The Dichotomy between Global Processing and Local Modeling
December 7-11, 2015
Berlin, Germany

Recent work in image processing repeatedly shows highly efficient reconstruction algorithms that lean on modeling of small overlapping patches. Such methods impose a local model in order to regularize a global inverse problem. Why does this work so well? Does this leave room for improvements? What does a local model imply globally on the unknown signal? In this talk we will start from algorithmic attempts that aim to understand this dichotomy in order to narrow the global-local gap. Gradually, we will turn the discussion to a theoretical point of view that provides a deeper understanding of such local models, and their global implications.

This was given as a plenary talk in the International Matheon Conference on Compressed-Sensing and its Applications. The talk is based on joint work with Dmitry Batenkov, Jeremias Sulam, Vardan Papyan, and Yaniv Romano.