Compressed sensing (CS) is a kind of sampling method based on signal sparse property, it can effectively extract the signal which was contained in the message. In this study, a new noise speech enhancement method was proposed based on CS process. Voice sparsity is used to this algorithm in the discrete fast Fourier transform (Fast Fourier transform, FFT), and observation matrix is designed in complex domain, and the noisy speech compression measurement and de-noising are made by soft threshold, and the speech signal is sparsely reconstructed and restored by separable approximation (Sparse Reconstruction by Separable Approximation, SpaRSA) algorithm, speech enhancement is improved. Experimental results show that the denoising compression reconstruction is made for the noisy signal in the algorithm, SNR margin is improved greatly, and the background noise can be more effectively suppressed. © 2016 Institute of Advanced Engineering and Science. All rights reserved.