Abstract: Signals can be expressed by some sparse form by certain transformation, and which is a precondition of compressed sensing. Orthogonal Fourier transform is widely used as a sparsity transformation. However, the speech signal is quasi-periodic, so its Fourier transform will result in spectral leakage, which causes the performance degradation of signal reconstruction. According to the quasi-periodic characteristics of speech signal, a kind of sparsity transformation matrix is presented based on the difference transform method, and then using OMP algorithm to reconstruct the speech signal. Experiments show that, when the Fourier transform method is used to transform the signal into sparsity and OMP algorithm is used to reconstruct the speech signal, the performance of difference transform method is better than that of orthogonal Fourier transform method. Namely, when the reconstruction performance of the two methods is same, the compression ratio of difference transform method is less than that of the orthogonal Fourier transform, which means that the difference transform method has greatly improved the compression performance of the speech signal. The quality evaluation of reconstructed signals by PESQ shows that the reconstructed signals by the difference transform method have higher MOS scores, which also shows that for this particular signal, the difference transform method has great advantages.