While the use of differential TomoSAR based on compressive sensing (CS) makes it possible to solve the layover problem and reconstruct the deformation information of an observed urban area scene acquired by moderate-high resolution SAR satellite, the performance of the reconstruction decreases for a sparse and structural observed scene due to ignoring the structural characteristics of the observed scene. To deal with this issue, the method for differential SAR tomography based on Khatri-Rao subspace and block compressive sensing (KRS-BCS) is proposed. The proposed method changes the reconstruction of the sparse and structural observed scene into a BCS problem under Khatri-Rao subspace, using the structure information of the observed scene and Khatri-Rao product property of the reconstructed observation matrix for differential TomoSAR, such that the KRS-BCS problem is efficiently solved with a block sparse l1/l2 norm optimization signal model, and the performance of resolution capability and reconstruction estimation is compared and analyzed qualitatively and quantitatively by the theoretical analysis and the simulation experiments, all of the results show the propose KRS-BCS method practicably overcomes the problems of CS method, as well as, quite maintains the high resolution characteristics, effectively reduces the probability of false scattering target and greatly improves the reconstruction accurate of scattering point. Finally, the application is taking the urban area of the Mobara(in Chiba, Japan) as the test area and using 34 ENVISAT-ASAR images, the accuracy is verifying with the reference deformations derived from first level point data and GPS tracking data, the results show the trend is consistent and the overall deviation is small between reconstruction deformations of the propose KRS-BCS method and the reference deformations, and the accuracy is high in the estimation of the urban area deformation.
[1] SANDWELL D T,SICHOIX L. Topographic Phase Recovery from Stacked ERS Interferometry and A Low-resolution Digital Elevation Model[J].Journal of Geophysical Research:Atmospheres,2000,205(B12):28211-28222.
[2] USAI S. A New Approach for Long Term Monitoring of Deformations by Differential SAR Interferometry[D]. Delft:Delft University of Technology, 2001.
[3] FERRETTI A, PRATI C, ROCCA F. Permanent Scatterers in SAR Interferometry[J]. IEEE Transactions on Geoscience and Remote Sensing, 2001, 39(1):8-20.
[4] HOOPER A, ZEBKER H, SEGALL P, et al. A New Method for Measuring Deformation on Volcanoes and Other Natural Terrains Using InSAR Persistent Scatterers[J]. Geophysical Research Letters, 2004, 31(23):L23611.
[5] KAMPES B M.Radar Interferometry:Persistent Scatterer Technique[M]. Netherlands:Springer, 2006.
[6] 李德仁, 廖明生, 王艳. 永久散射体雷达干涉测量技术[J]. 武汉大学学报(信息科学版), 2004, 29(8):664-668. LI Deren, LIAO Mingsheng, WANG Yan. Progress of Permanent Scatterer Interferometry[J]. Geomatics and Information Science of Wuhan University, 2004, 29(8):664-668.
[7] BERARDINO R, FORNARO G, LANARI R, et al. A New Algorithm for Surface Deformation Monitoring Based on Small Baseline Differential SAR Interferograms[J]. IEEE Transactions on Geoscience and Remote Sensing, 2002, 40(11):2375-2383.
[8] 邓琳, 刘国祥, 张瑞, 等. 多平台MC-SBAS长时序建模与形变提取方法[J]. 测绘学报, 2016, 45(2):213-223. DOI:10.11947/j.AGCS.2016.20140614. DENG Lin, LIU Guoxiang, ZHANG Rui, et al. A Multi-platform MC-SBAS Method for Extracting Long Gterm Ground Deformation[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(2):213-223. DOI:10.11947/j.AGCS.2016.20140614.
[9] 许文斌, 李志伟, 丁晓利, 等. 利用InSAR短基线技术估计洛杉矶地区的地表时序形变和含水层参数[J]. 地球物理学报, 2012, 55(2):452-461. XU Wenbin, LI Zhiwei, DING Xiaoli, et al. Application of Small Baseline Subsets D-InSAR Technology to Estimate the Time Series Land Deformation and Aquifer Storage Coefficients of Los Angeles Area[J]. Chinese Journal of Geophysics, 2012, 55(2):452-461.
[10] PERISSIN D, WANG Teng. Repeat-pass SAR Interferometry with Partially Coherent Targets[J]. IEEE Transactions on Geoscience and Remote Sensing, 2012, 50(1):271-280.
[11] 张永红, 龚文瑜, 张继贤, 等. 基于SAR干涉点目标分析技术的城市地表形变监测[J]. 测绘学报, 2009, 38(6):482-487. DOI:10.3321/j.issn:1001-1595.2009.06.003. ZHANG Yonghong, GONG Wenyu, ZHANG Jixian, et al. Monitoring Urban Subsidence Based on SAR Interferometric Point Target Analysis[J].Acta Geodaetica et Cartographica Sinica, 2009, 38(6):482-487. DOI:10.3321/j.issn:1001-1595.2009.06.003.
