Epigraphical splitting of convex constraints. Application to image recovery, supervised classification, and image forgery detection. (2015)
Abstract / truncated to 115 words
In this thesis, we present a convex optimization approach to address three problems arising in multicomponent image recovery, supervised classification, and image forgery detection. The common thread among these problems is the presence of nonlinear convex constraints difficult to handle with state-of-the-art methods. Therefore, we present a novel splitting technique to simplify the management of such constraints. Relying on this approach, we also propose some contributions that are tailored to the aforementioned applications. The first part of the thesis presents the epigraphical splitting of nonlinear convex constraints. The principle is to decompose the sublevel set of a block-separable function into a collection of epigraphs. So doing, we reduce the complexity of optimization algorithms when the ... toggle 9 keywordsconvex optimization – proximal methods – nonlinear constraints – multicomponent image restoration – nonlocal structure tensor – supervised classification – support vector machine – image forgery detection – PRNU.
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