We covered it last year ( Compressive Phase Retrieval Implementation ) but it seems the new algorithm is now using ADMM. As mentioned in the last review, it looks like ADMM (see here for Matlab scripts for ADMM from S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein) is becoming indeed a mainstay.
While compressive sensing (CS) has been one of the most vibrant research ﬁelds in the past few years, most development only applies to linear models. This limits its application in many areas where CS 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.
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