Research On Image Denoising Algorithm Based On Wavelet Sparse Representation

Digital images are often corrupted by noise during the acquisition and transmission process, Image denoising has been an essential part in the field of image processing. Undecimated dual-tree Complex wavelet transform provides a new kind of multi-scale analysis image processing tool, which is the improvement of the standard wavelets and overcome its shortcomings, and has approximate shift-invariance and multi-Directional Selectivity. Moreover the coefficient provides a richer statistical feature information in image analysis. Sparse representation is an emerging signal analysis and synthesis method, its aim is that the dictionary uses as few atoms as possible to represent signal. Sparse representation is widely used and has been successfully applied in the field of image denoising. During the process of sparse representation the noise can be filtered out. This thesis studies image denoising algorithm based on wavelet sparse representation. The main work is as follows:1. We overview the development status of image denoising, and briefly describe the image performance evaluation criteria of image denoising. We briefly introduce the concept of undecimated dual-tree Complex wavelet, and further focus on the advantage and of undecimated dual-tree Complex wavelet transform and the process of the wavelet decomposition and reconstruction.2. Firstly, Using the adaptive and anisoropic Non-Gaussian bivariate statistical model to simulate the statistical distribute of the the real and imaginary parts of coefficient; Then the joint distribution as a prior model is modeled with an adaptive and anisoropic Non-Gaussian bivariate statistical model as well as reflects the dependencies among coefficients. It finally uses a maximum posteriori probability from noise image to estimate the original image wavelet coefficients, so as to achieve the purpose of denoising. A denoising rule based on the adaptive and anisoropic bivariate model on undecimated dual-tree Complex wavelet transform domain is derived from the model. The experimental results demonstrate that the proposed method can obtain better performances.3. The shortcoming of image denoising algorithm based on spatial patch sparse representation is analyzed, image denoising algorithm based on wavelet domain patch sparse representation overcomes the weakness of producing an over-smoothed and artificial image. The sparse representation as a prior of the original image is modeled with the mean square error. A novel image denoising algorithm based on sparse representation is proposed; the simulation results show that the proposed method provides promising results.