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.