Wavelet Domain Image Denoising Via Sparse Representation

Image denoising is one of the key problems in image progressing field, which is also the basis of the follow-up processing. According to the character of noise, we have developed many methods, they all have their superiority in their own scope. Among all the above methods, wavelet threshold denoising is the most common one. But it may result in pseudo-Gibbs phenomenon in the discontinuous region and it deal with the wavelet coefficients one by one ignore the whole structure characteristics of the wavelet coefficients. Sparse signals have many excellent properties.In recent years, with the development of sparse representation and compressed sensing theory in the math and application domain, the sparse presentation theory and its application has aroused many researcher's attentions. The main contributions of this paper are as follows:Based on the depth research on the wavelet threshold denoising and sparse representation theory to the deficiencies of wavelet denoising method, combined with the advantages of sparse representation theory. A new wavelet denoising model based on sparse representation is presented. The traditional wavelet denoising problem is converted to an optimization problem. And then the noise-free wavelet coefficients are obtained by solving the optimization problem.The steepest descent method is used to solve the problem above and thus complement the signal and image denoising. This method considers the overall wavelet coefficients as a whole and makes use of the structure properties of the coefficients. It greatly overcomes the shortcomings of the wavelet threshold method which deals with the wavelet coefficients in a point-wise manner.In this paper we first use the proposal mode in one-dimensional signal fields, we get many objective data and visual maps.Experiments results show that the method of one-dimensional noise effect is obviously. On this basis, we combined the characteristics of two-dimensional image, the algorithm is improved in order to make it also useful in two-dimensional image denoising field, experimental results show that this method also has a good performance.