Two soft-thresholding based iterative algorithms for image deblurring

Iterative regularization algorithms, such as the conjugate gradient algorithm for least squares problems (CGLS) and the modified residual norm steepest descent (MRNSD) algorithm, are popular tools for solving large-scale linear systems arising from image deblurring problems. These algorithms, however, are hindered by a semi-convergence behavior, in that the quality of the computed solution first increases and then decreases. In this paper, in order to overcome the semi-convergence behavior, we propose two iterative algorithms based on soft-thresholding for image deblurring problems. One of them combines CGLS with a denoising technique like soft-thresholding at each iteration and another combines MRNSD with soft-thresholding in a similar way. We prove the convergence of MRNSD and soft-thresholding based algorithm. Numerical results show that the proposed algorithms overcome the semi-convergence behavior and the restoration results are slightly better than those of CGLS and MRNSD with their optimal stopping iterations.