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• W2962941403 abstract "We consider the recovery of a (real- or complex-valued) signal from magnitude-only measurements, known as phase retrieval. We formulate phase retrieval as a convex optimization problem, which we call PhaseMax. Unlike other convex methods that use semidefinite relaxation and lift the phase retrieval problem to a higher dimension, PhaseMax is a “non-lifting” relaxation that operates in the original signal dimension. We show that the dual problem to PhaseMax is basis pursuit, which implies that the phase retrieval can be performed using algorithms initially designed for sparse signal recovery. We develop sharp lower bounds on the success probability of PhaseMax for a broad range of random measurement ensembles, and we analyze the impact of measurement noise on the solution accuracy. We use numerical results to demonstrate the accuracy of our recovery guarantees, and we showcase the efficacy and limits of PhaseMax in practice." @default.
• W2962941403 created "2019-07-30" @default.
• W2962941403 creator A5060687985 @default.
• W2962941403 creator A5083617223 @default.
• W2962941403 date "2018-04-01" @default.
• W2962941403 modified "2023-10-13" @default.
• W2962941403 title "PhaseMax: Convex Phase Retrieval via Basis Pursuit" @default.
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• W2962941403 doi "https://doi.org/10.1109/tit.2018.2800768" @default.
• W2962941403 hasPublicationYear "2018" @default.
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