An iterative method with general convex fidelity term for image restoration

Authors:
Miyoun Jung;Elena Resmerita;Luminita Vese
Affiliations:
Department of Mathematics, University of California, Los Angeles and Industrial Mathematics Institute, Johannes Kepler University, Linz, Austria;Department of Mathematics, University of California, Los Angeles and Industrial Mathematics Institute, Johannes Kepler University, Linz, Austria;Department of Mathematics, University of California, Los Angeles and Industrial Mathematics Institute, Johannes Kepler University, Linz, Austria
Venue:
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part I
Year:
2010

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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 denoising 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 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.