Research And Application Of Signal Denoising Method Based On Group-sparse Prior

Signal denoising is a core task in the field of signal processing.In the process of signal denoising,we use the prior knowledge of the signal to select the regularizers,and then construct the mathematical model,therefore a priori knowledge plays a de-cisive role.This paper first proof the convergence of the Majorization-Minimization(MM)algorithm in theory.This guarantees the theoretical rationality of subsequent applications.Secondly,this paper uses the prior knowledge of the signal in the time domain to propose a denoising method based on sparse priors of different groups for multi-regular Lasso,called the denoising of different groups(DGDN-OGS)al-gorithm.Finally,this paper characterizes the group sparsity prior of the wavelet transform coefficients in the wavelet domain,and expresses it as the sparse regu-larity of the overlapping-group(OGS),and then uses the prior knowledge of signal in the wavelet domain to propose a wavelet transform(WT)domain denoising al-gorithms with the overlapping-group sparse regularizers.These two algorithms are based on the framework of MM algorithm,and use Proximal mapping to iteratively solve optimization problem that constructed in this paper.The experimental results on the data from the Michigan Heart Sound Databas show that the denoising al-gorithm in the wavelet domain proposed in this paper can effectively process Heart Sound signals.