Research On Single-channel Speech Enhancement Algorithm Based On RPCA

Speech enhancement(SE)is an effective method to reduce background noise in noisy speech,and single-channel SE(SCSE)is one of the most common application requirements.Robust principal component analysis(RPCA)is a theoretical model for sparse and low-rank matrix decomposition and can recover the low-rank components and sparse components from the data matrix,which is composed of these two components.It has been widely used in audio and video processing,computers vision,radar signal processing and other fields.Since the spectrogram of speech and the spectrogram of noise are sparse and low-rank,respectively,RPCA can be used to decompose the spectrogram of noisy speech into speech part and noise part,so as to separate speech from noise and achieve speech enhancement.This thesis mainly studies a class of SCSE algorithms with the RPCA theoretical model as the core,especially the SCSE algorithm based on RPCA and the SCSE algorithm based on constrained low-rank and sparse matrix decomposition(CLSMD).In the course of the research,it is found that these two algorithms have deficiencies.Since the rank of the spectrogram of white noise is approximately 1,which shows excellent low-rank characteristics,the RPCA-based SCSE algorithm and the CLSMD-based SCSE algorithm have better noise suppression performances in white noise environments,but their performances decrease in colored noise environments.Because some components in clean speech are low-rank,they will be decomposed into noise matrix in the RPCA-based SCSE algorithm,which makes the speech components lost and affects the performance of the algorithm.The CLSMD-based SCSE algorithm imposes the constrain for the rank of the low-rank matrix to alleviate the above phenomenon of the incorrect decomposition of the low-rank speech components.However,the sparsity of the sparse matrix is also constrained in the algorithm,which is achieved by using the hard threshold function and will cause more loss of speech components under the low signal-to-noise ratios(SNR).To address problems in the mentioned-above algorithms,a SCSE algorithm based on whitened spectrogram hash rearrangement RPCA(WSHRRPCA)is proposed in this thesis as an improved method of these two algorithms.In the proposed algorithm,colored noises are transformed into the white noise by the noise whitening technique.The Spectrogram rearrangement is used to change the spectrum distribution of low-rank speech components so that they no longer represent low-rank features and are correctly decomposed.Therefore,more speech components will be retained in enhanced speech.The main work and innovations of this thesis are as follows:First,short-time analysis techniques are introduced,which are widely used in speech signal processing,including signal framing,short-time Fourier transform,short-time synthesis,etc.The different characteristics of speech and noise in the time-frequency domain are presented.The indicators for evaluating the performance of SE algorithms and two classic unsupervised SCSE algorithms are introduced.Then,the theoretical model of RPCA is studied.This thesis introduces the commonly used augmented Lagrange multiplier method,which is used to implement the sparse and low-rank matrix decomposition.,and gives the principle and implementation steps of the algorithm.The RPCA-based SCSE algorithm and CLSMD-based SCSE algorithm are studied,and the principles and frameworks of the two algorithms are elaborated in detail.Data simulations are carried out,and the performances and shortcomings of the two algorithms are analyzed based on the simulation results.Finally,a SCSE algorithm based on WSHRRPCA is proposed in this thesis.In the new algorithm,the technologies of noise whitening and spectrogram rearrangement are used to address the problems of poor performance in the colored noise environment and loss of speech components,which exist in the RPCA-based SCSE algorithm and CLSMD-based SCSE algorithm.The noise whitening technology and spectrum rearrangement technology are studied in detail.The structure and the determination of the parameters of the proposed algorithm are shown.The related data simulation experiments are carried out on the algorithm proposed in this thesis,including the improvement results of the proposed algorithm on the RPCA-based SCSE algorithm,and the performance comparison with other four SCSE algorithms.The results of simulation show that the algorithm proposed in this thesis can better preserve speech components and has superior noise suppression performance under low SNR.