稀疏信号重构的迭代平滑l0范数最小化算法

压缩感知理论(Compressed Sensing,CS)是对信号压缩的同时进行感知的新理论,而如何通过有限的测量值重构稀疏信号是压缩感知理论中的核心问题.针对稀疏信号的重构问题,提出了迭代平滑l0范数最小化算法.该算法首先利用上次迭代得到的稀疏解估计部份支撑集I,然后建立并求解基于支撑集I的平滑l0范数最小化问题,最后对以上两步迭代少数几次得到稀疏解.数值仿真表明,本文所提出的算法重构信号需要测量值数少于已有的算法,且计算速度较快.

Sparse Signal Reconstruction Based on Iterative Smoothed l0 Norm Minimization

Compressed Sensing(CS) is a new framework for simultaneous sensing and compression,and how to reconstruct sparse signal form limited measurements is the key problem in CS.In this paper,a novel method called Iterative Smoothed l0-norm(ISL0) is proposed for sparse signal reconstruction.This method estimates a support set I from a current reconstruction and obtains a new reconstruction by solving the minimization problem based on the support set I,and it iterates these two steps for a small number of times.Simulation results show that the proposed method needs fewer measurements than existing methods,while needing the low computational cost.