介绍一种基于广义最小最大凹（generalized minimax concave，GMC）惩罚项的ISAR稀疏成像方法。该方法的惩罚项形式与L1范数最小化方法不同，不仅使最小二乘损失函数凸性最小，而且避免了L1范数最小化方法系统性幅值低估问题。通过仿真实验说明GMC算法在ISAR成像中的幅度保持特性。利用Yak-42飞机的实际数据进行ISAR成像，结果表明GMC算法在成像精度方面优势明显，具有更好的成像效果。
A sparse imaging algorithm of ISAR based on generalized minimax concave (GMC) penalty is deseribed in this paper. The penalty of the algorithm is different from that of the L1 norm regularization. The penalty function not only maintains the convexity of the least squares cost function to be minimized but also avoids the systematic underestimation characteristic of the L1 norm regularization. This work illustrates the amplitude preservation characteristics of GMC algorithm in ISAR imaging by simulation experiments and imaging results of real data of Yak-42 aircraft. The results show that GMC algorithm has obvious advantages in imaging accuracy and has better imaging effect.
[1] Özdemir. Inverse synthetic aperture radar imaging with MATLAB algorithms[M]. Hoboken:Wiley, 2012.
[2] 吴一戎, 洪文, 张冰尘, 等. 稀疏微波成像研究进展(科普类)[J]. 雷达学报, 2014, 3(4):383-395.
[3] Donoho D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4):1289-1306.
[4] Candes E J, Romberg J, Tao T. Robust uncertainty principles:exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2):489-509.
[5] Zhang B C, Hong W, Wu Y R. Sparse microwave imaging:principles and applications[J]. Science China Information Sciences, 2012, 55(8):1722-1754.
[6] 许学杰, 潘志刚, 刘畅. 基于压缩感知的SAR图像压缩算法[J]. 中国科学院大学学报, 2015, 32(6):790-796.
[7] Wright S J, Nowak R D, Figueiredo M A T. Sparse reconstruction by separable approximation[J]. IEEE Transactions on Signal Processing, 2009, 57(7):2479-2493.
[8] Quan X Y, Guo B, Lu Y, et al. Comparison of several sparse reconstruction algorithms in SAR imaging[C]//IET International Radar Conference 2015. Hangzhou:IET, 2015:1-5.
[9] Selesnick I. Sparse regularization via convex analysis[J]. IEEE Transactions on Signal Processing, 2017, 65(17):4481-4494.
[10] Bauschke H H, Combettes P L. Convex analysis and monotone operator theory in Hilbert spaces[M]. New York:Springer New York, 2011.
[11] Bi H, Zhang B C, Wang Z D, et al. L q, regularisation-based synthetic aperture radar image feature enhancement via iterative thresholding algorithm[J]. Electronics Letters, 2016, 52(15):1336-1338.
[12] Xu Z B, Zhang H, Wang Y, et al. L1/2 regularization[J]. Science China:Information Sciences, 2010, 53(6):1159-1169.
[13] Needell D, Vershynin R. Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit[J]. IEEE Journal of Selected Topics in Signal Processing, 2010, 4(2):310-316.
[14] Quan X Y, Zhang B C, Liu J G, et al. An efficient general algorithm for SAR imaging:complex approximate message passing combined with backprojection[J]. IEEE Geoscience & Remote Sensing Letters, 2016, 13(4):535-539.
[15] Daubechies I, Defrise M, Mol C D. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint[J]. Communications on Pure & Applied Mathematics, 2003, 57(11):1413-1457.
[16] Bredies K, Lorenz D A. Linear convergence of iterative soft-thresholding[J]. Journal of Fourier Analysis & Applications, 2008, 14(5/6):813-837.
[17] Zhang C H. Nearly unbiased variable selection under minimax concave penalty[J]. Annals of Statistics, 2010, 38(2):894-942.
