Abstract: In this paper, present a kind of observation matrix which combines the chaotic sequence with the sign function, which has good pseudo randomness.Firstly, the noisy speech signal is sparse in the DCT domain, then the observation matrix is used to preserve most of the speech features, finally based on the original reconstruction algorithm, this paper improves the reconstruction algorithm to speed up the reconstruction.The algorithm proposed in this paper makes the intelligibility and clarity of reconstructed speech signal be greatly improved, and the speech enhancement is realized.