Abstract

We propose a convergent iterative regularization procedure based on the square of a dual norm for image restoration with general (quadratic or non-quadratic) convex fidelity terms. Convergent iterative regularization methods have been employed for image deblurring or de- noising in the presence of Gaussian noise, which use L2 [1] and L1 [2] fidelity terms. Iusem-Resmerita [3] proposed a proximal point method using inexact Bregman distance for minimizing a general convex func- tion defined on a general non-reflexive Banach space which is the dual of a separable Banach space. Based on this, we investigate several ap- proaches for image restoration (denoising-deblurring) with different types of noise. We test the behavior of proposed algorithms on synthetic and real images. We compare the results with other state-of-the-art itera- tive procedures as well as the corresponding existing one-step gradient descent implementations. The numerical experiments indicate that the iterative procedure yields high quality reconstructions and superior re- sults to those obtained by one-step gradient descent and similar with other iterative methods.