Codes and Expansions (CodEx) Seminar


Yousef Qaddura (The Ohio State University):
Stable Weighted Phase Retrieval

The problem of stable weighted phase retrieval can be concisely framed as follows: Given an orthogonal representation of the circle group, find a bilipschitz embedding of its metric quotient. This problem is significant for several reasons. First, it naturally arises in machine learning applications, particularly in Cryogenic Electron Microscopy (Cryo-EM), where it plays a crucial role in data processing. Second, from a mathematical perspective, it represents a logical extension of the standard phase retrieval problem, broadening the framework. Third, it involves the simplest infinite group action, whose bilipschitz invariant theory remains incompletely understood.

In this talk, I will motivate the problem by discussing its connection to Cryo-EM, followed by a sketch of the proof demonstrating that recently proposed max filter invariants satisfy the bilipschitz property.