Synthetic Aperture Imaging and Motion Estimation Using Tensor Methods

We consider a synthetic aperture imaging configuration, such as synthetic aperture radar (SAR), where we want to first separate reflections from moving targets from those coming from a stationary background, and then to image separately the moving and the stationary reflectors. For this purpose, we introduce a representation of the data as a third order tensor formed from data coming from partially overlapping sub-apertures. We then apply a tensor robust principal component analysis (TRPCA) to the tensor data which separates them into the parts coming from the stationary and moving reflectors. Images are formed with the separated data sets. Our analysis shows a distinctly improved performance of TRPCA, compared to the usual matrix case. In particular, the tensor decomposition can identify motion features that are undetectable when using the conventional motion estimation methods, including matrix RPCA. We illustrate the performance of the method with numerical simulations in the X-band radar regime.

[1]  Namrata Vaswani,et al.  Video denoising via online sparse and low-rank matrix decomposition , 2016, 2016 IEEE Statistical Signal Processing Workshop (SSP).

[2]  Christopher J. Hillar,et al.  Most Tensor Problems Are NP-Hard , 2009, JACM.

[3]  Tamir Hazan,et al.  Non-negative tensor factorization with applications to statistics and computer vision , 2005, ICML.

[4]  Zhening Li,et al.  Bounds on the Spectral Norm and the Nuclear Norm of a Tensor Based on Tensor Partitions , 2016, SIAM J. Matrix Anal. Appl..

[5]  George Papanicolaou,et al.  Low Rank Plus Sparse Decomposition of Synthetic Aperture Radar Data for Target Imaging , 2019, IEEE Transactions on Computational Imaging.

[6]  Wei Liu,et al.  Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization , 2016, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[7]  Tamara G. Kolda,et al.  Tensor Decompositions and Applications , 2009, SIAM Rev..

[8]  Jon Rigelsford,et al.  Introduction to Airborne Radar, 2nd ed. , 2002 .

[9]  J. Fienup.  Detecting moving targets in SAR imagery by focusing , 2001 .

[10]  Müjdat Çetin,et al.  SAR imaging of moving targets by subaperture based low-rank and sparse decomposition , 2017, 2017 25th Signal Processing and Communications Applications Conference (SIU).

[11]  Fei Li,et al.  Ground Moving Target Extraction in a Multichannel Wide-Area Surveillance SAR/GMTI System via the Relaxed PCP , 2013, IEEE Geoscience and Remote Sensing Letters.

[12]  Xiang-Gen Xia,et al.  Dual-speed SAR imaging of moving targets , 2006, IEEE Transactions on Aerospace and Electronic Systems.

[13]  Aswin C. Sankaranarayanan,et al.  SpaRCS: Recovering low-rank and sparse matrices from compressive measurements , 2011, NIPS.

[14]  Philippe Forster,et al.  Low Rank Tensor STAP filter based on multilinear SVD , 2012, 2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop (SAM).

[15]  Joos Vandewalle,et al.  A Multilinear Singular Value Decomposition , 2000, SIAM J. Matrix Anal. Appl..

[16]  M. McCarthy,et al.  Tensor decomposition for multi-tissue gene expression experiments , 2016, Nature Genetics.

[17]  M. Kilmer,et al.  Factorization strategies for third-order tensors , 2011 .

[18]  I. Hajnsek,et al.  A tutorial on synthetic aperture radar , 2013, IEEE Geoscience and Remote Sensing Magazine.

[19]  Shmuel Friedland,et al.  Nuclear norm of higher-order tensors , 2014, Math. Comput..

[20]  Majid Moradikia,et al.  Joint SAR Imaging and Multi-Feature Decomposition From 2-D Under-Sampled Data Via Low-Rankness Plus Sparsity Priors , 2019, IEEE Transactions on Computational Imaging.

[21]  G. Sapiro,et al.  A collaborative framework for 3D alignment and classification of heterogeneous subvolumes in cryo-electron tomography. , 2013, Journal of structural biology.

[22]  E. Davidson,et al.  Strategies for analyzing data from video fluorometric monitoring of liquid chromatographic effluents , 1981 .

[23]  Gang Li,et al.  Moving target location and imaging using dual-speed velocity SAR , 2006, 2006 IEEE Antennas and Propagation Society International Symposium.

[24]  Andrzej Cichocki,et al.  Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis , 2014, IEEE Signal Processing Magazine.

[25]  Anna Scaglione,et al.  Autofocusing of SAR images based on the product high-order ambiguity function , 1998 .

[26]  Karen S. Braman.  Third-Order Tensors as Linear Operators on a Space of Matrices , 2010 .

[27]  Eric Jondeau,et al.  Moment Component Analysis: An Illustration With International Stock Markets , 2015 .

[28]  Yi Ma,et al.  Robust principal component analysis? , 2009, JACM.

[29]  Kang-Yu Ni,et al.  SAR moving target imaging using sparse and low-rank decomposition , 2014, Defense + Security Symposium.

[30]  Yi Ma,et al.  The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices , 2010, Journal of structural biology.

[31]  L. Tucker,et al.  Some mathematical notes on three-mode factor analysis , 1966, Psychometrika.

[32]  George W. Stimson,et al.  Introduction to Airborne Radar , 1983 .

[33]  Liliana Borcea,et al.  Motion Estimation and Imaging of Complex Scenes with Synthetic Aperture Radar , 2012, ArXiv.

[34]  Misha Elena Kilmer,et al.  Novel Methods for Multilinear Data Completion and De-noising Based on Tensor-SVD , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[35]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

[36]  Liliana Borcea,et al.  Synthetic Aperture Radar Imaging and Motion Estimation via Robust Principal Component Analysis , 2013, SIAM J. Imaging Sci..

[37]  Charles Edward Muehe,et al.  Displaced-Phase-Center Antenna Technique , 2000 .

[38]  Xiaodong Li,et al.  Stable Principal Component Pursuit , 2010, 2010 IEEE International Symposium on Information Theory.

[39]  Misha Elena Kilmer,et al.  Third-Order Tensors as Operators on Matrices: A Theoretical and Computational Framework with Applications in Imaging , 2013, SIAM J. Matrix Anal. Appl..

[40]  Mujdat Cetin,et al.  Low-rank sparse matrix decomposition for sparsity-driven SAR image reconstruction , 2014, 2015 3rd International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing (CoSeRa).