BCAM Severo Ochoa Course | Phase retrieval as a unified subject

Abstract

I will survey various aspects of the phase retrieval problem, that is, the problem of recovering a function from its absolute value and a collection of a priori constraints. Physically, this problem arises in signal processing, quantum mechanics, crystallography and speech recognition. Mathematically, it is a beautiful subject that connects a remarkable number of fields. 

The course is meant to give a broad but elentary overview of the topic. However, we will also discuss several cutting-edge directions that have recently become available with the use of AI.