Robust Computational Methods for Smoothed L0 Approximation

Wang Feng; Xiang Xin; Yi Ke-chu; Xiong Lei

doi:10.11999/JEIT141590

Volume 37 Issue 10

Sep. 2015

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Wang Feng, Xiang Xin, Yi Ke-chu, Xiong Lei. Robust Computational Methods for Smoothed L0 Approximation[J]. Journal of Electronics & Information Technology, 2015, 37(10): 2377-2382. doi: 10.11999/JEIT141590

Citation:

Wang Feng, Xiang Xin, Yi Ke-chu, Xiong Lei. Robust Computational Methods for Smoothed L0 Approximation[J]. Journal of Electronics & Information Technology, 2015, 37(10): 2377-2382. doi: 10.11999/JEIT141590

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Robust Computational Methods for Smoothed L0 Approximation

doi: 10.11999/JEIT141590

1.
2.
(State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an 710071, China)

Funds:

The National Natural Science Foundation of China (61379104)

Received Date: 2014-12-11
Rev Recd Date: 2015-06-03
Publish Date: 2015-10-19

Abstract

Abstract

Computational framework using surrogate functions and prior probability density functions, for smoothed L0 minimization approximation is studied in this paper, for the purpose of improving the recovery performance of non-convex compressed sensing. Firstly, a simple parameter adjusting strategy and modified SL0 and FOCUSS are presented, based on the convex-concave property analysis of approximation functions. Secondly, since L0 approximation problem can be viewed as a L0-Regularized Least Squares problem in noisy setting，a new computational framework called IRSL0 (Iteratively Reweighted SL0) is derived from the Newton direction, furthermore, a new surrogate function is also given. Finally, extensive numerical simulations demonstrate the robustness and applicability of the new theory and algorithms.
- Non-convex compressed sensing,
- Smoothed L0 approximation,
- Iteratively reweighted algorithms

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References(25)

References

Cands E J and Wakin M B. An introduction to compressive sampling[J]. IEEE Signal Processing Magazine, 2008, 25(2): 21-30.

Mohimani H, Zadeh M, and Jutten C. A fast approach for overcomplete sparse decomposition based on smoothed L0 norm[J]. IEEE Transactions on Signal Processing, 2009, 57(1): 289-301.

Hyder M M and Mahata K. An improved smoothed L0 approximation algorithm for sparse representation[J]. IEEE Transactions on Signal Processing, 2010, 58(4): 2194-2205.

Lv J, Huang L, Shi Y, et al.. Inverse synthetic aperture radar imaging via modified smoothed L0 norm[J]. IEEE Antennas and Wireless Propagation Letters, 2014, 13(7): 1235-1238.

Liu Z, You P, Wei X, et al.. Dynamic ISAR imaging of maneuvering targets based on sequential SL0[J]. IEEE Geoscience and Remote Sensing Letters, 2013, 10(5): 1041-1045.

Guo L and Wen X. SAR image compression and reconstruction based on compressed sensing[J]. Journal of Information Computational Science, 2014, 11(2): 573-579.

Liu Z, Wei X, and Li X. Aliasing-free micro-Doppler analysis based on short-time compressed sensing[J]. IET Signal Processing, 2013, 8(2): 176-187.

Liu T and Zhou J. Improved smoothed L0 reconstruction algorithm for ISI sparse channel estimation[J]. The Journal of China Universities of Posts and Telecommunications, 2014, 21(2): 40-47.

Ye X and Zhu W. Sparse channel estimation of pulse-shaping multiple-input-multiple-output orthogonal frequency division multiplexing systems with an approximate gradient L2-SL0 reconstruction algorithm[J]. IET Communications, 2014, 8(7): 1124-1131.

王军华, 黄知涛, 周一宇, 等. 基于近似L0 范数的稳健稀疏重构算法[J]. 电子学报, 2012, 40(6): 1185-1189.

Wang Jun-hua, Huang Zhi-tao, Zhou Yi-yu, et al.. Robust sparse recovery based on approximate L0 norm[J]. Acta Electronica Sinica, 2012, 40(6): 1185-1189.

赵瑞珍, 林婉娟, 李浩, 等. 基于光滑L0范数和修正牛顿法的压缩感知重建算法[J]. 计算机辅助设计与图形学学报, 2012, 24(4): 478-484.

Zhao Rui-zhen, Lin Wan-juan, Li Hao, et al.. Reconstruction algorithm for compressive sensing based on smoothed L0 norm and revised newton method[J]. Journal of Computer- Aided Design Computer Graphic, 2012, 24(4): 478-484.

杨良龙, 赵生妹, 郑宝玉, 等. 基于SL0 压缩感知信号重建的改进算法[J]. 信号处理, 2012, 28(6): 834-841.

Yang Liang-long, Zhao Sheng-mei, Zheng Bao-yu, et al.. The improved reconstruction algorithm for compressive sensing on SL0[J]. Signal Processing, 2012, 28(6): 834-841.

余付平, 沈堤. 基于拟牛顿方向的改进平滑L0 算法[J]. 计算机工程与应用, 2013, 49(22): 215-218.

Yu Fu-ping and Shen Di. Improved smoothed L0 approximation algorithm based on Quasi-Newton direction[J]. Computer Engineering and Applications, 2013, 49(22): 215-218.

贺亚鹏, 庄珊娜, 张燕洪, 等. 一种基于交叉验证的稳健SL0目标参数提取算法[J]. 系统工程与电子技术, 2012, 34(1): 64-68.

He Ya-peng, Zhuang Shan-na, Zhang Yan-hong, et al.. Cross validation based robust-SL0 algorithm for target parameter extraction[J]. Systems Engineering and Electronics, 2012, 34(1): 64-68.

邱伟, 赵宏钟, 陈建军, 等. 基于平滑L0 范数的高分辨雷达一维成像研究[J]. 电子与信息学报, 2011, 33(12): 2869-2874.

Qiu Wei, Zhao Hong-zhong, Chen Jian-jun, et al.. High- resolution radar one-dimensional imaging based on smoothed L0 norm[J]. Journal of Electronics Information Technology, 2011, 33(12): 2869-2874.

Gorodnitsky I F and Rao B D. Sparse signal reconstruction from limited data using FOCUSS: a reweighted minimum norm algorithm[J]. IEEE Transactions on Signal Processing, 1997, 45(3): 600-616.

Pant J K, Lu W, and Antoniou A. New improved algorithms for compressive sensing based on Lp norm[J]. IEEE Transactions on Circuits and Systems-II: Express Briefs, 2014, 61(3): 198-202.

Yuille A L and Rangarajan A. The concave-convex procedure [J]. Neural Computer, 2003, 15(4): 915-936.

Rao B D, Engan K, Cotter S F, et al.. Subset selection in noise based on diversity measure minimization[J]. IEEE Transactions on Signal Processing, 2003, 51(3): 760-770.

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