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 2  and L 1  fidelity terms. Iusem-Resmerita  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.
KeywordsImage Restoration General Convex Separable Banach Space Proximal Point Algorithm Proximal Point Method
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- 8.Benning, M., Burger, M.: Error estimates for variational models with non-gaussian noise. UCLA CAM Report 09-40 (2009)Google Scholar
- 10.Marques, A.M., Svaiter, B.: On the surjectivity properties of perturbations of maximal monotone operators in non-reflexive banach spaces (to be published)Google Scholar
- 12.Pöschl, C.: Regularization with a similarity measure. PhD Thesis, University of Innsbruc (2008)Google Scholar
- 13.Jung, M., Resmerita, E., Vese, L.: Dual norm based iterative methods for image restoration. UCLA C.A.M. Report 09-88 (2009)Google Scholar
- 14.Rudin, L., Osher, S.: Total variation based image restoration with free local constraints. IEEE ICIP, 31–35 (1994)Google Scholar
- 15.Burger, M., Resmerita, E., He, L.: Error estimation for bregman iterations and inverse scale space methods in image restoration. Computing (81)Google Scholar
- 17.Attouch, H., Buttazzo, G., Michaille, G.: Variational analysis in Sobolev and BV spaces (2006)Google Scholar