An Iterative Method with General Convex Fidelity Term for Image Restoration

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 denoising in the presence of Gaussian noise, which use

L

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[1] and

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1

[2] fidelity terms. Iusem-Resmerita [3] proposed a proximal point method using inexact Bregman distance for minimizing a general convex function defined on a general non-reflexive Banach space which is the dual of a separable Banach space. Based on this, we investigate several approaches 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 iterative 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 results to those obtained by one-step gradient descent and similar with other iterative methods.