Non-local Functionals Related to the Total Variation and Connections with Image Processing
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We consider multiagent decision making where each agent optimizes its convex cost function subject to individual and coupling constraints. The constraint sets are compact convex subsets of a Euclidean space. To learn Nash equilibria, we propose a novel dis ...
We develop a primal-dual convex minimization framework to solve a class of stochastic convex three-composite problem with a linear operator. We consider the cases where the problem is both convex and strongly convex and analyze the convergence of the propo ...
While phi-divergences have been extensively studied in convex analysis, their use in optimization problems often remains challenging. In this regard, one of the main shortcomings of existing methods is that the minimization of phi-divergences is usually pe ...
We present new results concerning the approximation of the total variation, integral(Omega)vertical bar del u vertical bar, of a function u by non-local, non-convex functionals of the form Lambda delta(u) = integral(Omega)integral(Omega)delta phi(vertical ...
The Mumford-Shah model is a very powerful variational approach for edge preserving regularization of image reconstruction processes. However, it is algorithmically challenging because one has to deal with a non-smooth and non-convex functional. In this pap ...
This paper is devoted to the study of the behavior of the unique solution u delta is an element of H-0(1)(Omega), as delta -> 0, to the equation div(s(delta)A del u(delta)) + k(2)s(0)Sigma u(delta) = s0 f in Omega, where Omega is a smooth connected bounded ...
Reconstruction of images from noisy linear measurements is a core problem in image processing, for which convex optimization methods based on total variation (TV) minimization have been the long-standing state-of-the-art. We present an alternative probabil ...
We introduce a novel generic energy functional that we employ to solve inverse imaging problems within a variational framework. The proposed regularization family, termed as structure tensor total variation (STV), penalizes the eigenvalues of the structure ...
Signals with discontinuities appear in many problems in the applied sciences ranging from mechanics, electrical engineering to biology and medicine. The concrete data acquired are typically discrete, indirect and noisy measurements of some quantities descr ...