Speech Compressed Sensing Based On MFCC Dictionary And Smoothed L0 Algorithm

The sampling rate of compressed sensing(CS)theory is lower than that of Nyquist sampling theorem.CS can not only realize compression and sampling simultaneously but also restruct signal with high quality.Speech signals have good sparse features in frequency domain and the discrete cosine transform domain and so on,which meet the prior condition of compression perception,so the speech signal processing can be researched based on CS.CS also renders great convenience to the sampling,storage and transmission of signal.Combing CS with speech signal processing will be of great significance.In this paper,the optimization of the sparse decomposition and reconstruction algorithm is taken into account so that the higher refactor quality and little refactor time can be obtained,which will lay the speech compression perception in the theoretical foundation of practical application.A redundant dictionary based on Mel frequency cepstrum coefficient(MFCC)of speech and the compressed speech reconstruction method based on smoothed L0(SL0)algorithm are proposed in this thesis.The main research content and innovation can be showed in the following.(1)The differences and relations of the compressed sensing and Nyquist sampling are introduced.The framework of compressed sensing theory is analyzed.And the application of compressed sensing in speech processing is detailed,which contains sparse representation,observation matrix and reconstruction algorithm.In the experimental process,speech signal's sparse features is verified,and refactoring performance with different sparse representation,observation matrix and reconstruction algorithm is compared.The experimental results show that speech signal reconstruction can be influenced by sparse matrix,observation matrix,reconstruction algorithm,the length of voice frame and compression ratio.(2)A method to design a redundant dictionary based on MFCC of speech signal is presented.The extraction process of speech signal's MFCC parameters is introduced.And speech compressed sensing is realized based on the redundant MFCC dictionary.Experiments prove that the speech signal is sparse in redundant MFCC dictionary.Under the condition of same quantity of taining signal and same size of dictionary,the redundant MFCC dictionary will take less time than the traditional K-SVD dictionary.The redundant MFCC dictionary enjoys the added advantage when the more quantity of taining signals.The using of redundant MFCC dictionary in the speech compression sensing is feasible and has great significance.(3)This paper proposes the compressed speech reconstruction method based smoothed L0(SL0)algorithm.SL0 algorithm uses a smooth function to approximate the L0 norm.For that the signal sparse degree need not to be known in advance,SL0 algorithm acquires low computation and high reconstruction quality.In addition,a new smooth function is proposed in this paper.And superiority of SL0 algorithm is verified based on gaussian function and the new smooth function respectively.The experimental results prove that the performance of SL0 algorithm based on two kinds of smooth functions is superior to the traditional OMP algorithm,BP algorithm and so on.In some certain circumstances,voice reconstruction quality of the SL0 algorithm using the new smooth function is higher than that of using the standard gaussian function.