# An Algorithm for Total Variation Minimization and Applications

@article{Chambolle2004AnAF, title={An Algorithm for Total Variation Minimization and Applications}, author={A. Chambolle}, journal={Journal of Mathematical Imaging and Vision}, year={2004}, volume={20}, pages={89-97} }

We propose an algorithm for minimizing the total variation of an image, and provide a proof of convergence. We show applications to image denoising, zooming, and the computation of the mean curvature motion of interfaces.

## 1,115 Citations

TOTAL VARIATION MINIMIZATION WITH AN H − 1 CONSTRAINT

- Mathematics
- 2009

This paper is concerned with the numerical minimization of total variation functionals with an H constraint. We present an algorithm for its solution which is based on the dual formulation of the…

Exact solutions for the denoising problem of piecewise constant images in dimension one

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In this paper we propose a method to determine explicitly the solution of the total variation denoising problem with an $L^p$ fidelity term, where $p>1$, for piecewise constant initial data in…

On Semismooth Newton’s Methods for Total Variation Minimization

- MathematicsJournal of Mathematical Imaging and Vision
- 2007

Based on the theory on semismooth operators,Semismooth Newton’s methods for total variation minimization are studied to show the effectiveness of the proposed algorithms.

AN ERROR ESTIMATE IN IMAGE PROCESSING

- Computer Science
- 2012

A new interpolation error estimate for a finite element method for image processing is proved and the numerical trials run confirm the accuracy of the restoration algorithm.

Total variational image denoising. Influence of noise distribution: Comparison analysis

- Mathematics2010 IEEE 9th International Conference on Cyberntic Intelligent Systems
- 2010

In this paper we review the total variation image denoising schemes and highlight the various approaches to tune the employed regularization parameters. An experimental set-up, which uses both the…

A Primal-Dual Approach for a Total Variation Wasserstein Flow

- MathematicsGSI
- 2013

A nonlinear fourth-order diffusion equation that arises in denoising of image densities is considered and an implicit time-stepping scheme that employs a primal-dual method for computing the subgradient of the total variation seminorm is proposed.

A Variational Model for Image Texture Identification

- Mathematics, Computer Science
- 2010

A second order variational model is tested to extract texture from an image and a fixed point algorithm is proposed to solve the discretized problem.

ITERATIVE SOLUTION OF A CONSTRAINED TOTAL VARIATION REGULARIZED MODEL PROBLEM

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The discretization of a bilaterally constrained total variation minimization problem with conforming low order finite elements is analyzed and three iterative schemes are proposed which differ in the…

A VARIATIONAL APPROACH TO REMOVE MULTIPLICATIVE NOISE

- Mathematics, Computer Science
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A functional is derived whose minimizer corresponds to the denoised image the authors want to recover and the existence of a minimizer is proved, and the capability of the model is shown on some numerical examples.

Restoration and Zoom of Irregularly Sampled, Blurred, and Noisy Images by Accurate Total Variation Minimization with Local Constraints

- GeologyMultiscale Model. Simul.
- 2006

We propose an algorithm to solve a problem in image restoration which considers several different aspects of it, namely irregular sampling, denoising, deconvolution, and zooming. Our algorithm is b...

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