Romain Petit
Speaker: Romain Petit (Malga, Gênes)
https://rpetit.github.io
Title: Reconstruction of piecewise constant images via total (gradient) variation regularization
Abstract:
In this talk, I will consider the reconstruction of some unknown image from noisy linear measurements using total (gradient) variation regularization. Empirical evidence and theoretical results suggest that this method is particularly well suited to recover piecewise constant images. It is therefore natural to study the case where the unknown image has precisely this structure. I will present two works on this topic, which are collaborations with Yohann De Castro and Vincent Duval. The first concerns a noise robustness result, stating that, in a low noise regime, the reconstruction is also piecewise constant, and one exactly recovers the number of shapes in the unknown image. The second is about introducing a new numerical method for solving the variational regularization problem. Its main feature is that it does not rely on the introduction of a fixed spatial discretization (e.g. a pixel grid), and builds a sequence of iterates that are linear combinations of indicator functions.