Sparse signal recovery from a mixture of linear and magnitude-only measurements

Mehmet Akçakaya, Vahid Tarokh

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We consider the problem of exact sparse signal recovery from a combination of linear and magnitude-only (phaseless) measurements. A k-sparse signal x in ∈ ℂn is measured as r = Bx and y = |Cx|, where B in ∈ ℂm1 × n and ∈ ℂm2 × n are measurement matrices and |·| is the element-wise absolute value. We show that if max(2m1,1) + m2 ≥ 4k - 1, then a set of generic measurements are sufficient to recover every k-sparse x exactly, establishing the trade-off between the number of linear and magnitude-only measurements.

Original languageEnglish (US)
Article number7010925
Pages (from-to)1220-1223
Number of pages4
JournalIEEE Signal Processing Letters
Volume22
Issue number9
DOIs
StatePublished - Sep 1 2015

Bibliographical note

Publisher Copyright:
© 2015 IEEE.

Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

Keywords

  • Compressed sensing
  • Phase retrieval
  • Sparse phase retrieval
  • Sparse signals

Fingerprint Dive into the research topics of 'Sparse signal recovery from a mixture of linear and magnitude-only measurements'. Together they form a unique fingerprint.

Cite this