ISPSeminar

**Title:** "On the decomposition of blurring operators in wavelet bases"

**Speaker:** Prof. Pierre Weiss, ITAV, U. Toulouse, France. (**invited talk**)

**Location:** "Shannon" Seminar Room, Place du Levant 3, Maxwell Building, 1st floor

**Date / Time (duration)**: Friday 11/03/2016, 10h45 (~ 45')

**Abstract:** Image deblurring is a fundamental image processing problem usually solved with computationally intensive procedures. After significant progresses due to advances in convex optimization (e.g. accelerated gradient schemes à la Nesterov), this problem however seemingly stalled for the last 5 years. In this talk, I will first provide a few properties of blurring operators (convolutions or more generally regularizing linear integral operators) when expressed in wavelet bases. These properties were one of the initial motivations of Y. Meyer to develop the wavelet theory. Surprisingly, they have been used extremely scarcely in image processing, despite the success of wavelets in that domain. We will then show that those theoretical results may have an important impact on the practical resolution of inverse problems and in particular deblurring. As an example, we will show that they allow gaining from one to two orders of magnitude in the speed of resolution of convex l1-l2 deblurring problems.

**Biography:** Pierre Weiss graduated from INSA de Toulouse in 2004. He received a PhD degree in mathematics and signal processing from the University of Nice-Sophia Antipolis in 2008 and did a post-doc at Hong Kong Baptist University in 2009. From 2010 to 2013 he served as an associate professor at INSA de Toulouse. Since 2013, he is a CNRS researcher at ITAV and IMT. His research interests are in the field of applied mathematics and biomedical imaging, and in particular in the study of algorithms for large scale optimization, inverse problems in imaging, sampling and approximation theory, magnetic resonance imaging (MRI), microscopy and satellite imaging.