Research On Image Restoration With Rician Noise Via Sparse Representation

Noisy image restoration problem is one of the most active research topics in the areas of applied mathematics and image processing. From the point of view of the whole image analysis, image restoration aims to preprocess the noisy images and improve the quality of images for further image processing. The key of noisy image restoration is to retain the edges and details of image in denoising. Recently, with the development of nuclear magnetic resonance technology, Rican noise removing in Magnetic Resonance Image(MRI) attracts more and more researchers’ attention and a series of methods of removing the Rician noise has been proposed. To address the image restoration problem with Rician noise, this dissertation presents some novel denoising approaches to improve the existing algorithms and achieves superior denoising performance.The dissertation involves five chapters. The first two chapters are the introduction and the related work. The fifth Chapter draws the conclusions. The contributions are given in chapter 3 to chapter 4, which mainly contain the following two aspects.Chapter 3 proposes an algorithm of removing the Rician noise based on the Alternating Direction Method of Multipliers(ADMM). ADMM is an effective tool for solving convex optimization and the theory of ADMM algorithm is excellent. Instead of the classic original dual algorithm, this chapter utilizes ADMM to solve the model of removing the Rician noise and obtains better denoising results. To tackle the denoising model, the original problem is firstly transformed into some optimal sub-problems via variable separation method and then ADMM algorithm is performed. The algorithm is theoretically shown to be convergence. The experimental results show the effectiveness of the algorithm.The fourth chapter develops a new model based on sparse representation of Rician noise removing. The sparse feature representation is adopted to replace the regularization term of the original denoising model and the Split-Bregman Iteration algorithm is subsequently employed to solve the new model. We design appropriate dictionary to adapt the sparse model in the process of sparse representation. To obtain suitable dictionary for image restoration, K-SVD algorithm is used to update the dictionary, which describes the image content effectively. The results show that our image restoration method based on sparse feature representation can make the details of image more clearly and the edge more sharpening in the recovery process. Meanwhile, our method is able to avoid the “block” problem encountered in the model with total variation regularization term.