Research On The Iterative Algorithm Design And Analysis On The Problem Of Image Restoration

Nowadays, we often use optimal problem in science and engineering fields such as signal processing, image processing. Over the past few decades, the researchers solved the smooth optimization problem very well. However,nonsmooth optimization problems are more common. Using the method of optimization can solve the problem of image processing. It can better reveal the existence of the edge, texture and smoothness of the regional characteristics.We propose a smoothing quadratic regularization method for solving box constrained Non-Lipschitz optimization problem. Firstly, smoothing approximation for the target function, putting forward SQR algorithm and finding the problem of local optimal solution of the necessary conditions; Secondly, and we define an? scaled first order stationary point, then we prove that any cluster point of ? scaled first order stationary point satisfies a first order necessary condition for local minimizer. Next, we analysis the existence of convergence settlement of the algorithm and the iteration complexity of the SQR algorithm for finding an? scaled first order stationary point. Finally, we give the complexity of the algorithm analysis and testing example and show good performance of the SQR algorithm for image restoration.