采用正交多项匹配的块稀疏信号重构算法

Block-Sparse Signals Recovery using Orthogonal Multimatching

压缩感知,通过测量矩阵将原始信号从高维空间投影到低维空间,然后求解优化问题,从少量投影中重构出原始信号,是一种有效的信号采集技术。块稀疏信号是具有特殊结构的稀疏信号,其非零值是成块出现的。针对该信号的特点,提出一种采用正交多项匹配的块稀疏信号重构算法。该算法每次迭代选择多个最大相关子块,然后更新块索引集,以及迭代余量,最后求广义逆运算重构出原始信号。仿真结果表明,相比于大多数的现有算法,本文算法重构成功率较高,运行时间较短,复杂度较低。

Compressed Sensing is an efficient signal acquisition approach that projects input signals, embedded in a high-dimensional space,into signals that lie in a space of significantly smaller dimensions, and solves an optimization problem, then recovers the input signals from the projections. Block-spase signal is a typical sparse signal, the units in the same block can simultaneously tend to be zeros or nonzeros. As to the feature of block-sparse signal, an orthogonal muhimatching pursuit algorithm （BOMMP） for block-sparse signals recovery has been proposed in this paper. The algorithm picks at least one correct index at each iteration,additionaly,the support set and the residual will be refined, finally, the recovery signal can be determined by the pseudo-inverse. The simulation results demonstrate that the recovery probability of BOMMP is higher than most existing algorithms.