[12] 王明洲, 李陶, 江利明, 等. 地表形变监测的改进相干目标法[J]. 测绘学报, 2016, 45(1):36-43. DOI:10.11947/j.AGCS.2016.20140617. WANG Mingzhou, LI Tao, JIANG Liming, et al. An Improved Coherent Targets Technology for Monitoring Surface Deformation[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(1):36-43. DOI:10.11947/j.AGCS.2016.20140617.
[13] HOOPER A. A Multi-temporal InSAR Method Incorporating Both Persistent Scatterer and Small Baseline Approaches[J]. Geophysical Research Letters, 2008, 35(16):L16302.
[14] HETLAND E A, MUSÉ P, SIMONS M, et al. Multiscale InSAR Time Series(MinTS) Analysis of Surface Deformation[J]. Journal of Geophysical Research:Solid Earth, 2012, 117(B2):B02404.
[15] LOMBARDINI F.Differential Tomography:A New Framework for SAR Interferometry[J]. IEEE Transactions on Geoscience and Remote Sensing, 2005, 43(1):37-44.
[16] SERAFINO F, SOLDOVIERI F,LOMBARDINI F, et al. Singular Value Decomposition Applied to 4D SAR Imaging[C]//Proceedings of International Geoscience and Remote Sensing Symposium. Seoul, Korea:IEEE, 2005:2701-2704.
[17] 任笑真, 杨汝良. 一种基于逆问题的差分干涉SAR层析成像方法[J]. 电子与信息学报, 2010, 32(3):582-586. REN Xiaozhen, YANG Ruliang. An Inverse Problem Based Approach for Differential SAR Tomography Imaging[J]. Journal of Electronics & Information Technology, 2010, 32(3):582-586.
[18] 孙希龙, 余安喜, 董臻, 等. 一种差分SAR层析高分辨成像方法[J]. 电子与信息学报, 2012, 34(2):273-278. SUN Xilong, YU Anxi, DONG Zhen, et al. A High Resolution Imaging Method for Differential SAR Tomography[J]. Journal of Electronics & Information Technology, 2012, 34(2):273-278.
[19] ZHU Xiaoxiang,BAMLER R. Superresolving SAR Tomography for Multidimensional Imaging of Urban Areas:Compressive Sensing-based TomoSAR Inversion[J]. IEEE Signal Processing Magazine, 2014, 31(4):51-58.
[20] WANG Yuanyuan, ZHU Xiaoxiang, BAMLER R. An Efficient Tomographic Inversion Approach for Urban Mapping Using Meter Resolution SAR Image Stacks[J]. IEEE Geoscience and Remote Sensing Letters, 2014, 11(7):1250-1254.
[21] 廖明生, 魏恋欢, 汪紫芸, 等. 压缩感知在城区高分辨率SAR层析成像中的应用[J]. 雷达学报, 2015, 4(2):123-129. LIAO Mingsheng, WEI Lianhuan, WANG Ziyun, et al. Compressive Sensing in High-resolution 3D SAR Tomography of Urban Scenarios[J]. Journal of Radars, 2015, 4(2):123-129.
[22] SIDDIQUE M A, HAJNSEK I, AERSOSPACE G, et al. Investigating the Combined Use of Differential SAR Tomography and PSI for Spatio-temporal Inversion[C]//Proceedings of 2015 Joint Urban Remote Sensing Event(JURSE). Lausanne, Switzerland:IEEE, 2015:1-4.
[23] DONOHO D L. Compressed Sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4):1289-1306.
[24] ZHU Xiaoxiang,BAMLER R. Super-resolution Power and Robustness of Compressive Sensing for Spectral Estimation with Application to Spaceborne Tomographic SAR[J]. IEEE Transactions on Geoscience and Remote Sensing, 2012, 50(1):247-258.
[25] 张冰尘, 王万影, 毕辉, 等. 基于压缩多信号分类算法的森林区域极化SAR层析成像[J]. 电子与信息学报, 2015, 37(3):625-630. ZHANG Bingchen, WANG Wanying, BI Hui, et al. Polarimetric SAR Tomography for Forested Areas Based on Compressive Multiple Signal Classification[J]. Journal of Electronics & Information Technology, 2015, 37(3):625-630.
[26] 王爱春, 向茂生. 基于块压缩感知的SAR层析成像方法[J]. 雷达学报, 2016, 5(1):57-64. WANG Aichun, XIANG Maosheng. SAR Tomography Based on Block Compressive Sensing[J]. Journal of Radars, 2016, 5(1):57-64.
[27] ELDAR Y C,KUPPINGER P,BOLCSKEI H.Block-sparse Signals:Uncertainty Relations and Efficient Recovery[J]. IEEE Transactions on Signal Processing, 2010, 58(6):3042-3054.
[28] FU Yuli, LI Haifeng, ZHANG Qiheng, et al. Block-sparse Recovery via Redundant Block OMP[J]. Signal Processing, 2014, 97:162-171.
