Research On Key Issues Of Speech Compressed Sensing

Signal sparse property is the application premise of compressed sensing theory， which usesthe least number of observation to signal compressed sampling, realizes the dimension reduction ofsignal processing, saves the cost of sampling and transmission and brings a new revolution to signalsampling technology. For speech signal, since it has approximate sparse property, it can becombined with compressed sensing theory, breaking the traditional speech signal processing modeestablished by Nyquist sampling. Replacing the traditional Nyquist sample of speech signal bycompressed sensing observation sequence, will lead to fundamental changes in the signalcharacteristics, thus affecting all areas of speech signal processing applications. On the basis ofdepth research on compressed sensing theory, compressed sensing observation sequence of speechsignal is studied. Based on further study on compressed sensing theory and reconstructiontechnology of speech compressed sensing observation sequence under different sparse domain,endpoint detection algorithm based on cepstral distance of compressed sensing observationsequence of speech signal is proposed, a new algorithm of compressed sensing of speech signalbased on special row echelon observation matrix and dual affine scaling interior pointreconstruction method is proposed, Volterra model as the second model of compressed sensingobservation sequence of speech signal based on row echelon measurement matrix is studied,andaccording to speech compressed sensing, codebook mapping combiningl1reconstructionalgorithm is proposed. Main work and innovation are as follows:(1)Reconstruction technology of speech compressed sensing observation sequence under differentsparse domain is studied, sparse property of speech signal in DCT, DFT, DWT and K-L transformdomain is studied, although the coefficient in K-L transform is sparsest, it is difficult to be realizedin the practical application because the reconstruction needs the original signal autocorrelationmatrix, and in the first three sparse domain, the sparse property of DCT transform is the best.Reconstructions of BP and OMP under random Gaussian projection matrix are studied.Experimental results show that for speech signal, at the same observation numbers, BPreconstruction performance is better than OMP, but it has large computing complexity. In addition,the complete cosine dictionary and KSVD dictionary of compressed sensing speech signal arestudied, due to the increase of sparseness of the coefficient, the CS reconstruction effect is slightlyincreased than DCT basis,and the KSVD dictionary has better reconstruction effect than the complete cosine dictionary. According to the decentralization characteristic of amplitude spectrumdistribution and difference of amplitude spectrum of compressed sensing observation sequence ofspeech and non-speech signal, endpoint detection algorithm based on cepstral distance ofcompressed sensing observation sequence is proposed to analyze the original speech signalaccording to the observation sequence characteristic directly. Endpoint detection simulationexperiments under different signal-to-noise ratio of speech show this method has the sameperformance as the traditional cepstral distance endpoint detection under Nyquist sampling, and itcan reduce the computational complexity.(2) Based on the approximate sparse property in DCT basis, a new algorithm of compressed sensingof speech signal based on special row echelon observation matrix and dual affine scaling interiorpoint reconstruction method is proposed. This algorithm can resolve the problem of large error ofdominant coefficient because of inaccuracy of location of reconstruction coefficient which is zero ornearly zero based on Gaussian observation matrix. The simulation results show this algorithm cangive more accurate location of reconstruction coefficient, and get better performance than Gaussianobservation matrix, and the computation and data size are reduced greatly. Therefore, the specialrow echelon observation matrix is the ideal observation matrix for speech compressed sensing.(3) In view of the strong correlation of the observation sequence of row echelon observation matrix,Volterra model as the second model of compressed sensing observation sequence of speech signalbased on row echelon measurement matrix is proposed. The prediction effects of input dimensionsand order of Volterra model are studied. Wiener filter is used in order to improve the accuracy ofprediction result. The reconstruction based on part of observation sequence, Volterra model andWiener filter is realized.(4) At the end of this dissertation, in view of the problem of large amount of calculation of CSreconstruction algorithm, according to the advantage of codebook mapping reconstructionmethod which can directly get the reconstruction coefficient from codebook, with much lesscomputation than BP and OMP algorithms, considering the reconstruction performance also,codebook mapping combiningl1reconstruction algorithm is proposed.This method gets speechcodebook and observation sequence codebook in stage of training,in stage of testing,estimates SNRof testing speech first,then chooses the energy threshold according to the SNR andcompression ratio, when the frame energy of observation sequence is above,it choosesl1 reconstruction, when the energy is below,it chooses codebook mapping reconstructionalgorithm. Experiments show codebook mapping combiningl1reconstruction is better thanl1reconstruction with certain energy threshold under low and middle SNR conditions, under highSNR and clean conditions,when the number of codebook mapping is about3/10of total, thisalgorithm can has the same performance asl1method.It can save computations in codebookmapping reconstruction part because the reconstruction needn’t nonlinear optimization algorithmwhich has large amount of calculation.