Abstract

In this talk, I will present recent results regarding the geometry of solutions of inverse problems regularized by a convex regularizer. I will give a particular attention to the case of convex gauges, including all l1 analysis or synthesis priors (e.g. l1 norm, total variation, TGV), both in a discrete and in a continuous setting. We will see that the geometry is mostly determined by the extreme points of the unit ball associated to the gauge. This yields a lot of insight on when a convex regularizer is adapted to a given task.

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