Reconstruction of Compressive Sensing-based SAR Imaging Using Nesterov’s Algorithm

Synthetic Aperture Radar (SAR) is a 2-D imaging technique. In this technique, to reconstruct high resolution images, wide bandwidth transmission signal and short length antenna are required and leading large data storage, high speed A/D converter (ADC) and short swath. To improve these drawbacks, using a recent developed theory known as compressive sensing (CS), it is possible to reconstruct high resolution image using undersampled data. This paper presents a new reconstruction algorithm based on Nesterov’s algorithm. The simulation demonstrates promising results and indicates that the proposed algorithm has the advantage of high speed of convergence and accuracy. Keywords: Synthetic aperture radar; compressive sensing; 1l minimization; Nesterov’s algorithm References: Baraniuk, R., & Steeghs, P. (2007). Compressive Radar Imaging. Paper presented at the Radar Conference, 2007 IEEE. Beck, A., & Teboulle, M. (2009). A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems. SIAM Journal on Imaging Sciences, 2(1), 183-202. doi:doi:10.1137/080716542 Becker, S., Bobin, J., & Candes, E. (2011). NESTA: A Fast and Accurate First-Order Method for Sparse Recovery. SIAM Journal on Imaging Sciences, 4(1), 1-39. doi: 10.1137/090756855 Candes, E. J., & Tao, T. (2005). Decoding by linear programming. IEEE Transactions on Information Theory, 51(12), 4203-4215. doi:10.1109/TIT.2005.858979 Cumming, I. G., & Wong, F. H. (2005). Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation: Norwood, MA: Artech House. Elad, M. (2010). Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing: Springer Publishing Company, Incorporated. Eldar, Y. C., & Kutyniok, G. (2012). Compressed Sensing: Theory and Applications: Cambridge University Press. Figueiredo, M. A. T., Nowak, R. D., & Wright, S. J. (2007). Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems. IEEE Journal of Selected Topics in Signal Processing, 1(4), 586-597. doi:10.1109/jstsp.2007.910281 Jing, L., Shunsheng, Z., & Junfei, C. (2012). Two-dimensional random sparse sampling for high resolution SAR imaging based on compressed sensing. Paper presented at the Radar Conference (RADAR), 2012 IEEE. JunGang, Y., Thompson, J., Xiaotao, H., Tian, J., & Zhimin, Z. (2013). Segmented Reconstruction for Compressed Sensing SAR Imaging. Geoscience and Remote Sensing, IEEE Transactions on, 51(7), 4214-4225. doi:10.1109/tgrs.2012.2227060 Nesterov, Y. (1983). A method of solving a convex programming problem with convergence rate O (1/k2). Soviet Mathematics Doklady, 27(2), 372-376. Nesterov, Y. (2005). Smooth minimization of non-smooth functions. Mathematical Programming, 103(1), 127-152. doi:10.1007/s10107-004-0552-5 Patel, V. M., Easley, G. R., Healy, D. M., Jr., & Chellappa, R. (2010). Compressed Synthetic Aperture Radar. Selected Topics in Signal Processing, IEEE Journal, 4(2), 244-254. doi:10.1109/jstsp.2009.2039181 Tropp, J. A., & Gilbert, A. C. (2007). Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit. Information Theory, IEEE Transactions on, 53(12), 4655-4666. doi:10.1109/tit.2007.909108 van den Berg, E., & Friedlander, M. (2008). Probing the Pareto frontier for basis pursuit solutions. SIAM Journal on Scientific Computing, 31, 890-912. doi: 10.1137/080714488 Wang, B. C. (2008). Digital signal processing techniques and applications in radar image processing: John Wiley. Wei, S. J., Zhang, X. L., Shi, J., & Xiang, G. (2010). Sparse reconstruction for SAR imaging based on compressed sensing. Progress In Electromagnetics Research, 109, 63-81. Xu, J., Pi, Y., & Cao, Z. (2012). Bayesian compressive sensing in synthetic aperture radar imaging. Radar, Sonar & Navigation, IET, 6(1), 2-8. doi:10.1049/iet-rsn.2010.0375 Zyl, J. J. V. (2011). Synthetic Aperture Radar Polarimetry: Wiley.