Journal
MATHEMATICAL PROGRAMMING
Volume 149, Issue 1-2, Pages 47-81Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10107-013-0738-9
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Funding
- European Research Council (ERC)
- ERC Invariant-Class [320959]
- [ANR10-BLAN-0126]
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Phase retrieval seeks to recover a signal from the amplitude of linear measurements . 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.
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