Phase Retrieval Using Feasible Point Pursuit: Algorithms and Cramér-Rao Bound

Abstract

Reconstructing a signal from squared linear (rank-one quadratic) measurements is a challenging problem with important applications in optics and imaging, where it is known as phase retrieval. This paper proposes two new phase retrieval algorithms based on non-convex quadratically constrained quadratic programming (QCQP) formulations, and a recently proposed approximation technique dubbed feasible point pursuit (FPP). The first is designed for uniformly distributed bounded measurement errors, such as those arising from high-rate quantization (B-FPP). The second is designed for Gaussian measurement errors, using a least squares criterion (LS-FPP). Their performance is measured against state-of-the-art algorithms and the Cramér-Rao bound (CRB), which is also derived here. Simulations show that LS-FPP outperforms the state-of-art and operates close to the CRB. Compact CRB expressions, properties, and insights are obtained by explicitly computing the CRB in various special cases -- including when the signal of interest admits a sparse parametrization, using harmonic retrieval as an example.

13 pages, 13 figures

References in corpus (5)

• Phase Retrieval via Wirtinger Flow: Theory and Algorithms
• Parallel and Distributed Methods for Nonconvex Optimization--Part II: Applications
• Feasible Point Pursuit and Successive Approximation of Non-convex QCQPs
• Parallel and Distributed Methods for Nonconvex Optimization-Part I: Theory
• Reconstruction of Signals from Magnitudes of Redundant Representations

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