Phase Recovery: Very New Results on a Very Old Problem

Program Description

The phase recovery problem is at the core of diffraction imaging techniques. It is usually solved using greedy algorithms without any convergence guarantees or stability results. Very recently however, it was shown that efficient algorithms derived for the collaborative filtering (NETFLIX) problem could be directly adapted to the phasing problem. These methods formulate phase recovery as a convex program, which can be solved efficiently. The key to their performance on molecular imaging problems is the availability of several randomly coded diffraction patterns extracted from a single molecule. We will present several numerical experiments on imaging problems and discuss open questions related to their implementation.

Joint work with Fajwel Fogel, Irène Waldspurger and Stéphane Mallat