DEM Estimation for LASAR Based on Variational Model

This paper discusses the digital elevation model (DEM) estimation problem for the linear array synthetic aperture radar based on the variational model. Compared with the sparse recovery model, the one-to-one mapping between the horizontal grid nodes and the elevations is preserved explicitly, which is important for the topographic surveying and mapping mission. During the research, we find that since the mean square error criterion is insensitive to the amount of the elevation offsets, the numerical method by solving the Euler-Lagrange equation is unreliable and the global optimization method is necessary to solve the variational problem. With the ambiguity function localization and the sliding-window architecture, the global optimal path can be obtained by solving a series of local optimization problems provided that the observation matrix is row full rank. Furthermore, the local optimization problem can be relaxed as a sparse recovery problem and can be solved by a modified orthogonal matching pursuit (OMP) method (named as Var-OMP), whose computational cost is acceptable for the actual data processing. By a series of numerical experiments, we show that the performance of Var-OMP is influenced by both the resolution enhancement factor (L) and the signal-to-noise ratio (SNR). The larger the SNR is, the better the performance is; the smaller L is, the more stable and faster the Var-OMP algorithm is. Compared with the sparse recovery methods, the variational model and the Var-OMP algorithm are more suitable for the DEM estimation application in the face of all kinds of terrains.

[1]  Michael Elad,et al.  From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images , 2009, SIAM Rev..

[2]  Gilda Schirinzi,et al.  Three-Dimensional SAR Focusing From Multipass Signals Using Compressive Sampling , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[3]  Matthias Weiss,et al.  Initial ARTINO Radar Experiments , 2010 .

[4]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[5]  Richard Bamler,et al.  Demonstration of Super-Resolution for Tomographic SAR Imaging in Urban Environment , 2012, IEEE Transactions on Geoscience and Remote Sensing.

[6]  Gangyao Kuang,et al.  Truncated SVD-Based Compressive Sensing for Downward-Looking Three-Dimensional SAR Imaging With Uniform/Nonuniform Linear Array , 2015, IEEE Geoscience and Remote Sensing Letters.

[7]  Xiaoxiang Zhu,et al.  Robust Reconstruction of Building Facades for Large Areas Using Spaceborne TomoSAR Point Clouds , 2015, IEEE Transactions on Geoscience and Remote Sensing.

[8]  Richard Bamler,et al.  An Efficient Tomographic Inversion Approach for Urban Mapping Using Meter Resolution SAR Image Stacks , 2014, IEEE Geoscience and Remote Sensing Letters.

[9]  Alberto Moreira,et al.  Polarimetric 3-D Reconstruction From Multicircular SAR at P-Band , 2012, IEEE Geoscience and Remote Sensing Letters.

[10]  Jianyu Yang,et al.  APC Trajectory Design for "One-Active" Linear-Array Three-Dimensional Imaging SAR , 2010, IEEE Trans. Geosci. Remote. Sens..

[11]  Richard Bamler,et al.  Tomographic SAR Inversion by $L_{1}$ -Norm Regularization—The Compressive Sensing Approach , 2010, IEEE Transactions on Geoscience and Remote Sensing.

[12]  Emre Ertin,et al.  Sparse Signal Methods for 3-D Radar Imaging , 2011, IEEE Journal of Selected Topics in Signal Processing.

[13]  Michael Elad,et al.  Stable recovery of sparse overcomplete representations in the presence of noise , 2006, IEEE Transactions on Information Theory.

[14]  Davide Giudici,et al.  Generation and Calibration of High-Resolution DEM From Single-Baseline Spaceborne Interferometry: The “Split-Swath” Approach , 2014, IEEE Transactions on Geoscience and Remote Sensing.

[15]  Informationstechnik Berlin,et al.  Exact and Approximate Sparse Solutions of Underdetermined Linear Equations , 2007 .

[16]  Deanna Needell,et al.  CoSaMP: Iterative signal recovery from incomplete and inaccurate samples , 2008, ArXiv.

