2024/07/01 by Cole Brabec, Sivan Trajtenberg‐Mills, Brabec, Cole +5
Materials Science · Physics and Astronomy · #Advanced X-ray Imaging Techniques #Electron and X-Ray Spectroscopy Techniques #FOS: Electrical engineering #Image and Video Processing (eess.IV) #Nuclear Physics and Applications #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2407.01350
openalex publication_date 2024/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present the first phase retrieval algorithm guaranteed to solve the multidimensional phase retrieval problem in polynomial arithmetic complexity without prior information. The method successfully terminates in O(N log(N)) operations for Fourier measurements with cardinality N. The algorithm is guaranteed to succeed for a large class of objects, which we term "Schwarz objects". We further present an easy-to-calculate and well-conditioned diagonal operator that transforms any feasible phase-retrieval instance into one that is solved by our method. We derive our method by combining techniques from classical complex analysis, algebraic topology, and modern numerical analysis. Concretely, we pose the phase retrieval problem as a multiplicative Cousin problem, construct an approximate solution using a modified integral used for the Schwarz problem, and refine the approximate solution to an exact solution via standard optimization methods. We present numerical experimentation demonstrating our algorithm's performance and its superiority to existing method. Finally, we demonstrate that our method is robust against Gaussian noise.