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.