Phase recovery, MaxCut and complex semidefinite programming
Phase retrieval seeks to recover a signal x ∈ C p from the amplitude | A x | of linear measurements A x ∈ C n . We cast the phase retrieval problem as a non-convex quadratic program over a complex phase vector and formulate a tractable relaxation (called PhaseCut ) similar to the classical MaxCut se...
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| Vydané v: | Mathematical programming Ročník 149; číslo 1-2; s. 47 - 81 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.02.2015
Springer Nature B.V |
| Predmet: | |
| ISSN: | 0025-5610, 1436-4646 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | Phase retrieval seeks to recover a signal
x
∈
C
p
from the amplitude
|
A
x
|
of linear measurements
A
x
∈
C
n
. We cast the phase retrieval problem as a non-convex quadratic program over a complex phase vector and formulate a tractable relaxation (called
PhaseCut
) similar to the classical
MaxCut
semidefinite program. We solve this problem using a provably convergent block coordinate descent algorithm whose structure is similar to that of the original greedy algorithm in Gerchberg and Saxton (Optik 35:237–246,
1972
), where each iteration is a matrix vector product. Numerical results show the performance of this approach over three different phase retrieval problems, in comparison with greedy phase retrieval algorithms and matrix completion formulations. |
|---|---|
| Bibliografia: | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 0025-5610 1436-4646 |
| DOI: | 10.1007/s10107-013-0738-9 |