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Computer Science > Information Theory

arXiv:1403.1458 (cs)
[Submitted on 6 Mar 2014 (v1), last revised 7 Mar 2014 (this version, v2)]

Title:Phase Transitions in Phase Retrieval

Authors:Dustin G. Mixon
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Abstract:Consider a scenario in which an unknown signal is transformed by a known linear operator, and then the pointwise absolute value of the unknown output function is reported. This scenario appears in several applications, and the goal is to recover the unknown signal -- this is called phase retrieval. Phase retrieval has been a popular subject of research in the last few years, both in determining whether complete information is available with a given linear operator, and in finding efficient and stable phase retrieval algorithms in the cases where complete information is available. Interestingly, there are a few ways to measure information completeness, and each way appears to be governed by a phase transition of sorts. This chapter will survey the state of the art with some of these phase transitions, and identify a few open problems for further research.
Comments: Book chapter, survey of recent literature, submitted to Excursions in Harmonic Analysis: The February Fourier Talks at the Norbert Wiener Center
Subjects: Information Theory (cs.IT); Algebraic Geometry (math.AG); Functional Analysis (math.FA)
Cite as: arXiv:1403.1458 [cs.IT]
  (or arXiv:1403.1458v2 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.1403.1458

Submission history

From: Dustin Mixon [view email]
[v1] Thu, 6 Mar 2014 14:49:03 UTC (42 KB)
[v2] Fri, 7 Mar 2014 13:25:00 UTC (42 KB)
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