Near-optimal phase retrieval of sparse vectors

Afonso Bandeira, Dustin G. Mixon

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In several applications the signal in question is believed to be sparse. In this paper, we use ideas from the recently developed polarization method for phase retrieval and provide an algorithm that is guaranteed to recover a sparse signal from a number of phaseless linear measurements that scales linearly with the sparsity of the signal (up to logarithmic factors). This is particularly remarkable since it is known that a certain popular class of convex methods is not able to perform recovery unless the number of measurements scales with the square of the sparsity of the signal. This is a shorter version of a more complete publication that will appear elsewhere.

Original languageEnglish (US)
Title of host publicationWavelets and Sparsity XV
Volume8858
DOIs
StatePublished - 2013
EventWavelets and Sparsity XV - San Diego, CA, United States
Duration: Aug 26 2013Aug 29 2013

Other

OtherWavelets and Sparsity XV
CountryUnited States
CitySan Diego, CA
Period8/26/138/29/13

Fingerprint

Phase Retrieval
retrieval
Sparsity
Polarization
Logarithmic
Imaging techniques
Recovery
Linearly
recovery
Imaging
polarization

Keywords

  • Angular Synchronization
  • Phase Retrieval
  • Polarization
  • Sparse Recovery

ASJC Scopus subject areas

  • Applied Mathematics
  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Bandeira, A., & Mixon, D. G. (2013). Near-optimal phase retrieval of sparse vectors. In Wavelets and Sparsity XV (Vol. 8858). [88581O] https://doi.org/10.1117/12.2024355

Near-optimal phase retrieval of sparse vectors. / Bandeira, Afonso; Mixon, Dustin G.

Wavelets and Sparsity XV. Vol. 8858 2013. 88581O.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Bandeira, A & Mixon, DG 2013, Near-optimal phase retrieval of sparse vectors. in Wavelets and Sparsity XV. vol. 8858, 88581O, Wavelets and Sparsity XV, San Diego, CA, United States, 8/26/13. https://doi.org/10.1117/12.2024355
Bandeira A, Mixon DG. Near-optimal phase retrieval of sparse vectors. In Wavelets and Sparsity XV. Vol. 8858. 2013. 88581O https://doi.org/10.1117/12.2024355
Bandeira, Afonso ; Mixon, Dustin G. / Near-optimal phase retrieval of sparse vectors. Wavelets and Sparsity XV. Vol. 8858 2013.
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