CAJ | 학술논문

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。
최소이승시현유탐람질대류압축감지중구산법중통용적신호고계방법，기미고필도가능장량측조성인입신호고계적정황。침대이상불족，제출일충기우 Monte Carlo 채양적압축감지약필배거조중구산법。해산법재미지신호희소도선험적조건하，통과인입체추 Bayesian 고계감소량측조성적간우；동시，이약필배적방식사선출유효적원자，병척제용여원자진이중구원신호。신산법계승료현유탐람질대류산법적유효성，동시피면료인조성간우혹희소도미지도치적중구실패。이론분석화실험표명，신산법재동등조건，우기시비고사조성정황하，중구성능우우현유전형탐람질대류산법，차기운산시간저우 BPDN 산법화동류적 KF-SAMP 산법。
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 interfer-ence 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 inter-ference or unknown sparsity as well when it retains the effectivity of other greedy algorithms.The theoretical analyses and experi-ment simulations prove that the performance of the proposed algorithm is better than that of the existing greedy iterative inversion al-gorithms 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.