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- Antonin Chambolle, Thomas Pock
- Journal of Mathematical Imaging and Vision
- 2010

In this paper we study a first-order primal-dual algorithm for non-smooth convex optimization problems with known saddle-point structure. We prove convergence to a saddle-point with rate O(1/N) inâ€¦ (More)

- Antonin Chambolle
- Journal of Mathematical Imaging and Vision
- 2004

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 curvatureâ€¦ (More)

We study here a classical image denoising technique introduced by L. Rudin and S. Osher a few years ago, namely the constrained minimization of the total variation (TV) of the image. First, we giveâ€¦ (More)

- Antonin Chambolle
- EMMCVPR
- 2005

We observe that there is a strong connection between a whole class of simple binary MRF models and the Rudin-Osher-Fatemi Total Variation minimization approach to image denoising. This leads to newâ€¦ (More)

- Jean-FranÃ§ois Aujol, Antonin Chambolle
- International Journal of Computer Vision
- 2005

Following a recent work by Y. Meyer, decomposition models into a geometrical component and a textured component have recently been proposed in image processing. In such approaches, negative Sobolevâ€¦ (More)

- Thomas Pock, Antonin Chambolle
- 2011 International Conference on Computer Vision
- 2011

In this paper we study preconditioning techniques for the first-order primal-dual algorithm proposed in [5]. In particular, we propose simple and easy to compute diagonal preconditioners for whichâ€¦ (More)

- Antonin Chambolle, Ronald A. DeVore, Nam-Yong Lee, Bradley J. Lucier
- IEEE Trans. Image Processing
- 1998

This paper examines the relationship between wavelet-based image processing algorithms and variational problems. Algorithms are derived as exact or approximate minimizers of variational problems; inâ€¦ (More)

- Thomas Pock, Antonin Chambolle, Daniel Cremers, Horst Bischof
- 2009 IEEE Conference on Computer Vision andâ€¦
- 2009

In this work we propose a convex relaxation approach for computing minimal partitions. Our approach is based on rewriting the minimal partition problem (also known as Potts model) in terms of aâ€¦ (More)

- Jean-FranÃ§ois Aujol, Gilles Aubert, Laure Blanc-FÃ©raud, Antonin Chambolle
- Journal of Mathematical Imaging and Vision
- 2005

We construct an algorithm to split an image into a sum u + v of a bounded variation component and a component containing the textures and the noise. This decomposition is inspired from a recent workâ€¦ (More)

- Antonin Chambolle, Thomas Pock
- Math. Program.
- 2016

We revisit the proofs of convergence for a first order primal-dual algorithm for convex optimization which we have studied a few years ago. In particular, we prove rates of convergence for a moreâ€¦ (More)