基于自相关观测的语音信号压缩感知

本文基于压缩感知技术，根据语音信号的特点，提出了一种基于自相关特性的截断循环自相关矩阵作为观测矩阵，并在此基础上，从实用的角度出发，提出了基于模板匹配的近似截断循环自相关矩阵作为观测矩阵，并证明其满足RIP特性。由语音信号与截断循环自相关矩阵、近似截断循环自相关矩阵和高斯随机矩阵分别构造相应的观测，采用BP算法来重构原始语音信号。实验表明，由2个模板元素线性组合而成的近似截断循环自相关矩阵重构原始语音信号的性能与截断循环自相关矩阵的重构性能相当，且优于经典高斯随机矩阵，而且在相同的重构性能下，其压缩比远大于高斯随机观测矩阵，对语音信号的压缩性能有了明显地提高。 

Compressed Speech Signal Sensing Based on Autocorrelative Measurement

Abstract: A new measurement matrix—truncated circulant autocorrelation matrix is presented based on the Compressed Sensing theory and features of speech signals in this paper. From a practical point of view,an approximate truncated circulant autocorrelation matrix based on template matching as the measurement matrix is proposed in this paper and it proves that the new measurement matrix satisfies the restricted isometry property(RIP).By speech signals and the truncated circulant autocorrelation matrix, the approximate truncated circulant autocorrelation matrix and the Gaussian random matrix respectively, BP algorithm is used to reconstruct the original speech signal. Simulation results demonstrate that the performance of the approximate truncated circulant autocorrelation matrix created by a linear combination of two template elements to reconstruct the original speech signal is almost the same as the truncated circulant autocorrelation matrix, and greatly better than the classic Gaussian random matrix.Moreover,in terms of the same reconstruction performance,the ratio of compression realized by the approximate truncated circulant autocorrelation matrix created by a linear combination of two template elements is far bigger than that of the Gaussian random matrix,which means that the new measurement matrix can significantly enhance the performance of compression for speech signals.