A Research On The Reconstruction Method Of Speech Signal Based On Compressed Sensing

The vigorous theory of compressed sensing (CS) provides a very simple and effective signal acquisition method, which can sample signal below the Nyquist rate and recover the original signal by means of reconstruction algorithm. With the extensive application of CS theory in the field of signal processing, its application in the audio and speech signal processing is also unfolding.This thesis focuses on the application of CS theory in the aspect of speech signal reconstruction. The author first introduces the basic theory of CS, then studies the sparsity of the speech signal on different bases, and finally makes an analysis towards the effects of measurement matrix and reconstruction algorithm on the of CS theory in speech signal processing in the mobile communication system. The main work is summarized as follows:●The thesis analyzes the sparsity of the speech signal on different bases, and accomplishes the speech signal’s sparse decomposition by using DCT and wavelet transform. Besides, this thesis discusses the efficiency of non-related measurement by using random cycle and Toeplitz matrix, and then compares the recover efficiency of using reconstruction algorithm BP, OMP and StOMP. The experiment results show that, for speech signal, the reconstruction result which is obtained by using cyclic matrix as measurement matrix has a stronger stability and lower error rate than that using the other two matrixes; while the use of StOMP algorithm makes the reconstruction time greatly reduced, but leads the general effect.●The thesis studies the effect of the selection of measurement matrix for the speech signal reconstruction. After some related contents about structured random matrix are introduced, the measurement matrixes such as random, toeplitz and cycle matrix are improved, while the sparse diagonal matrix is used as measurement matrix to complete the non-coherent measurement of the speech signal. The experiments, which are made on the speech signal, use sparse diagonal structure measurement matrix and traditional measurement matrix respectively and compare the reconstructing efficiency by using StOMP algorithm. The experiment results show that the speech signal’s reconstruction accuracy, which is reconstructed by using the improved sparse matrix compared with traditional matrix, has a significantly improved accuracy and a shorter run-time.●Based upon mobile communication systems, the thesis designs a compressed sensing theory which applies the CS theory to the speech signal processing in the new mobile communication system. In the system, the speech signal is compressed by CS modulation in the transmission side and reconstructed by anti-CS modulation in the receiving side, while the system data transfer rate increases and the speech signal can be reconstructed without the loss of important information. The simulation results on real speech signal indicate that, this system can effectively reconstruct the speech signal with a smaller error. When compared with wavelet compression with different parameters and the same compression rate, CS has a better performance and a lower error.