基于卡尔曼滤波的压缩感知弱匹配去噪重构

现有的贪婪迭代类压缩感知重构算法均基于最小二乘对信号进行波形估计，未考虑到可能将量测噪声引入信号估计的情况.针对以上不足，提出了一种基于线性Kalman滤波的压缩感知弱匹配去噪重构算法.该算法不需已知稀疏度先验，通过引入Kalman滤波，在最小均方误差准则下，每次迭代都获得最佳信号估计；并以弱匹配的方式同时筛选出有效的原子，并剔除冗余原子进而重构原信号.新算法继承了现有贪婪迭代类算法的有效性，同时避免了因噪声干扰或稀疏度未知导致的重构失败.理论分析和实验表明，新算法在同等条件下，重构性能优于现有典型贪婪迭代类算法，且其运算时间低于BPDN算法和同类的KFCS算法.

Weakly Matching Pursuit Denoising Recovery for Compressed Sensing Based on Kalman Filtering

Almost all of the existing greedy iterative compressed sensing reconstruction algorithms estimate the signal by the method of least squares,which introduces the measure noise into the signal estimation.Aiming at this problem,a new weakly matching pursuit denoising recovery for compressed sensing based on Kalman filtering is proposed.The new algorithm does not need the sparse prior while it estimates the signal best for each iteration according to the minimum mean-square error criterion by Kalman filtering.Meanwhile,weakly matching pursuit is used to sift the effective support set and pick out the redundancy to recover the original signal.The new algorithm is as effective as other greedy ones and is able to avoid recovery failure due to noise interference or unknown sparsity as well.The theoretical analysis and experimental simulation prove that the performance of the new algorithm is better than that of the existing greedy iterative reconstruction algorithms in the same condition.The operation time of the new algorithm is shorter than that of BPDN and the similar KFCS algorithm.