CHEN Peng-qing, HUANG Wei. Block-Sparse Signal Recovery Based on l1-l2 Norm Minimization[J]. Applied Mathematics and Mechanics, 2017, 38(8): 932-942. doi: 10.21656/1000-0887.370230
 Citation: CHEN Peng-qing, HUANG Wei. Block-Sparse Signal Recovery Based on l1-l2 Norm Minimization[J]. Applied Mathematics and Mechanics, 2017, 38(8): 932-942.

Block-Sparse Signal Recovery Based on l1-l2 Norm Minimization

doi: 10.21656/1000-0887.370230
Funds:  The Major Research Plan of the National Natural Science Foundation of China(91538112);The National Science Fund for Young Scholars of China（11201450）
• Rev Recd Date: 2017-05-19
• Publish Date: 2017-08-15
• Compressed sensing (CS) is a newly developed theoretical framework for information acquisition and processing. Through the solution of non-linear optimization problems, sparse and compressible signals can be recovered from small-scale linear and non-adaptive measurements. Block-sparse signals as typical sparse ones exhibit additional block structures where the non-zero elements occur in blocks (or clusters). Based on the previous l1-2 norm minimization method given by YIN Peng-hang, LOU Yi-fei, HE Qi, et al. for common sparse signal recovery, the l1-l2 minimization recovery algorithm was extended to the block-sparse model, the properties of thel1-l2 norm were proved and the sufficient condition for block-sparse signal recovery was established. Meanwhile, an iterative method for block-sparsel1-l2 minimization was presented by means of the DCA (difference of convex functions algorithm) and the ADMM (alternating direction method of multipliers). The numerical simulation results demonstrate that the signal recovery success rate of the proposed algorithm is higher than those of the existing algorithms.
•  [1] Donoho D L. Compressed sensing[J]. IEEE Trans on Information Theory,2006,52(4):1289-1306. [2] Candès E, Wakin M. An introduction to compressive sampling[J].IEEE Signal Process Magazine,2008,25(2): 21-30. [3] Candès E, Romberg J, Tao T. Stable signal recovery from incomplete and inaccurate measurements[J]. Communications on Pure and Applied Mathematics,2006,59(8):1207-1223. [4] Lustig M, Donoho D L, Pauly J M. Rapid MR imaging with compressed sensing and randomly under-sampled 3DFT trajectories[C]// Proceeding of the 14th Annual Meeting of ISMRM.Seattle: WA, 2006. [5] Duarte M F, Davenport M A, Takbar D, et al. Single-pixel imaging via compressive sampling[J].IEEE Signal Processing Magazine,2008,25(2): 83-91. [6] Baraniuk R, Steeghs P. Compressive radar imaging[C]// Proceedings of the IEEE Radar Conference.Washington DC, USA, 2007: 128-133. [7] Bajwa W, Haupt J, Sayeed A, et al. Joint source-channel communication for distributed estimation in sensor networks[J]. IEEE Transactions on Information Theory,2007,53(10):3629-3653. [8] YIN Peng-hang, LOU Yi-fei, HE Qi, et al. Minimization of 〖KG*4〗l1-2 for compressed sensing[J]. SIAM Journal on Scientific Computing,2015,37(1): A536-A563. [9] Baraniuk R G, Cevher V, Duarte M F, et al. Model-based compressive sensing[J]. IEEE Trans on Information Theory,2010,56(4): 1982-2001. [10] Eldar Y C, Kuppinger P, Bolcskei H. Block-sparse signals: uncertainty relations and efficient recovery[J]. IEEE Transactions on Signal Processing,2010,58(6): 3042-3054. [11] 李小燕, 高英. 多目标优化问题Proximal真有效解的最优性条件[J]. 应用数学和力学, 2015,36(6): 668-676.(LI Xiao-yan, GAO Ying. Optimality conditions for proximal proper efficiency in multiobjective optimization problems[J]. Applied Mathematics and Mechanics,2015,36(6): 668-676.(in Chinese)) [12] 唐莉萍, 李飞, 赵克全, 等. 关于向量优化问题的Δ函数标量化刻画的某些注记[J]. 应用数学和力学, 2015,36(10): 1095-1106.(TANG Li-ping, LI Fei, ZHAO Ke-quan, et al. Some notes on the scalarization of function Δ for vector optimization problems[J]. Applied Mathematics and Mechanics,2015,36(10): 1095-1106.(in Chinese)) [13] Eldar Y C, Mishali M. Robust recovery of signals from a structured union of subspaces[J]. IEEE Trans on Information Theory,2009,55(11): 5302-5316. [14] Huang B X, Zhou T. Recovery of block sparse signals by a block version of StOMP[J].Signal Processing,2015,109(C): 231-244. [15] Yang M, De Hoog F. Orthogonal matching pursuit with thresholding and its application in compressive sensing[J]. IEEE Transactions on Signal Processing,2013,63(20): 5479-5486. [16] Hu R, Xiang Y, Fu Y, et al. An orthogonal matching pursuit with thresholding algorithm for block-sparse signal recovery[C]//2015 Second International Conference on Soft Computing and Machine Intellige.Hong Kong, 2015: 56-59. [17] 〖JP3〗Wang Y, Wang J, Xu Z. Restricted p-isometry properties of nonconvex block-sparse compressed sensing[J].Signal Processing,2014,104: 188-196. [18] Tao P D, An T H. Optimization algorithm for solving the trust-region subproblem[J].SIAM Journal on Optimization,1998,8(2): 476-505. [19] Tao P D, An T H. Convex analysis approach to dc programming: theory,algorithms and applications[J]. Acta Mathematica Vietnamica,1997,22(1): 289-355. [20] Gabay D, Mercier B. A dual algorithm for the solution of nonlinear variational problems via finite element approximation[J]. Computers Mathematics With Applications,1976,2(1): 17-40. [21] Boyd S, Parikh N, Chu E, et al. Distributed optimization and statistical learning via the alternating direction method of multipliers[J].Foundations Trends in Machine Learning,2011,3(1): 1-122. [22] LOU Yi-fei, Osher S, Xin J. Computational Aspects of Constrained L1-L2 Minimization for Compressive Sensing[M]//Modelling, Computation and Optimization in Information Systems and Management Sciences.Springer International Publishing, 2015: 169-180. [23]

Catalog

通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142