recently found to carry a great significance also for land use classification [2]. However, disadvantages of analysis techniques based on coherence are the large volume of data to be manipulated, with the resulting computational cost, and possibly the difficulty for users to recover single-look complex (SLC) data of historical image sequences, as these data were intermediate products that may not have been saved after multi-look SAR processing [3]. Under this perspective, it is desirable to calculate coherence estimates from multi-look images, which may be considerably smaller in size than SLC images, especially whenever a decision must be quickly made about which of a number of available scenes are useful
for a particular analysis. A more accurate coherence analysis will be performed on SLC data, only once the most suitable pairs have been recognized by the fast method. This issue will grow in importance in a very near future, when the SLC data to be retrieved will generally be remote to the user and quick-look icons of small size, and hence large number of looks, will be available to browse by coherence the data base of SLC images. In this work an application of “browsing by coherence” is presented. An interferometric pair of SLC ERS-1/2 images is multi-look processed and the outcome realvalued images are compressed through a hierarchical JPEG-based method to yield quick-looks that may be browsed at different spatial resolutions, i.e. number of looks. Pairs of quick-look icons are utilized to estimate coherence and the outcome maps are compared with spatially degraded versions of the coherence map calculated from the original SLC data, with 5-look coherent averaging of the interferogram. Although the theoretical foundations of the coherence estimation method were developed in [4], the present experiments are aimed at showing that the method yields steady results varying with the number of looks of icons that are browsed. Furthermore, the method is relatively insensitive to (lossy) compression of bitmaps, provided that compression ratios are not too large. In that case, speckle is filtered out by the compression algorithm and coherence estimation may fail. An application scenario is presented as well. A catalogue of SLC SAR images of the same scene is constituted by compressed multi-look amplitude bitmaps. Such a catalogue is remotely accessed via Internet and the user makes a quick coherence analysis of several pairs as possible candidates of further more accurate investigations. Only the pair which exhibits the most favourable coherence characteristics for the target application, e.g. high coherence for interferometry, low coherence to possibly detect changes, like floods or fires, will be downloaded in SLC format to locally carry out the desired analysis on a data set of reduced size, yet meaningful for application.
2
A REVIEW OF COHERENCE ESTIMATION
Let z1 (m, n) and z2 (m, n) denote the one-look complex SAR data at pixel position (m, n) in two overlapped observations taken at different times: z = [z] + j · [z], in which [z] and [z] are the zero-mean in-phase and quadrature components of the envelope. Let us define the complex cross-correlation function between z1 and z2 as the normalized complex covariance [5] C(m, n) =
E[z1 (m, n) · z2∗ (m, n)] E[|z1 (m, n)|2 ] · E[|z2 (m, n)|2 ]
(1)
where z ∗ denotes the complex conjugate of z and E[·] the ensemble expectation. The complex cross-correlation (1) may be written as C(m, n) = γ(m, n) exp{−jβ(m, n)}. The modulus 0 ≤ γ(m, n) ≤ 1 is a measurement of the temporal coherence between the two images at pixel position (m, n). The phase β(m, n) is the ML estimator of the interferometric phase. In practice, given the high noisiness of the data, the size of the local window in which (1) is estimated may be crucial. The trade-off between spatial resolution and accuracy of the estimate may be overcome by resorting to unbiased estimators [6]. Coherence estimators operating on real-valued, and possibly multi-look data, were investigated in the literature during the last decade [5]. The starting point was a property, first noticed by Rignot and van Zyl [7], that on homogeneous areas the square root of the correlation coefficient (CC) between the detected intensities of a pair of SAR images yields an estimate of coherence, provided that the number of looks is not too large (2 or 3, at most). The crucial point is that intensity CC is extremely sensitive to textures, that may cause large overestimation of the desired parameter. In the presence of textures, especially when images are multi-looked, this property no longer holds: as the number of looks increases, the dependence on the squared coherence vanishes and the intensity CC approximates the temporal CC of texture [7]. Practically, the intensity CC cannot be utilized for number of looks > 3. Hence, the main reason that prevents one from obtaining accurate coherence estimates from a pair of detected SAR images, i.e. real-valued magnitude of the complex backscatter, is that edges and textures of radar reflectance do not obey to the stationarity requirement. Therefore, edge pixels and textured areas must be carefully recognized before correlation is measured. Furthermore, incoherent multi-look processing reduces speckle and enhances textures [3]. Thus, rejection of textured pixels before TCC is calculated may become crucial. Practically, intensity correlation successfully applies only to one-look intensity data, e.g. to provide quick and dirty coherence maps for use in interferometric applications [8]. In a very recent paper [4], the authors approached
