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Total Variation Based Oversampling of Noisy Images
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A nonlinear entropic variational model for image filtering
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Convergence of Fixed Point Iteration for Modified Restoration Problems
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An Improved FoE Model for Image Deblurring
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Some First-Order Algorithms for Total Variation Based Image Restoration
Journal of Mathematical Imaging and Vision
A weberized total variation regularization-based image multiplicative noise removal algorithm
EURASIP Journal on Advances in Signal Processing
Generic Self-calibration of Central Cameras from Two Rotational Flows
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SIAM Journal on Scientific Computing
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SIAM Journal on Imaging Sciences
An edge preserving regularization model for image restoration based on hopfield neural network
ISNN'06 Proceedings of the Third international conference on Advnaces in Neural Networks - Volume Part II
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SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
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Linear convergence analysis of the use of gradient projection methods on total variation problems
Computational Optimization and Applications
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Journal of Mathematical Imaging and Vision
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In this paper we show that the lagged diffusivity fixed point algorithm introduced by Vogel and Oman in [ SIAM J. Sci. Comput., 17 (1996), pp. 227--238] to solve the problem of total variation denoising, proposed by Rudin, Osher, and Fatemi in [ Phys. D, 60 (1992), pp. 259--268], is a particular instance of a class of algorithms introduced by Voss and Eckhardt in [ Computing, 25 (1980), pp. 243--251], whose origins can be traced back to Weiszfeld's original work for minimizing a sum of Euclidean lengths [ Tôhoku Math. J., 43 (1937), pp. 355--386]. There have recently appeared several proofs for the convergence of this algorithm [G. Aubert et al., Technical report 94-01, Informatique, Signaux et Systèmes de Sophia Antipolis, 1994], [A. Chambolle and P.-L. Lions, Technical report 9509, CEREMADE, 1995], and [D. C. Dobson and C. R. Vogel, SIAM J. Numer. Anal., 34 (1997), pp. 1779--1791]. Here we present a proof of the global and linear convergence using the framework introduced in [H. Voss and U. Eckhart, Computing, 25 (1980), pp. 243--251] and give a bound for the convergence rate of the fixed point iteration that agrees with our experimental results. These results are also valid for suitable generalizations of the fixed point algorithm.