Phasebook: A Survey of Selected Open Problems in Phase Retrieval
Marc Allain, Selin Aslan, Wim Coene, Sjoerd Dirksen, Jonathan Dong, Julien Flamant, Mark Iwen, Felix Krahmer, Tristan van Leeuwen, Oleh Melnyk, Andreas Menzel, Allard P. Mosk, Viktor Nikitin, Gerlind Plonka, Palina Salanevich, Matthias Wellershoff
TL;DR
This survey reviews key open problems in phase retrieval, highlighting its importance in imaging and physics, and discusses recent research directions from a dedicated workshop.
Contribution
It compiles and analyzes critical open questions in phase retrieval, connecting theoretical challenges with practical applications.
Findings
Identified fundamental open problems in phase retrieval
Connected theoretical and practical research directions
Summarized recent workshop discussions on open challenges
Abstract
Phase retrieval is an inverse problem that, on one hand, is crucial in many applications across imaging and physics, and, on the other hand, leads to deep research questions in theoretical signal processing and applied harmonic analysis. This survey paper is an outcome of the recent workshop Phase Retrieval in Mathematics and Applications (PRiMA) (held on August 5--9 2024 at the Lorentz Center in Leiden, The Netherlands) that brought together experts working on theoretical and practical aspects of the phase retrieval problem with the purpose to formulate and explore essential open problems in the field.
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Taxonomy
TopicsX-ray Diffraction in Crystallography