An improved iterative regularization algorithm based on varying the singular values

Abstract

We consider the numerical solution of the first kind Fredholm integral equations. Such integral equations occur in signal processing and image recovery problems among others. The common used methods to solve it are Tikhonov regularization and the iterative Tikhonov regularization methods. In this paper, we proposed an improved iterative Tikhonov regularization method. We compares traditional Tikhonov regularization, iterative Tikhonov regularization with our proposed method in numerical experiments. The results indicate that our proposed method can provide a decrease in error of about two orders of magnitude.