[17]  R. O. Schmidt,et al.  Multiple emitter location and signal Parameter estimation , 1986 .

[18]  R. Sundaram.  A First Course in Optimization Theory: Optimization in ℝ n , 1996 .

[19]  M. Weib,et al.  A 3D imaging radar for small unmanned airplanes - ARTINO , 2005, European Radar Conference, 2005. EURAD 2005..

[20]  Richard Bamler,et al.  Very High Resolution Spaceborne SAR Tomography in Urban Environment , 2010, IEEE Transactions on Geoscience and Remote Sensing.

[21]  Alexander G. Yarovoy,et al.  A Sparse Aperture MIMO-SAR-Based UWB Imaging System for Concealed Weapon Detection , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[22]  S. Rosset,et al.  Piecewise linear regularized solution paths , 2007, 0708.2197.

[23]  Xiaoling Zhang,et al.  Signal Processing for Microwave Array Imaging: TDC and Sparse Recovery , 2012, IEEE Transactions on Geoscience and Remote Sensing.

[24]  Xiaoling Zhang,et al.  Linear Array SAR Imaging via Compressed Sensing , 2011 .

[25]  Vijay K. Madisetti,et al.  The Digital Signal Processing Handbook , 1997 .

[26]  Yanping Wang,et al.  Polar Format Imaging Algorithm With Wave-Front Curvature Phase Error Compensation for Airborne DLSLA Three-Dimensional SAR , 2014, IEEE Geoscience and Remote Sensing Letters.

[27]  Hui Lin,et al.  On the Performance of Reweighted $L_{1}$ Minimization for Tomographic SAR Imaging , 2015, IEEE Geoscience and Remote Sensing Letters.

[28]  A. Brenner,et al.  ARTINO: A New High Resolution 3D Imaging Radar System on an Autonomous Airborne Platform , 2006, 2006 IEEE International Symposium on Geoscience and Remote Sensing.

[29]  R. Tibshirani,et al.  Least angle regression , 2004, math/0406456.

[30]  Nikola S. Subotic,et al.  Compressive sensing and 3-D radar imaging , 2012, 2012 IEEE Statistical Signal Processing Workshop (SSP).

[31]  Gangyao Kuang,et al.  Imaging of Downward-Looking Linear Array Three-Dimensional SAR Based on FFT-MUSIC , 2015, IEEE Geoscience and Remote Sensing Letters.

[32]  Yi Su,et al.  An ISAR Imaging Method Based on MIMO Technique , 2010, IEEE Transactions on Geoscience and Remote Sensing.

[33]  Shunjun Wei,et al.  SPARSE RECONSTRUCTION FOR SAR IMAGING BASED ON COMPRESSED SENSING , 2010 .

[34]  Gang Li,et al.  Bistatic Linear Antenna Array SAR for Moving Target Detection, Location, and Imaging With Two Passive Airborne Radars , 2007, IEEE Transactions on Geoscience and Remote Sensing.

[35]  Shun-Jun Wei,et al.  Sparse Autofocus Recovery for Under-Sampled Linear Array SAR 3-D Imaging , 2013 .

[36]  Xiaoxiang Zhu,et al.  Facade Reconstruction Using Multiview Spaceborne TomoSAR Point Clouds , 2014, IEEE Transactions on Geoscience and Remote Sensing.

[37]  Xiaoling Zhang,et al.  Sparse Array Microwave 3-D Imaging: Compressed Sensing Recovery and Experimental Study , 2013 .

[38]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[39]  Daniel Liberzon,et al.  Calculus of Variations and Optimal Control Theory: A Concise Introduction , 2012 .

[40]  W. Kummer,et al.  Basic array theory , 1992, Proc. IEEE.

[41]  Wang Yanping,et al.  Efficient Pseudopolar Format Algorithm for Down-Looking Linear-Array SAR 3-D Imaging , 2015 .