面向压缩感知的块稀疏度自适应迭代算法

Block Sparsity Adaptive Iteration Algorithm for Compressed Sensing

块稀疏信号是一种典型的稀疏信号,目前在块稀疏信号的压缩感知问题中,大多数信号重构算法要求信号的块稀疏度已知且算法复杂度高.针对实际应用中信号块稀疏度未知的情况,提出了一种块稀疏度自适应迭代算法,用于信号重构.首先,该算法初始化一个块稀疏度,其值按设定步长进行增加.对每一个块稀疏度的迭代,算法都会找到信号支撑块的一个子集,并修正更新上一次找到的信号支撑块,最后找到信号的整个支撑块,从而重构出源信号.该算法不需要信号的块稀疏度作为先验知识,而且算法复杂度低.仿真实验表明,该算法的重构概率较已有大多数块稀疏信号重构算法的重构概率高,在块稀疏信号的压缩感知问题中具有实际意义.

Block-sparse signal is a typical sparse signal.Among the block-sparse signal problems for compressed sensing,the most existing recovery algorithms require block sparsity as prior knowledge and have a high complexity.In this paper,a block sparsity adaptive iteration algorithm for compressed sensing has been proposed when the block sparsity is unknown.Firstly,the algorithm initializes a block sparsity which will increase by steps.Subsequently,for each block sparsity,a sub-set of the signal support set can be determined by the algorithm,which updates the previous one,until the exact support set is acquired,finally the original signal can be reconstructed through the exact support set.This algorithm doesn＇t require block sparsity as prior knowledge and has a low complexity.Simulation results demonstrate its high recovery probability than most existing algorithms,which makes it a promising for practical block-sparse signal compressed sensing task.