CWI Inverse Problems Seminar - Palina Salanevich (UU)

Title: Phase retrieval with Gabor frames: stability and reconstruction algorithm

Abstract: Phase retrieval is the non-convex inverse problem of signal reconstruction from intensity measurements with respect to a frame. Even though it has been studied for a long time, until recently very little was known about how to achieve stable and efficient reconstruction, and the existing reconstruction methods lacked rigorous mathematical understanding. Nowadays, the case of a Gaussian measurement frame is sufficiently well studied, but still very little is known in the case of structured frames. In the talk, we are going to discuss the role of frame order statistics in establishing stability of phase retrieval problem in the case of structured measurement frames. For the particular case of Gabor frames with a random window, we will show how bounds on frame order statistics allow to construct an efficient and robust phase retrieval algorithm that uses a close to optimal number of time-frequency structured measurements, and to show reconstruction and robustness guarantees for its performance.