Reconstruction method for unknown sparsity noisy signals based on Kalman filtering matching pursuit

Aiming at the problem that the anti-noise performance of the existing fast convergent and easily realized greedy iterative algorithms is deficient, a novel sparsity adaptive matching pursuit with Kalman filtering (KF-SAMP) algorithm is proposed for unknown sparsity noisy signal compressed sensing (CS) recovery. To start with, the concrete Kalman filtering (KF) equation set are come up with according to the CS signal model; secondly, KF is introduced into recovery iterations and the signal is optimal estimated by the mean-squared error minimization criterion at each time; the last but not least, sparsity adaptive matching pursuit is used to sift the effective support set and pick out the redundancy and then recover the original signal. The new algorithm is 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 experiment simulation prove that the performance of the new algorithm is better than that of the traditional greedy iterative reconstruction algorithms in the same condition.