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pro vyhledávání: '"Duval, Vincent"'
In this work we analyze the Total Variation-Wasserstein minimization problem. We propose an alternative form of deriving optimality conditions from the approach of Calier\&Poon'18, and as result obtain further regularity for the quantities involved.
Externí odkaz:
http://arxiv.org/abs/2308.10753
This work is concerned with the recovery of piecewise constant images from noisy linear measurements. We study the noise robustness of a variational reconstruction method, which is based on total (gradient) variation regularization. We show that, if
Externí odkaz:
http://arxiv.org/abs/2307.03709
We propose a variational approach to approximate measures with measures uniformly distributed over a 1 dimentional set. The problem consists in minimizing a Wasserstein distance as a data term with a regularization given by the length of the support.
Externí odkaz:
http://arxiv.org/abs/2304.14781
Autor:
Duval, Vincent, Tovey, Robert
In this work we consider algorithms for reconstructing time-varying data into a finite sum of discrete trajectories, alternatively, an off-the-grid sparse-spikes decomposition which is continuous in time. Recent work showed that this decomposition wa
Externí odkaz:
http://arxiv.org/abs/2112.11378
We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed mesh, our
Externí odkaz:
http://arxiv.org/abs/2104.06706
Autor:
Duval, Vincent
Describing the solutions of inverse problems arising in signal or image processing is an important issue both for theoretical and numerical purposes. We propose a principle which describes the solutions to convex variational problems involving a fini
Externí odkaz:
http://arxiv.org/abs/1912.13224
Akademický článek
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Akademický článek
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Autor:
Boyer, Claire, Chambolle, Antonin, de Castro, Yohann, Duval, Vincent, de Gournay, Frédéric, Weiss, Pierre
We establish a result which states that regularizing an inverse problem with the gauge of a convex set $C$ yields solutions which are linear combinations of a few extreme points or elements of the extreme rays of $C$. These can be understood as the \
Externí odkaz:
http://arxiv.org/abs/1812.04355
This paper showcases the theoretical and numerical performance of the Sliding Frank-Wolfe, which is a novel optimization algorithm to solve the BLASSO sparse spikes super-resolution problem. The BLASSO is a continuous (i.e. off-the-grid or grid-less)
Externí odkaz:
http://arxiv.org/abs/1811.06416