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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… (More)

In a recent paper [13], Y. Boykov et al. propose an approach for computing curve and surface evolution using a variational approach and the geo-cuts method of Boykov and Kol-mogorov [11]. We recall in this paper how this is related to well-known approaches for mean curvature motion, introduced by F. Almgren et al. [3] and S. Luckhaus and T. Sturzen-hecker… (More)

We propose simple and extremely efficient methods for solving the basis pursuit problem min{{u1 : Au = f, u ∈ R n }, which is used in compressed sensing. Our methods are based on Bregman iterative regularization, and they give a very accurate solution after solving only a very small number of instances of the unconstrained problem min u∈R n μu1 + 1 2 Au − f… (More)

The problem of person recognition and verification based on their hand images has been addressed. The system is based on the images of the right hands of the subjects, captured by a flatbed scanner in an unconstrained pose at 45 dpi. In a pre-processing stage of the algorithm, the silhouettes of hand images are registered to a fixed pose, which involves… (More)

We present an original method to segment color images using a classification in the 3-D color space. In the case of ordinary images, clusters that appear in 3-D histograms usually do not fit a well-known statistical model. For that reason , we propose a classifier that relies on mathematical morphology , and more precisely on the watershed algorithm. We… (More)

Synthetic aperture radar (SAR) images, like other coherent imaging modalities, suffer from speckle noise. The presence of this noise makes the automatic interpretation of images a challenging task and noise reduction is often a prerequisite for successful use of classical image processing algorithms. Numerous approaches have been proposed to filter speckle… (More)

We present an efficient algorithm for nonlocal image filtering with applications in electron cryomicroscopy. Our denoising algorithm is a rewriting of the recently proposed nonlocal mean filter. It builds on the separable property of neighborhood filtering to offer a fast parallel and vectorized implementation in contemporary shared memory computer… (More)

Département TSI 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… (More)

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… (More)