Research On Speech Sparse Basis And Projection Matrix Based On Compressed Sensing

Communication has played an important role in our daily life. The speech signal is an analog signal which has a continuous waveform in the time-domain. It must be digitalized before being processed by the computer. The first step of digitalization is sampling. Nyquist Sampling Theory is usually adopted in the digitalization. But it would bring about a large number of data, and cost much resource in the transmitting and storage. In order to reduce the amount of data, Daonodo and Candes have proposed the compressed sensing. The theory proves that the sampling and compression are working simultaneously which can reduce the amount of data in the transmitting and storage.If a signal can be represented sparsely, it can adopt compressed sensing. However, the speech signal hasn't enough sparsity in the traditional basis. We should find a fit basis in which the signal can be represented sparsely, and then be projected into a projection matrix. There are three main points in the thesis. At first the residual of the signal can be considered into choosing an adaptive projection matrix according to the energy distribution of the signal. Secondly, based on the characteristics of coefficients of speech signal at low frequency and high frequency after wavelet transformation, the trained overcomplete dictionary using K-SVD is applied to the low frequency coefficients after wavelet transformation to decrease the computation of the sparse decomposition. Lastly, the variable step has been adopted into the K-LMS to decrease the error rate. At the beginning of the iterations, the step is large to speed up the rate of convergence. As the number of iterations increase, the step is reduced to get a low error rate.In the end of the thesis,we conclude the paper as well as the future direction of research and improvement of compressed sensing in speech signal.