Research On Measurement Matrix Of Speech Enhancement Based On Compressed Sensing

In recent years, compressed sensing technology has increasingly become a hot topic in the field of speech signal processing, which is a new theory and complements signal sampling and data compression simultaneously, and the theory breaks through the limitations of traditional Nyquist sampling theorem. In the process of compressed sensing, the measurement matrix plays an important role in the signal reconstruction process, Therefore, the research of measurement matrix for the compressed sensing technology has important theoretical significance. At the present stage, most of the compressed sensing study is remained in the field of speech enhancement in the sparse representation and signal reconstruction, but the influence of measurement matrix for speech enhancement has been less studied. Since the different measurement matrix and reconstruction algorithms have different effects on the noise performance of the noisy speech signal. Therefore, the thesis focused on measurement matrix and reconstruction algorithm for the influences of speech enhancement by combining with the characteristic of measurement matrix and reconstruction algorithm. The main work is as follows:Firstly, we studied the influence of measurement matrix for speech enhancement, The main work was to select the five kinds of common measurement matrix to carry on experimental simulation under different noise environments and different signals-to-noise ratio, then by five kinds of measurement matrix from enhanced speech signal are analyzed for the noisy words, terms and sentences. Finally by using two kinds of objective evaluation methods, voice quality denoised was evaluated. Experimental results show, whether from a waveform diagram denoising signals or through objective evaluation indicators, denoising effect of Toeplitz matrix and Circulant matrix are better than the other three measurement matrixes. For white noise noisy speech, performance of Circulant matrix is better, and the average PESQ of the matrix speech denoising speeds up 66.16% than Bernoulli matrix with bad performance in low SNR situation. Yet in high SNR situation, it improves 13.54%. than Gaussian random matrix with relatively bad performance.Secondly, two kinds of reconstruction algorithms were described, including Orthogonal Matching Pursuit(OMP) algorithm and Sparsity adaptive matching pursuit(SAMP) algorithm, then the influence of reconstructed algorithm for speech enhancement was analyzed and studied. The experiments of reconstruction simulation performed on the speech with noise added white noise, then comparison of the two reconstruction algorithm performances will be obtained from the analysis of the results of the signal-to noise ratio(SNR). Experimental results showed, whether from a waveform diagram denoising signals or through objective evaluation indicators, SAMP algorithm can effectively reduce the noise component of noisy speech and improve the signal-to noise ratio of the speech denoising compared to the traditional OMP algorithm. The SAMP algorithm SNR of reconstructed speech signal speeds up about 8d B than that of the OMP algorithm. Relatively speaking, denoising effect of OMP algorithm is poor, and reconstructed speech also contains a lot of noise.