The Model Of Image Restoration Problem And Research Of The Efficient Iterative Algorithms

Digital image restoration has important applications in many fields,such as medical and astronomical imaging,image and video decoding and computer vision.Image restoration using some prior knowledge of digital image to improve image quality.The digital image restoration problem can be expressed simplified model : b equals Ax.where,A is a blurring matrix,b is the observation image that contaminated by a random noise,x is the unknown true image.Because A is severely ill-conditioned and the noise in b,if solving min||Ax-b||₂² directly,usually only get a huge residual.The general method is to use regularization that less sensitive to noise in b solving image restoration problem.In this paper,studies Tikhonov regularization method and iterative regularization method.This paper first introduces Tikhonov regularization method to solve image restoration problem,and project to the Krylov subspace for image restoration problem and the Iterative Reweighted Norm?IRN?algorithm of solving the general image restoration problem model;second studies the total variation regularization algorithm for solving image restoration problem,presents additive half-quadratic anisotropic regularization algorithm based on generalized Krylov subspace,this is the innovation of the paper;last researches iterative regularization method for solving image restoration problem,include algebraic reconstruction techniques?ART?and simultaneous iterative reconstruction technique?SIRT?.The research work of this paper provides a series of numerical methods for image restoration problem,supplies a theoretical and practical reference for digital image restoration.