the problem of coherence estimation from multi-look real-valued data as measurement of the temporal CC (TCC) between a pair of temporal observations. Under RCS stationarity assumptions, TCC is equivalent to intensity CC. The square-rooted CC of intensity has been replaced by the CC of the square-rooted intensity, i.e. of amplitude, as a coherence estimator. Although the latter is a rough approximation of the former for one-look images in the absence of texture, it can be demonstrated that if images are textured, the temporal CC of amplitude is a better and better approximation of coherence, as the number of looks increases. This effect depends on the compressed range of amplitude values, together with imperfect texture rejection of estimation algorithms. To avoid drawbacks occurring from the presence of textures, a method was developed that relies on estimation of the speckle variances after applying a transformation between corresponding pixels in the two multi-temporal observations. A reversible transformation consisting of pixel geometric mean and ratio, is applied to the pair of images to extract their common signal and the change occurred between the two pass dates, in the present case to expedite assessment of speckle patterns correlation. The space-varying TCC of speckle is estimated by means of a scatter-plot based method applied to small image blocks by inverting the relationship yielding the noise variances of the transformed data [4]. Experiments on a high-coherence pair of SAR images have shown a good degree of accuracy. The method yields acceptable results also in the presence of strong textures and permanent scatterers, e.g. on urban areas, where it was found that intensity-based coherence estimators fail. Perhaps, the most interesting application of the proposed method is for information mining [9], i.e. for browsing archives of SLC images to quickly find pairs having desired coherence characteristics [10]. Such pairs may be identified by simply processing their integervalued multi-look icons (quick-looks). The accuracy of the coherence estimated by the method utilized is generally more than acceptable for quick-look applications [4].
3
COHERENCE ESTIMATION PROCEDURE
Given a pair of co-registered real-valued SAR images of the same area, a transformation suitable for highlighting temporal correlation of speckle is given by the geometric mean and ratio of a pair of overlapped real-valued images, either intensity or amplitude: G(m, n) R(m, n)
g1 (m, n) · g2 (m, n) g1 (m, n) = g2 (m, n) =
(2)
in which g1 (m, n) and g2 (m, n) are the original speckled images, while G(m, n) and R(m, n) the transformed
ones. The inverse transformation is given by g1 (m, n) g2 (m, n)
= G(m, n) · R(m, n) G(m, n) . = R(m, n)
the approximation being more accurate for larger number of looks. From Eq. (8), the TCC is easily derived as
The geometric mean strengthens the time-correlated component of the radar reflectance, thus resulting in an SNR that is generally higher than in each individual observation. Conversely, the ratio removes the timecorrelated signal component and highlights changes in backscatter, as well as decorrelation of noise patterns. The multiplicative noise and texture [3] models still hold for both the transformed images. Let us assume that the radar reflectivity in a pair of SAR observations may be expressed as a common signal s(m, n) modulated by the square root of a change term c(m, n), and by its reciprocal, respectively. Both s(m, n) and c(m, n) are spatially correlated space-varying processes, yielding positive values and thus having nonzero means. Two speckle terms u1 (m, n) and u2 (m, n), with E[u1 (m, n)] = E[u2 (m, n)] = 1, E[u21 (m, n)] = E[u22 (m, n)] = 1 + σu2 , and being correlated with each other through a coefficient ρT (m, n), where E[u1 (m, n)u2 (m, n)] − 1 ρT (m, n) σu2
(4)
multiplicatively affect the radar reflectances in the two observations: g1 (m, n) = s(m, n) · c(m, n) · u1 (m, n) s(m, n) · u2 (m, n). (5) g2 (m, n) = c(m, n) Eq. (5) defines a multiplicative temporal change model, analogous to the multiplicative texture model. If (2) is applied to (5), the transformed images may be written as G(m, n) = s(m, n) · uG (m, n) (6) R(m, n) = c(m, n) · uR (m, n) in which uG (m, n)
uR (m, n)
2 2 (m, n) − σR (m, n) 4σG 2 2 (m, n) . 4σG (m, n) + σR
(9)
Eq. (9) states that the space-varying TCC between speckles may be estimated from the non-stationary variances of the speckles affecting the geometric mean and ratio images, respectively. The TTC is independent of σu2 , provided that the latter does not change from one image to another. Since coherence is a local feature, individual values of TCC may not be estimated on large image blocks. Hence, the geometric mean and ratio images are partitioned into small square blocks and the scatter-plot base estimation procedure [4] is applied to each block separately to 2 2 and σR . Local sample statistics, however, measure σG are calculated across adjacent blocks, except for image edges, in which pixels are mirrored, on 3 × 3 or 5 × 5 windows. 4
EXPERIMENTAL RESULTS & DISCUSSION
An ERS-1/2 Tandem pair of SLC images collected on Central Italy on 20/21 August 1995 was utilised. Amplitudes of 5-look detected intensities are shown in Figs. 1 and 2. The image pair is shown in SAR coordinated with non-uniform ground resolution, approximately equal to 12.5 m. The area portrayed includes the city of Florence and the surrounding settlements. The northern mountainous region and the southern hilly terrain, together with the textured urban area, have been intentionally chosen as a challenging trial to assess the estimation procedure. The coherence map calculated from the SLC data is shown in Fig. 3. The interferogram was coherently averaged on 5 × 5 pixels; the outcome coherence was incoherently averaged on 5-looks along azimuth. Due to close pass dates, seasonal changes are missing and the primary source of coherence loss is given by shadow effects caused by terrain relief in the upper part, originating processing artifacts, as well as to the presence of the Arno river crossing the region and of a couple of water basins. The average coherence is 0.449.
