Title: Structured measurements in phase retrieval: theory and challenges
Abstract: Phase retrieval is the task of reconstructing a signal or object when only the magnitudes of certain measurements are available and all phase information is lost. This challenge appears throughout science and engineering—from X-ray crystallography to audio processing and modern imaging technologies. In many practical situations, these measurements are not arbitrary but come with additional structure.
In this talk, we explore phase retrieval when the data arise from time–frequency–localized measurements, specifically those coming from the short-time Fourier transform (STFT). I will explain why this setting is both natural and useful, describe what makes recovery difficult, and present recent progress on understanding when unique and stable reconstruction is possible. Along the way, we will see how tools from harmonic and complex analysis, signal processing, and inverse problems interact to reveal both fundamental limitations and promising strategies for overcoming them.