Survey Of Sparse Decomposition Algorithm Based On Overcomplete Dictionary Representation

Sparse representation is one of the important research topics within big data processing and analysis, and structuring a overcomplete dictionary to realize sparse decomposition is a significant branch of sparse representation theory. It could efficiently extract the most essential features of information with fewer nonzero element, and reduce the amount of data need to be processed. This paper mainly research in the sparse decomposition algorithm based on overcomplete dictionary representation, the innovative results are as follows:(1) An algorithm of fuzzy pruning threshold sparsity adaptive matching pursuit(FPTSAMP) is proposed in this paper. Firstly, adding clipping threshold and stopping threshold to SAMP algorithm is to get the clipping threshold sparsity adaptive matching pursuit(CTSAMP) algorithm. Secondly, FPTSAMP algorithm is acquired by appending a fuzzy pretreatment to select the larger relevance atoms candidate set, which solves the problem of double increasing atoms candidate set at ever iteration step and wasting storage space, then theoretically proves the feasibility of the algorithm. Finally, simulation results highlight the advantage of the new algorithm, reduce the iteration time and the images have an obvious increase in performance after thinning the sparse decomposition.(2) An algorithm of QR decomposition random bilateral projection(QR-KRBP) dictionary learning is proposed in this paper. It introduces QR decomposition and random bilateral projection strategy that implement mandatory mode conversion, with good low rank approximation method to get the low rank approximation of error matrix. Those make up for the deficiencies of only using largest singular values and its corresponding singular vectors of the K-SVD algorithm and discarding rest parts. Thus QR-KRBP algorithm could reduce computational complexity and theoretically realize effectiveness. Simulation experiments show that the new algorithm not only cut down operation time, but else have higher performance on sparse representation of video frames.(3) A generalized sparse bayesian learning KSVD(GSBL-KSVD) dictionary learning algorithm is proposed in this paper. It first applies maximum expected algorithm to maximize parameters in likelihood function, then parameters selection determined by loss function, last introduces matrix generalized inverse for calculation. Those eliminate the defects of signal atoms not enough sparse and algorithm none convergence in SBL-KSVD dictionary learning algorithm, all of this reduce the algorithm complexity and theoretically make the algorithm convergence. Experimental results show that the new algorithm has a good performance of sparse learning model, and compared with other optimization algorithms of sparse learning mechanism is more efficient.