Nonlinear total variation based noise removal algorithms
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Iterative Total Variation Regularization with Non-Quadratic Fidelity
Journal of Mathematical Imaging and Vision
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Numerical Optimization: Theoretical and Practical Aspects (Universitext)
A Variational Approach to Reconstructing Images Corrupted by Poisson Noise
Journal of Mathematical Imaging and Vision
Error estimation for Bregman iterations and inverse scale space methods in image restoration
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Some First-Order Algorithms for Total Variation Based Image Restoration
Journal of Mathematical Imaging and Vision
Total Variation Processing of Images with Poisson Statistics
CAIP '09 Proceedings of the 13th International Conference on Computer Analysis of Images and Patterns
Fast numerical algorithms for total variation based image restoration
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SIAM Journal on Scientific Computing
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IEEE Transactions on Image Processing
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An iterative method with general convex fidelity term for image restoration
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part I
Variational Methods in Imaging
Variational Methods in Imaging
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
Journal of Mathematical Imaging and Vision
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A convergent iterative regularization procedure based on the square of a dual norm is introduced for image restoration models with general (quadratic or non-quadratic) convex fidelity terms. Iterative regularization methods have been previously employed for image deblurring or denoising in the presence of Gaussian noise, which use L 2 (Tadmor et al. in Multiscale Model. Simul. 2:554---579, 2004; Osher et al. in Multiscale Model. Simul. 4:460---489, 2005; Tadmor et al. in Commun. Math. Sci. 6(2):281---307, 2008), and L 1 (He et al. in J. Math. Imaging Vis. 26:167---184, 2005) data fidelity terms, with rigorous convergence results. Recently, Iusem and Resmerita (Set-Valued Var. Anal. 18(1):109---120, 2010) proposed a proximal point method using inexact Bregman distance for minimizing a convex function defined on a non-reflexive Banach space (e.g. BV(驴)), which is the dual of a separable Banach space. Based on this method, we investigate several approaches for image restoration such as image deblurring in the presence of noise or image deblurring via (cartoon+texture) decomposition. We show that the resulting proximal point algorithms approximate stably a true image. For image denoising-deblurring we consider Gaussian, Laplace, and Poisson noise models with the corresponding convex fidelity terms as in the Bayesian approach. We test the behavior of proposed algorithms on synthetic and real images in several numerical experiments and compare the results with other state-of-the-art iterative procedures based on the total variation penalization 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 standard gradient descent, with faster computational time.