Representing the solutions of total variation regularized problems

Abstract: Representing the solutions of total variation regularized problems

The total (gradient) variation is a regularizer which has been widely used in inverse problems arising in image processing, following the pioneering work of Rudin, Osher and Fatemi. In this talk, I will describe the structure the solutions to the total variation regularized variational problems when one has a finite number of measurements. First, I will present a general representation principle for the solutions of convex problems, then I will apply it to the total variation by describing the faces of its unit ball.

It is a joint work with Claire Boyer, Antonin Chambolle, Yohann De Castro, Frédéric de Gournay and Pierre Weiss.

analysis of PDEsfunctional analysisgeneral mathematicsnumerical analysisoptimization and controlprobabilitystatistics theory

Audience: researchers in the topic

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One World seminar: Mathematical Methods for Arbitrary Data Sources (MADS)

Series comments: Description: Research seminar on mathematics for data

The lecture series will collect talks on mathematical disciplines related to all kind of data, ranging from statistics and machine learning to model-based approaches and inverse problems. Each pair of talks will address a specific direction, e.g., a NoMADS session related to nonlocal approaches or a DeepMADS session related to deep learning.

Approximately 15 minutes prior to the beginning of the lecture, a zoom link will be provided on the official website and via mailing list. For further details please visit our webpage.

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