An Adaptive Fixed-point Algorithm For Image Restoration

The Total Variation model proposed by Rudin, ROF Osher and Fatemi is very efficient in image restoration. All the image restoration models promoted from the TV model can be attributed to optimization problems about a composition of two convex functions. Due to the non-smoothness of the objective function, the problem is very difficult to solve. By using the nature of the proximity operator, Micchelli proposed a general fixed point algorithms which can be specialized to many other algorithms. We can also provide a necessary conditions for the convergence of the fixed-point algorithm. It is a powerful tool for us to analyze and improve existing algorithms. Split Bregman algorithm is a famous tool for resolving TV model which used to remove Gause noise. Based on the characteristics of the Split Bregman algorithm, we propose a new algorithm, and then using fixed- point theory to ensure its convergence. At last we improve the algorithm by changing the parameter during the iteration and then using the improved algorithm to remove Gause noise in image.