Constrained Convex Neyman-Pearson Classification Using an Outer Approximation Splitting Method

This paper presents an algorithm for Neyman-Pearson classification. While empirical riskminimization approaches focus on minimizing a global risk, the Neyman-Pearson frameworkminimizes the type II risk under an upper bound constraint on the type I risk. Sincethe 0=1 loss function is not convex, optimization methods employ convex surrogates thatlead to tractable minimization problems. As shown in recent work, statistical bounds canbe derived to quantify the cost of using such surrogates instead of the exact 1/0 loss.However, no specific algorithm has yet been proposed to actually solve the resulting minimizationproblem numerically. The contribution of this paper is to propose an efficientsplitting algorithm to address this issue. Our method alternates a gradient step on the objectivesurrogate risk and an approximate projection step onto the constraint set, which isimplemented by means of an outer approximation subgradient projection algorithm. Experimentson both synthetic data and biological data show the efficiency of the proposed method

Proximal method for geometry and texture image decomposition

International audienceWe propose a variational method for decomposing an image into a geometry and a texture component. Our model involves the sum of two functions promoting separately properties of each component, and of a coupling function modeling the interaction between the components. None of these functions is required to be differentiable, which significantly broadens the range of decompositions achievable through variational approaches. The convergence of the proposed proximal algorithm is guaranteed under suitable assumptions. Numerical examples are provided that show an application of the algorithm to image decomposition and restoration in the presence of Poisson noise

Proximal algorithms for multicomponent image recovery problems

International audienceIn recent years, proximal splitting algorithms have been applied to various monocomponent signal and image recovery problems. In this paper, we address the case of multicomponent problems. We first provide closed form expressions for several important multicomponent proximity operators and then derive extensions of existing proximal algorithms to the multicomponent setting. These results are applied to stereoscopic image recovery, multispectral image denoising, and image decomposition into texture and geometry components

Iterative image deconvolution using overcomplete representations

electronic version (5 pp.)International audienceWe consider the problem of deconvolving an image with a priori information on its representation in a frame. Our variational approach consists of minimizing the sum of a residual energy and a separable term penalizing each frame coef - cient individually. This penalization term may model various properties, in particular sparsity. A general iterative method is proposed and its convergence is established. The novelty of this work is to extend existing methods on two distinct fronts. First, a broad class of convex functions are allowed in the penalization term which, in turn, yields a new class of soft thresholding schemes. Second, while existing results are restricted to orthonormal bases, our algorithmic framework is applicable to much more general overcomplete representations. Numerical simulations are provided

Algorithmes de projections convexes généralisées et applications en imagerie médicale

PARIS-BIUSJ-Thèses (751052125) / SudocPARIS-BIUSJ-Physique recherche (751052113) / SudocPARIS-BIUSJ-Mathématiques rech (751052111) / SudocSudocFranceF

Estimating first-order finite-difference information in image restoration problems

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Image deconvolution with total variation bounds

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Estimating first-order finite-difference information in image restoration problems

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