基于Monte Carlo采样的压缩感知弱匹配去噪重构

最小二乘是现有贪婪迭代类压缩感知重构算法中通用的信号估计方法,其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,提出一种基于Monte Carlo采样的压缩感知弱匹配去噪重构算法.该算法在未知信号稀疏度先验的条件下,通过引入递推Bayesian估计减小量测噪声的干扰;同时,以弱匹配的方式筛选出有效的原子,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,尤其是非高斯噪声情况下,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KF-SAMP算法.

Monte Carlo Matching Pursuit Denoising lnversion for Compressed Sensing

The method of least squares,which introduces the measuring noise into the state estimates,is wildly used in the greedy iterative compressed sensing inversion algorithms.Aimed at this problem,a Monte Carlo matching pursuit denoising inversion algorithm for compressed sensing is proposed.The proposed algorithm does not need the sparse prior while it eliminates the interference of measuring noise by recursive Bayesian estimation.Meanwhile,weakly matching pursuit is used to sift the effective support set and pick out the redundancy to inverse the original states.The new algorithm is able to avoid inversion failure due to noise interference or unknown sparsity as well when it retains the effectivity of other greedy algorithms.The theoretical analyses and experiment simulations prove that the performance of the proposed algorithm is better than that of the existing greedy iterative inversion algorithms in the same condition,especially in the non-Gaussian noise situation,and its operating time is shorter than that of BPDN and similar to that of KF-SAMP.