On non-uniqueness of phase retrieval in multidimensions
Roman Novikov, Tianli Xu
TL;DR
This paper demonstrates extensive non-uniqueness in multidimensional phase retrieval problems, using oblique tensorization and one-dimensional results, including cases with disconnected support.
Contribution
It introduces a broad class of non-uniqueness examples in multidimensional phase retrieval, expanding understanding of when solutions are not unique.
Findings
Examples of non-uniqueness in multidimensional phase retrieval
Use of oblique tensorization for constructing non-unique solutions
Includes functions with disconnected compact support
Abstract
We give a large class of examples of non-uniqueness for the phase retrieval problem in multidimensions. Our constructions are based on "oblique tensorization", where one-dimensional results are strongly used, and its generalizations towards complete description of non-uniqueness. Our examples include the case of functions with strongly disconnected compact support.
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Taxonomy
TopicsAdvanced X-ray Imaging Techniques · X-ray Diffraction in Crystallography