New provable non-convex algorithms for generalized phase retrieval

Abstract

This thesis addresses the critical challenge of generalized phase retrieval, which involves reconstructing a length-n signal from phaseless samples—a problem of great importance in fields such as X-ray crystallography, astronomy, quantum mechanics, and diffraction imaging. Despite the development of numerous provable algorithms, significant gaps in the underlying theories persist, particularly regarding convergence rates and practical applicability, especially in the context of the Coded Diffraction Pattern (CDP) model. To address these issues, we propose a unified framework for Riemannian gradient descent methods and introduce the Weighted Riemannian Gradient Descent (WRGD) algorithm, along with the Revised Truncated Amplitude Flow (RTAF) algorithm tailored for the CDP model. Our comprehensive theoretical analysis and numerical experiments demonstrate that these algorithms significantly improve convergence speeds compared to existing methods, thereby enhancing the practical applicability of phase retrieval techniques in signal reconstruction.

Date of Award	2025
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology
Supervisor	Jianfeng CAI (Supervisor) & Yang WANG (Supervisor)