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Phase retrieval by linear algebra. (English) Zbl 1375.49035

Summary: The null vector method, based on a simple linear algebraic concept, is proposed as an initialization method for nonconvex approaches to the phase retrieval problem. For the stylized measurement with random complex Gaussian matrices, a nonasymptotic error bound is derived, stronger than that of the spectral vector method. Numerical experiments show that the null vector method also has a superior performance for the realistic measurement of coded diffraction patterns in coherent diffractive imaging.

MSC:

49K35 Optimality conditions for minimax problems
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)
49M30 Other numerical methods in calculus of variations (MSC2010)

Software:

Wirtinger Flow
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Full Text: DOI arXiv

References:

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