Iterative Methods For The Application And Study On Image Restoration

Ill-posed inverse problems have aroused in many important applications, which arealways ill-posed, there must use special method to get the stable approximate solutionof this class, as we all known, some regularization techniques are effective tools. Aproblem, if it has unique solution, and its solution continuous with input data, we saythe problem is the well-posed; else it is ill-posed. Ill-posed problems have extensive andimportant application backgrounds; its theory has the distinct novelty and challenging.Image reconstruction problems, which belong to2-D deconvolution problems, have thecharacter of inverse problems.Image is an important way of recording and transmitting useful information. Itplays an critical role in human senses and has pervaded every aspect of engineeringapplications and sciences. During the formation, recording, processing and transmitting,imperfect imaging systems, recording equipments and transmission medium will resultin the degradation of images. Image restoration, which is the reconstruction of theoriginal image from a degrade observation with a priori knowledge of images toimprove the quality of images.The main purpose of this paper is to use better splitting iterative methods to obtaina stable approximate solution of image reconstruction problems, which have fastconvergence behavior. First, the math model for image reconstruction are introduced，and some difficult in the solution of image reconstruction are claimed. Then, manyiteration regularization methods and some methods of choosing regularizationparameters are introduced. At last, based on the splitting iterative method, a specialHermitian and skew-Hermitian splitting(NSHSS) iterative method is established forsolving the linear systems from image restoration, while the convergence and operationcost of the NSHSS iterative method are discussed. The spectral radius of the iterationmatrix is derived.NSHSS algorithm are also given in this paper. Numerical experiments are madeand fully analyzed the results, they shown that the NSHSS iterative method for solvingthe linear systems from image restoration adopted in this paper is effective and feasible. Proved the advantages of the method by compared it to the SHSS iterative method andHSS iterative method.