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.