Marc Sigelle

The use of levelable regularization functions for MRF restoration of SAR images

Abstract

It is well-known that Total Variation (TV) minimization with L2 data fidelity terms (which corresponds to white Gaussian additive noise) yields a restored image which presents some loss of contrast. The same behavior occurs for TVmodels with non-convex data fidelity terms that represent speckle noise. In this note we propose a new approach to cope with the restoration of Synthetic Aperture Radar images while preserving the contrast.

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A note on nice-levelable MRFs for SAR image denoising with contrast preservation

Abstract

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Image restoration with discrete constrained Total Variation—part I: Fast and exact optimization

Abstract

This paper deals with the total variation minimization problem in image restoration for convex data fidelity functionals. We propose a new and fast algorithm which computes an exact solution in the discrete framework. Our method relies on the decomposition of an image into its level sets. It maps the original problems into independent binary Markov Random Field optimization problems at each level. Exact solutions of these binary problems are found thanks to minimum cost cut techniques in graphs. These binary solutions are proved to be monotone increasing with levels and yield thus an exact solution of the discrete original problem. Furthermore we show that minimization of total variation under $L^1$ data fidelity term yields a self-dual contrast invariant filter. Finally we present some results.

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Image restoration with discrete constrained Total Variation—part II: Levelable functions, convex priors and non-convex case

Abstract

In Part II of this paper we extend the results obtained in Part I for total variation minimization in image restoration towards the following directions: first we investigate the decomposability property of energies on levels, which leads us to introduce the concept of levelable regularization functions (which TV is the paradigm of). We show that convex levelable posterior energies can be minimized exactly using the level-independant cut optimization scheme seen in part I. Next we extend this graph cut scheme optimization scheme to the case of non-convex levelable energies. We present convincing restoration results for images corrupted with impulsive noise. We also provide a minimum-cost based algorithm which computes a global minimizer for Markov Random Field with convex priors. Last we show that non-levelable models with convex local conditional posterior energies such as the class of generalized gaussian models can be exactly minimized with a generalized coupled Simulated Annealing.

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Fast and exact discrete image restoration based on total variation and on its extensions to levelable potentials

Abstract

We investigate the decomposition property of posterior restoration energies on level sets in a discrete Markov Random Field framework. This leads us to the concept of ’levelable’ potentials (which TV is shown to be the paradigm of). We prove that convex levelable posterior energies can be minimized exactly with level-independant binary graph cuts. We extend this scheme to the case of non-convex levelable energies, and present convincing restoration results for images degraded by impulsive noise.

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A fast and exact algorithm for total variation minimization

Abstract

This paper deals with the minimization of the total variation under a convex data fidelity term. We propose an algorithm which computes an exact minimizer of this problem. The method relies on the decomposition of an image into its level sets. Using these level sets, we map the problem into optimizations of independent binary Markov Random Fields. Binary solutions are found thanks to graph-cut techniques and we show how to derive a fast algorithm. We also study the special case when the fidelity term is the $L^1$-norm. Finally we provide some experiments.

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A fast and exact algorithm for total variation minimization

Abstract

This paper deals with the minimization of the total variation under a convex data fidelity term. We propose an algorithm which computes an exact minimizer of this problem. The method relies on the decomposition of an image into its level sets. Using these level sets, we map the problem into optimizations of independent binary Markov Random Fields. Binary solutions are found thanks to graph-cut techniques and we show how to derive a fast algorithm. We also study the special case when the fidelity term is the $L^1$-norm. Finally we provide some experiments.

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Exact optimization of discrete constrained total variation minimization problems

Abstract

This paper deals with the total variation minimization problem when the fidelity is either the $L^2$-norm or the $L^1$-norm. We propose an algorithm which computes the exact solution of these two problems after discretization. Our method relies on the decomposition of an image into its level sets. It maps the original problems into independent binary Markov Random Field optimization problems associated with each level set. Exact solutions of these binary problems are found thanks to minimum-cut techniques. We prove that these binary solutions are increasing and thus allow to reconstruct the solution of the original problems.

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Exact optimization of discrete constrained total variation minimization problems

Abstract

This paper deals with the total variation minimization problem when the fidelity is either the $L^2$-norm or the $L^1$-norm. We propose an algorithm which computes the exact solution of these two problems after discretization. Our method relies on the decomposition of an image into its level sets. It maps the original problems into independent binary Markov Random Field optimization problems associated with each level set. Exact solutions of these binary problems are found thanks to minimum-cut techniques. We prove that these binary solutions are increasing and thus allow to reconstruct the solution of the original problems.

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