<span lang="EN-US">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. </span><span lang="EN-US">V</span><span lang="EN-US">oice sparsity </span><span lang="EN-US">is </span><span lang="EN-US">use</span><span lang="EN-US">d to this a</span><span lang="EN-US">lgorithm in the discrete fast Fourier transform (Fast Fourier transform, FFT),</span><span lang="EN-US">and observation matrix is designed</span><span lang="EN-US"> in </span><span lang="EN-US">complex domain, and the noisy speech compression measurement and de-noising are made by soft threshold, and the speech signal is sparsely reconstructed</span><span lang="EN-US"> and </span><span lang="EN-US">restore</span><span lang="EN-US">d</span><span lang="EN-US"> by separable approximation (Sparse Reconstruction by Separable Approximation, SpaRSA) algorithm, speech enhancement</span><span lang="EN-US">is improved. Experimental results show that the denoising compression reconstruction is </span><span lang="EN-US">made for </span><span lang="EN-US">the noisy signal in the algorithm, SNR margin is improved greatly, and the background noise can be more effectively suppressed .</span>