u1 (m, n) · u2 (m, n) u1 (m, n) . u2 (m, n)
(7)
The variances of the noise terms uG (m, n) and uR (m, n) can be approximated by taking the first-order Taylor developments of the square root and of the ratio in (7): 2 (m, n) = σG
ρT (m, n) =
(3)
2 σu 2
· [1 + ρT (m, n)]
2 (m, n) = 2 · σu2 · [1 − ρT (m, n)] σR
(8)
The TCC method for coherence estimation was applied with block sizes 32 × 32, 16 × 16 and 8 × 8 blocks. The data utilised were uncompressed 8-bit versions of master and slave (exactly those displayed in Figs. 1 and 2) as well as quick-look compressed versions (≈ 27 dB PSNR) achieved by JPEG 2000 at 2 bits per image pixel. The latter are typical products suitable for browsing. The estimated maps of TCC are shown in Figs. 4(a), (c) and (e) for uncompressed data; in Figs. 4(b), (d) and (f) for compressed data. The three sets of maps at different resolutions are largely similar. Those calculated
Figure 1: 1024 × 1024 image from ERS-1/2 Tandem pair portraying the city of Florence, in Italy: master image acquired on 20/08/95, shown in SAR coordinates (slant-range) in a 5-look amplitude format.
on uncompressed data are unbiased with respect to the true coherence in Fig. 3 (averages are 0.446, 0.449 and 0.466 for decreasing block size). Instead JPEG 2000 compression acts as a low-pass filter, which abates the noise: hence, the maps are biased by defect on 16 × 16 and 8 × 8 blocks (averages are 0.455, 0.370 and 0.368 for decreasing block size) and a few outlier blocks appear. The inter-scale analysis reveals that coherence is a local feature, which loses this peculiarity if estimated on large blocks. In fact, major differences can be noticed whenever coherence variations occur within the estimation block. The scatter-plot based noise variance estimation method clamps the subset of homogeneous pixels found within the block and accordingly yields a TCC value, which does not consider heterogeneous pixels within the same block, possibly having different speckle TCC, but containing texture at the same time and therefore being discarded from computation.
A further experiment is aimed at testing the robustness of the method when the number of looks is large. Figs. 5(a) and (b) show 20-look versions with size 512 × 512 of the master and slave images. Due to incoherent average of intensities, speckle noise, as well as subtle details, are largely removed. Textures appear enhanced on the whole and this seems an inconvenience for the estimation method which relies on speckle correlation across time and suffers from the presence of strong textures. The estimated maps of TCC are shown in Figs. 5(c) and (e) for 8-bit uncompressed data; in Figs. 5(d) and (f) for JPEG 2000 compressed data (2 bit/pixel). The two sets of maps at different resolutions are similar to the corresponding entries in Fig. 4. All maps are biased with respect to the true coherence in Fig. 3 (averages are 0.516, 0.530, 0.519 and 0.533 for Fig. 5(c)-(f), respectively) regardless of compression. Few outlier blocks appear in maps achieved from compressed data.
Figure 2: 1024 × 1024 image from ERS-1/2 Tandem pair portraying the city of Florence, in Italy: slave image acquired on 21/08/95. 5
CONCLUSIONS
The method proposed for coherence estimation of multi-look detected SAR images may find applications in the analysis of historical series of SAR images, whose SLC products are no longer available, and for “browsing by coherence” of large archives of SLC images, through their integer and possibly compressed multi-look icons. Experiments on a pair of ERS-1/2 Tandem SAR images are have demonstrated that the method yields steady results also when the number of looks of icons that are browsed is as large as twenty. Furthermore, the method is relatively insensitive to (lossy) compression of bitmaps, provided that compression ratios are not too large. In that case, speckle is filtered out by the compression algorithm and coherence estimation may fail. The main drawback of TCC as coherence estimator is its reduced spatial resolution with respect to conventional
coherence analysis carried out on SLC data. When the speckle TCC is estimated on 8 × 8 blocks, the resolution is acceptable, but the “noisiness” of the map may be unsuitable for an accurate analysis, due the presence of outliers caused by statistical instability, when the method operates on strongly textured and inhomogeneous areas. In this case, however, post-processing of the estimated map to remove such outliers, may be recommended.
