The Application Of The Regularization Method In Image Restoration

The image is a representation of the objective object. The digital image iscomposed of a finite number of elements, each element called pixel has a special placeand value. Any image acquired by optical or electronic means is likely to be degradedby the sensing environment, a degraded image is often a blurry and noisy image. Imagerestoration is one most important and basic research topic of the digital imageprocessing. The goal of image restoration is to reconstruct or recover an image using apriori knowledge about the degradation. The discretization model of image restoration isdescribed as g=Af+ε, image restoration is a ill-posed problem. Because of theinterference of noise standard methods solving image restoration exhibit an interesting"semiconvergence" behavior, so the solution is not ideal.In this paper, the characteristic of the image restoration model is discussed, manyregularization methods are considered to compute a slightly stabilized and ideal solutionfor image restoration which is less sensitive to errors. regularization methods is dividedinto direct regularization methods and iterative regularization methods. Some effectiveand reliable regularization methods solving digital image restoration are studied in thispaper.We consider the implementation of the LSMR method for computing anapproximate solution of an ill-posed problem arising from image restoration. Whenequipped with a stopping rule based on the discrepancy principle, the LSMR methodacts as a regularization method. The numerical examples illustrate that the LSMRmethod is able to give restored images of higher quality with less computational effortthan the other widely used regularization method.An SOR-like method for ill-posed problems from image restoration is presented.We discuss the convergence and give the choice of the relaxation parameter for theproposed method. Finally, some numerical examples are given to illustrate theeffectiveness of the SOR-like method.