中文摘要：

信号在某种变换下可以稀疏表示是压缩感知研究的先验条件,正交傅里叶变换则是应用非常广泛的一种稀疏变换。但是,由于语音信号是准周期信号,对其进行傅里叶变换会造成频谱泄漏,因而引起信号重构性能的降低本文基于语音信号准周期性的特点,提出了一种基于差分变换的语音稀疏化变换矩阵,在此基础上采用OMP优化算法来重构语音信号。实验表明,与采用正交傅里叶变换方法对语音信号进行稀疏化变换、OMP算法对语音信号进行重构的方法相比,差分变换方法的性能明显优于正交傅里叶变换的方法,即在相同重构性能时,差分变换的压缩比小于正交傅里叶变换,因而差分变换的方法大大提高了信号的压缩性能。PESQ对重构语音质量评测的结果表明差分变换方法重构的语音信号MOS得分较高,这也说明对于语音信号这一特殊信号,差分变换法具有很大的优越性。

英文摘要：

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.