ACKNOWLEDGEMENTS The authors wish to thank Paolo Pampaloni of IFACCNR for kindly providing the ERS data and ESA for the software package BEST. This work was supported in part by the Italian Ministry of Education, University and Research (MIUR) under Project COFIN 2002 Processing and analysis of multitemporal and hyper-temporal remote-sensing images for environmental monitoring.
Figure 3: 1024 × 1024 coherence map estimated from the 5120 × 1024 SLC data with 5 × 5 coherent averaging of the interferogram and 5-look incoherent averaging along azimuth of the outcome; average is 0.449. References [1] P. A. Rosen, S. Hensley, I. R. Joughin, F. K. Li, S. N. Madsen, E. Rodriguez, and R. M. Goldstein, “Synthetic Aperture Radar interferometry,” Proc. of the IEEE, vol. 88, no. 3, pp. 333–382, Mar. 2000. [2] T. Strozzi, P. B. G. Dammert, U. Wegmuller, J.-M. Martinez, J. I. H. Askne, A. Beaudoin, and M. T. Hallikainen, “Landuse mapping with ERS SAR interferometry,” IEEE Trans. Geosci. Remote Sensing, vol. 38, no. 2, pp. 766– 775, Mar. 2000. [3] C. Oliver and S. Quegan, Understanding Synthetic Aperture Radar Images, Artech House, Boston, MA, 1998. [4] B. Aiazzi, L. Alparone, S. Baronti, and A. Garzelli, “Coherence estimation from incoherent multilook SAR imagery,” IEEE Trans. Geosci. Remote Sensing, vol. 41, no. 11, pp. 2531–2539, Nov. 2003. [5] R. Touzi, A. Lop`es, J. Bruniquel, and P. W. Vachon, “Coherence estimation for SAR imagery,” IEEE Trans. Geosci. Remote Sensing, vol. 37, no. 1, pp. 135–149, Jan. 1999.
[6] C. H. Gierull, “Unbiased coherence estimator for SAR interferometry with application to moving target detection,” Electronics Lett., vol. 37, no. 14, pp. 913–915, July 2001. [7] E. M. Rignot and J. J. van Zyl, “Change detection techniques for ERS-1 SAR data,” IEEE Trans. Geosci. Remote Sensing, vol. 31, no. 4, pp. 896–906, July 1993. [8] A. Monti Guarnieri and C. Prati, “SAR interferometry: a “quick and dirty” coherence estimator for data browsing,” IEEE Trans. Geosci. Remote Sensing, vol. 35, no. 3, pp. 660–669, May 1997. [9] M. Datcu, H. Daschiel, A. Pelizzari, M. Quartulli, A. Galoppo, A. Colapicchioni, M. Pastori, K. Seidel, P. G. Marchetti, and S. D’Elia, “Information mining in remote sensing image archives: system concepts,” IEEE Trans. Geosci. Remote Sensing, vol. 41, no. 12, pp. 2923–2936, Dec. 2003. [10] M. Schr¨oder, H. Rehrauer, K. Seidel, and M. Datcu, “Interactive learning and probabilistic retrieval in remote sensing image archives,” IEEE Trans. Geosci. Remote Sensing, vol. 38, no. 5, pp. 2288–2298, Sept. 2000.
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Figure 4: 1024 × 1024 coherence maps estimated from the 5-look amplitude data shown in Fig. 1 and Fig. 2 as temporal correlation coefficient of speckle: 32×32 blocks on (a) 8-bit uncompressed and (b) 2-bit JPEG2000-compressed quick-looks of the 5-look images; 16 × 16 blocks on (c) 8-bit uncompressed and (d) 2-bit JPEG2000 compressed data; 8 × 8 blocks on (e) 8-bit uncompressed and (f) 2-bit JPEG2000 compressed data.
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Figure 5: 512 × 512 (a) master and (b) slave (20-look incoherent amplitudes of 5120 × 1025 SLC). 512 × 512 coherence maps estimated as temporal correlation of speckle from the 20-look master and slave: 16 × 16 blocks on (c) 8-bit uncompressed and (d) 2-bit JPEG2000 compressed data; 8 × 8 blocks on (e) 8-bit uncompressed and (f) 2-bit JPEG2000 compressed data.
