Compressed Sensing for Speech Processing Based on Wavelet Transform

Sampling is the bridge between analog source signal and digital signal. With the rapid progress of information technologies. The demands for information are increasing dramatically. So the existing systems are very difficult to meet the challenges of high speed sampling, large volume data transmission and storage. How to acquire information in signal efficiently is an urgent problem in electronic information fields. In recent years, an emerging theory of signal acquirement-compressed sensing (CS) provides an opportunity for solving this problem. CS is a research focus rising in the last few years. It is a new sampling theory and points out that if a signal can be compressed under some condition, a very accurate reconstruction can be obtained from a relatively small number of non-traditional samples. In this paper, the CS framework is introduced firstly, and then the approximate sparsity in the wavelet domain of male and female speech signals is analyzed. Secondly, the CS algorithm preserves the low frequency wavelet transform coefficients but compresses the high frequency wavelet transform coefficients of the speech signal. Two methods are proposed to compress the high frequency wavelet transform coefficients of the speech signal. One is compressing them separately, and the other is compressing them together. Finally, the high frequency wavelet transform coefficients are recovered by using Orthogonal Matching Pursuit algorithm, and then the reconstruction of the speech signal can be achieved by the inverse wavelet transform. Simulation results show that whether male or female speech signals, the first method can acquire better reconstruction performance and it needs less time than the second one at the same measurement number.