Phase Retrieval in $\ell_2(\RR)$
Sara Botelho-Andrade, Peter G. Casazza, Desai Cheng, John Haas, and, Tin T. Tran
TL;DR
This paper reviews finite-dimensional real phase retrieval results, extends some to infinite dimensions, provides counterexamples, and highlights open problems in the infinite-dimensional setting of b5_2().
Contribution
It extends finite-dimensional phase retrieval results to infinite dimensions, provides counterexamples, and identifies open problems in b5_2().
Findings
Many theorems hold in infinite dimensions.
Counterexamples show some results fail in infinite dimensions.
Finite-dimensional results for b5_2 are still unknown.
Abstract
We will review the major results in finite dimensional real phase retrieval for vectors and projections. We then (1)prove that many of these theorems hold in infinite dimensions, (2) give counter-examples to show that many others fail in infinite dimensions, (3)list finite dimensional results are unknown for .
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Taxonomy
TopicsAdvanced X-ray Imaging Techniques · Advancements in Photolithography Techniques · Advanced Electron Microscopy Techniques and Applications