一种改进的压缩感知信号重构算法

针对支撑集未知且变化时的稀疏信号的重构问题，本文基于卡尔曼滤波思想，结合压缩感知算法，给出了一种改进的卡尔曼-压缩感知（Modified Kalman Filter Compressive Sensing，MKFCS）信号重构算法，该算法首先利用Kalman滤波获得信号残差的有效估计，然后根据残差变突情况，用改进的CS算法估计突变位置以确定信号的新的支撑集，最后用最小二乘方法重构信号，从而自适应的实现支撑集未知且变化的稀疏信号的重构。最后对所改进的通过重构精度、重构误差、稳健性等方面进行了仿真，仿真结果表明所提算法重构信号具有需要量测个数少、重构精度高、鲁棒性强等特点。 

A Modified Signal Reconstruction Algorithm Via Compressive Sensing

Based on Kalman filter(KF) and compressive sensing(CS) theory,we proposed a modified KF compressive sensing(MKFCS) algorithm which aims at reconstructing time sequences of spatially sparse signals with unknown and time varying sparsity supports.First,the residual of the signal,which could indicate the position of the new supports,is estimated using KF.Then a new supports is decided by means of a modified CS algorithm.Finally,the signal with unknown and time varying sparsity support is reconstructed using least square via the updated supports adaptively.And the MKFCS algorithm is performed through simulating reconstruction accuracy,reconstruction error and its stability to validate the algorithm.Simulation results and theoretical anylasis show that the proposed method has many advantages such as needing fewer measurements than existing methods,having higher reconstruct accuracy and better robust etc.