Research On Signal Sparse Representation Theory And Its Applications

Signal processing plays an important role in various fields nowadays. Especially with theexplosion of information, concise representation of the data has become a hot issue. Sparserepresentation of signals is presented in twentieth Century at the beginning of the nineteen’s,which is a new signal representation method. As part of basic research of signal, it is used inface recognition, image denoising, image restoration, direction of arrival estimation, blindsource separation and other fields.Sparse representation is put forward originally accompanied with a new greedyalgorithm, then continuously improved by the scholars. Various new evaluation criterion anddecomposition algorithm are generated with the research of the mathematical model of sparserepresentation. This paper researched the basic technology of sparse signal representation,mainly about the decomposition algorithm and dictionary learning, and used in classicalimage denoising problems. First, the paper introduced the research status of the sparserepresentation at home and abroad, and stated the main problems and difficulties in theresearch. Then, it gave sparse representation model, metrics and some important theoremsfrom the signal approximation theory.This paper researched the sparse decomposition algorithm based on Lp norm, in whichSL0algorithm implemented sparse method in a new vision. In the ideal conditions with thecontinuous function and control factor involved, the algorithm can solve the Non-convexoptimization problems. In this paper, the main contents are as follows:In the research of SL0algorithm, the paper analyzed the important parameter of thealgorithm, and set the parameters of the algorithm SL0according to the results of theexperiment, and then compared the stable SL0algorithm and other convex optimizationmethods. The experimental results show that the SL0algorithm has advantages in theoperating speed and signal reconstruction quality.After getting a stable SL0algorithm, the paper applied it to the sparse representation inanother important research field, namely the dictionary learning. The K-SVD dictionarylearning algorithm of dictionary learning is more practical because of its low computationcost, but the original algorithm using the OMP algorithm for sparse coding, gives a fixednumber of coefficients, and dictionary quality is inappropriate in a different application, so using SL0algorithm, K-SVD algorithm sparse coding improves code quality. Because ofsparse representation of signal is the essential representation of signal, better able to reflectthe signal characteristics than other representation methods, so it is advisable to use sparserepresentation in image denoising. The specific method is based on the training results ofdictionary, using a maximum a posterior (MAP) estimation method to obtain an estimationresult of the original image, and the denosing image, and contrasted the calculating methodand nonlocal mean filtering denoising method. The experimental results show that imagedenoising algorithm based on the sparse representation has superior quality in denoisingfields.