Research On Image Denoising Based On Sparse Representation

Image denoising is one of the important branches in the field of signal processing. Sparse representation has also attracted researchers' attention recently especially with the development of the new compressed sensing theory. Therefore image denoising based on sparse representation becomes one of the frontier issues in signal processing.The main contributions of this paper are as follows: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 thresholding method which deals with the wavelet coefficients in a point-wise manner. The experimental results show that the algorithm is efficient especially for those signals and images with low signal to noise ratios.An idea of the iterative threshold is introduced to OMP algorithm for signal and image denoising. As the OMP algorithm is only effective for image reconstruction and doesn't have the denoising property, the idea of the iterative threshold is introduced in the iterative process of the OMP algorithm, which could make the reconstructed wavelet coefficients sparser. The experimental results show that the method is efficient for one-dimensional signal denoising.