Two New Efficient Iterative Regularization Methods for Image Restoration Problems

Abstract

Iterative regularization methods are efficient regularization tools for image restoration problems. The IDR($s$) and LSMR methods are state-of-the-arts iterative methods for solving large linear systems. Recently, they have attracted considerable attention. Little is known of them as iterative regularization methods for image restoration. In this paper, we study the regularization properties of the IDR($s$) and LSMR methods for image restoration problems. Comparative numerical experiments show that IDR($s$) can give a satisfactory solution with much less computational cost in some situations than the classic method LSQR when the discrepancy principle is used as a stopping criterion. Compared to LSQR, LSMR usually produces a more accurate solution by using the $L$-curve method to choose the regularization parameter.