Fast Image Processing Algorithms Based On Sparse Representation

Image restoration is a typical ill-posed inverse problem. In-painting, de-noising and de-blurring are the main contents in image restoration area. And the restore quality and speed also become a hotspot and difficulty. Since Mallet proposed the sparse representation theory, convex optimization model which based on sparse representation has become one of the most effective methods to solve the problem of image restoration. Total variation norm becomes the minimum calculation complexity sparse representation method for holding the edge of the image. How to use sparse regularization and total variation regularization model fast recover high-quality images is the field of research focus in recent years. Fixed point iteration is a class of efficient and effective methods for solving sparse representation convex optimization model, which consists of the forward gradient descent step and backward shrinkage threshold step. Although the method has achieved success, the recovery quality and speed still need to be improved.Recent years, fast iterative threshold shrinkage algorithm (FISTA) and alternating direction multiplier method (ADMM) have achieved a great success in accelerating the speed of machine learning and training. In this paper, FISTA and ADMM algorithm were used to accelerate the solution process of optimization model, and simultaneously improve the recovery quality. Two innovation points of this paper is as follows:(1) FISTA acceleration method was applied to wavelet sparse representation regularization image restoration model; the convergence can be obtained I/k2theoretically. Experimental results demonstrate the present algorithm is fast, and improves the quality of image restoration at the same time. When dealing with the backward threshold step, we propose a new dynamic threshold strategy. Experiments show that the proposed method has better results in the same number of iterations.(2) Using total variation (TV) sparse representation regularization to de-noising and in-painting, forward backward splitting method and alternative direction multiplier method were used to solve. Since fixed step size can not be both fast and convergence, we proposed variable step method. The method can quickly converge to the nearby of the ideal solution with long step, then apply short step to approach optimal solution, to achieve the purpose of fast convergence. In solving process. FISTA was used to accelerate. Experimental results show that variable step size algorithm greatly improves the convergence of the algorithm, and significantly improves the restoration quality (PSNR).