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CPRL -- An Extension of Compressive Sensing to the Phase Retrieval Problem
Henrik Ohlsson · Allen Y Yang · Roy Dong · Shankar Sastry

Thu Dec 06 02:00 PM -- 12:00 AM (PST) @ Harrah’s Special Events Center 2nd Floor #None

While compressive sensing (CS) has been one of the most vibrant and active research fields in the past few years, most development only applies to linear models. This limits its application and excludes many areas where CS ideas could make a difference. This paper presents a novel extension of CS to the phase retrieval problem, where intensity measurements of a linear system are used to recover a complex sparse signal. We propose a novel solution using a lifting technique -- CPRL, which relaxes the NP-hard problem to a nonsmooth semidefinite program. Our analysis shows that CPRL inherits many desirable properties from CS, such as guarantees for exact recovery. We further provide scalable numerical solvers to accelerate its implementation. The source code of our algorithms will be provided to the public.

Author Information

Henrik Ohlsson (Linköping university)
Allen Y Yang (Department of EECS, UC Berkeley)
Roy Dong (University of California - Berkeley)
Shankar Sastry (Department of EECS, UC Berkeley)

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