基于l1-l2范数的块稀疏信号重构

压缩感知(compressed sensing，CS) 是一种全新的信息采集与处理的理论框架，借助信号内在的稀疏性或可压缩性，可以从小规模的线性、非自适应的测量中通过求解非线性优化问题重构原信号.块稀疏信号是一种具有块结构的信号，即信号的非零元是成块出现的.受YIN Peng-hang, LOU Yi-fei, HE Qi等提出的l_1-2范数最小化方法的启发，将基于l₁-l₂范数的稀疏重构算法推广到块稀疏模型，证明了块稀疏模型下l₁-l₂范数的相关性质，建立了基于l₁-l₂范数的块稀疏信号精确重构的充分条件，并通过DCA(difference of convex functions algorithm) 和ADMM(alternating direction method of multipliers)给出了求解块稀疏模型下l₁-l₂范数的迭代方法.数值实验表明，基于l₁-l₂范数的块稀疏重构算法比其他块稀疏重构算法具有更高的重构成功率.

Block-Sparse Signal Recovery Based on Norm Minimization

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 the l1-l2 norm were proved and the sufficient condition for block-sparse signal recovery was established.Meanwhile,an iterative method for block-sparse l1-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.