Research On Projection Matrix And De-noising Of Speech Compressed Sensing Based On Overcomplete Dictionary

In recent years,compressed sensing theory has become a research hotspot in signal processing,which creatively solves the problem of high sampling rate and high data redundancy,and requires only a small amount of sampling values to accurately or nearly reconstruct the original signal.The inherent sparsity of speech signals determines that the combination of speech and compression sensing technology is an inevitable choice,which will bring great changes to the whole speech signal processing field.Under this background,the thesis studies one of the problems that must be solved in the process of speech processing based on compressed perception: the technique of speech denoising in compressed sampling system.The main research works and innovations in this thesis are as follows:Firstly,this thesis introduces the background knowledge of compressed sensing,summarizes the practical application of compressed sensing theory in recent years,and introduces the application and development of speech compressed sensing technology.Secondly,from three aspects to detail the compressed sensing.Then,for the specific application of speech,the feasibility of compressed sensing in speech signal processing is verified through analysis and simulation.At last,the influence of noise on the whole compressed sampling system is analyzed.Then,an improved K-SVD dictionary learning method based on fast iterative shrinkage threshold algorithm is proposed.A K-SVD dictionary learning algorithm based on fast iterative shrinkage threshold algorithm is proposed by introducing fast iterative shrinkage threshold algorithm into dictionary training process.In this algorithm,the sparse coding stage of the K-SVD dictionary learning algorithm is completed by a fast iterative shrinkage threshold algorithm.The updated dictionary uses the classical update method of K-SVD so that two-step iteration of sparse coding and dictionary updating is to get a new dictionary.This algorithm is applied to the speech signal compressed sensing process.The results show that the proposed algorithm is faster than the classical K-SVD algorithm and has lower RMSE.The experimental results show that the proposed algorithm has higher output signal-to-noise ratio than the classical K-SVD algorithm.performance.Finally,a joint design method is proposed to improve the reconstruction and de-noising performance in compressed sensing applications.Based on the premise that a given dictionary exists in a closed form,the dictionary SVD is decomposed and the expression of the projection matrix is obtained by mathematical derivation.At this time,the projection matrix and dictionary multiplication is a tight frame.The optimized projection matrix can be obtained from dictionary.Simulation results show that compared with other methods,the new method proposed in this thesis has good de-noising performance for speech signal.