Two-Dimensional l1-Norm Minimization in SAR Image Reconstriction

Lazarov, A.; Minchev, D.

doi:10.1515/cait-2015-0091

Abstract

A nonconventional image algorithm, based on compressed sensing and l₁-norm minimization in Synthetic Aperture Radar (SAR) application is discussed. A discrete model of the earth surface relief and mathematical modeling of SAR signal formation are analytically described. Sparse decomposition in Fourier basis to solve the SAR image reconstruction problem is discussed. In contrast to the classical one-dimensional definition of l₁-norm minimization in SAR image reconstruction, applied to an image vector, the present work proposes a two-dimensional definition of l₁-norm minimization to the image. To verify the correctness of the algorithm, results of numerical experiments are presented.

References

1. Nicolas, J.-M., G. Vasile, M. Gay, F. Tupin, Em. Trouvé. SAR Processing in the Temporal Domain: Application to Direct Interferogram Generation and Mountain Glacier Monitoring Can. – J. Remote Sensing, Vol. 33, 2007, No 1, pp. 52-59.10.5589/m07-005
Search in Google Scholar
2. Leijen, V., F. R. Hanssen. Interferometric Radar Meteorology: Resolving the Acquisition Ambiguity. – In: CEOS SAR Workshop, Ulm Germany, 27-28 May 2004, pp. 6-14.
Search in Google Scholar
3. Colesanti, C., A. Ferretti, F. Novali, C. Prati, F. Rocca. SAR Monitoring of Progressive and Seasonal Ground Deformation Using the Permanent Scatterers Technique. – IEEE Transactions on Geoscience and Remote Sensing, Vol. 41, July 2003, No 7, pp. 1685-1701.10.1109/TGRS.2003.813278
Search in Google Scholar
4. Figueiredo, M. A. T., R. D. Nowak, S. J. Wright. Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems. – IEEE Journal of Selected Topics in Signal Processing, Vol. 1, December 2007, No 4, pp. 586-597.10.1109/JSTSP.2007.910281
Search in Google Scholar
5. Tropp, J. Just Relax: Convex Programming Methods for Identifying Sparse Signals. – IEEE Transactions on Information Theory, Vol. 51, 2006, pp. 1030-1051.10.1109/TIT.2005.864420
Search in Google Scholar
6. Kim, S.-J., K. Koh, M. Lustig, S. Boyd, D. Gorinevsky. An Interior-Point Method for Large-Scale l₁-Regularized Least Squares. – IEEE Journal of Selected Topics in Signal Processing, Vol. 1, 4 December 2007, pp. 606-617.10.1109/JSTSP.2007.910971
Search in Google Scholar
7. Donaho, D. L. Compressed Sensing. – IEEE Trans. on Inf. Theory, Vol. 52, 2006, No 4, pp.1289-1306.10.1109/TIT.2006.871582
Search in Google Scholar
8. Hayashi, K., M. Nagahara, T. Tanaka. A User’s Guide to Compressed Sensing for Communication Systems. – IEICE Trans. on Communications, Vol. E96-B, March 2013, No 3, pp. 685-712.10.1587/transcom.E96.B.685
Search in Google Scholar
9. Gurbuza, A. C., J. H. McClellanb, W. R. Scott, B. Jr. Compressive Sensing for Subsurface Imaging Using Ground Penetrating Radar. – Signal Processing, Vol. 89, October 2009, No 10, pp. 1959-1972.10.1016/j.sigpro.2009.03.030
Search in Google Scholar
10. Cai, J.-L., C.-M. Tong, W.-J. Zhong, W.-J. Ji. 3D Imaging Method for Stepped Frequency Ground Penetrating Radar Based on Compressive Sensing. – Progress in Electromagnetics Research M, Vol. 23, 2012, pp. 153-165.10.2528/PIERM11121206
Search in Google Scholar
11. McClellan, C. J. H., W. R. Scott. A Compressive Sensing Data Acquisition and Imaging Method for Stepped-Frequency GPRs. – IEEE Transation on Signal Processing, Vol. 57, July 2009, No 7, pp. 2640-2650.10.1109/TSP.2009.2016270
Search in Google Scholar
12. Shastry, M. C., R. M. Narayanan, M. Rangaswamy. Analysis of the Tolerance of Compressive Noise Radar Systems to Multiplicative Perturbations. – In: Proc. of SPIE’9109, Compressive Sensing III, 910905, 23 May 2014.10.1117/12.2053116
Search in Google Scholar
13. Lin, Y. G., B. C. Zhang, W. Hong, Y. R. Wu. Along-Track Interferometric SAR Imaging Based on Distributed Compressed Sensing. – Electronics Letters, Vol. 46, 10 June 2010, No 12, p. 858-860.10.1049/el.2010.0710
Search in Google Scholar
14. Yang, J., J. Thompson, X. Huang, T. Jin. Random-Frequency SAR Imaging Based on Compressed Sensing. – IEEE Trans. on Geoscience and Remote Sensing, Vol. 51, February 2013, No 2, pp. 983-994.10.1109/TGRS.2012.2204891
Search in Google Scholar
15. Li, J., S. Zhang, J. Chang. Applications of Compressed Sensing for Multiple Transmitters Multiple Azimuth Beams SAR Imaging. – Progress in Electromagnetics Research, Vol. 127, 2012, pp. 259-275.10.2528/PIER12021307
Search in Google Scholar
16. Wei, S.-J., X.-L. Zhang, J. Shi. Linear Array SAR Imaging Via Compressed Sensing. – Progress in Electromagnetics Research, Vol. 117, 2011, pp. 299-319.10.2528/PIER11033105
Search in Google Scholar
17. Wei, S.-J., X.-L. Zhang, J. Shi, G. Xiang. Sparse Reconstruction for SAR Imaging Based on Compressed Sensing. – Progress in Electromagnetics Research, Vol. 109, 2010, pp. 63-81.10.2528/PIER10080805
Search in Google Scholar
18. Qiu, W., E. Giusti, A. Bacci, M. Martorella, F. Berizzi et al. Compressive Sensing for Passive ISAR with DVB-T Signal. – In: Proc. of IRS-2013, 19-21 June 2013, pp. 113-118.
Search in Google Scholar
19. Kim, S., K. Koh, M. Lustig, S. Boyd, D. Gorinvesky. A Method for Large-Scale ℓ₁-Regularized Least Squares Problems with Applications in Signal Processing and Statistics. Tech. Report, Dept. of Electrical Engineering, Stanford University, 2007. www.stanford.edu/~boyd/l1_ls.html10.1109/JSTSP.2007.910971
Search in Google Scholar

Two-Dimensional l1-Norm Minimization in SAR Image Reconstriction

Abstract

Paradigm

My account