Abstract: The speech recovery discussed by this paper aims at improving the intelligibility of noisy speech. By comparing of auditory masking and vision occlusion and inspired by image denoising idea base on sparse representation, this paper proposes a speech recovery model over sparse representation based on compressive sensing theory, its mathematical expression and the algorithm. Different from traditional speech enhancement algorithms, the superiority of this model and algorithm lies in its twofold ability of effectively eliminating global noise interference and recovering local incomplete speech components masked by noise interference, which improves the intelligibility of processed speech. Simulation experiments and objective speech quality measures verify that the proposed model and algorithm are feasible, effective and superior.