Compressive Sensing Of The Speech Signal And Its Application In Speech Coding

Compressive sensing (CS) is an innovative signal sampling theory on the condition that the signal is sparse or compressible. It has the ability of compressing a signal during the process of sampling. Many problems are worth studying in this field. Reconstruction algorithm is one of the key portions in CS, and it is of great importance to reconstruct a signal and verify the sampling accuracy.In this thesis, properties of the compressive sensing theory and the speech coding theory are firstly analyzed. A DCT sparse basis and wavelet sparse basis is used to verity that the speech signal is K-sparse. How to determine the K for the speech signal under 8kHz sampling frequency is discussed thoroughly in this thesis. Also the condition of short-term stationarity and the selection of frame length are discussed. In the aspect of the measurement matrix, the proximate QR factorization of measurement matrix is proposed. In the aspect of the reconstruction algorithm, we use the OMP algorithm to reconstruct the speech signal. Then we discuss the Bayesian theory and put forward Bayesian algorithm, fast Bayesian matching pursuit (FBMP) algorithm and tree-structured wavelet Bayesian algorithm (TSW-CS). The main work of this paper are summed up as follows.The basic knowledge of the speech signal processing is introduced in this thesis firstly. Then whether speech signal can be sparse represented is validated by both the DCT method and the wavelet method. Under 8 kHz sampling and the premise of short-term stationarity, the most appropriate K and frame length for speech signal is determined by experimental method. The OMP algorithm is used to reconstruct the speech signal. It is very common, but the reconstruction accuracy is low. Under the framework of the Bayesian, the inversion of compressive measurements from a Bayesian perspective is considered. The reconstruction of speech signal by the Bayesian algorithm and FBMP algorithm is presented. Also it is verified that the reconstruction precision can be improved to some extent.Finally, under the framework of the Bayesian, combined with wavelet tree structure and the MCMC method, the TSW-CS algorithm is put forward. The experimental results show that TSW-CS algorithm is very powerful and the AFSNR is up to 19.5dB, which is superior to other algorithms.