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Poster
Blind Deconvolutional Phase Retrieval via Convex Programming
Ali Ahmed · Alireza Aghasi · Paul Hand

Wed Dec 05 02:00 PM -- 04:00 PM (PST) @ Room 210 #81
in Wed Poster Session B »
We consider the task of recovering two real or complex $m$-vectors from phaseless Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on a lifted matrix recovery formulation that allows a nontrivial convex relaxation of the bilinear measurements from convolution. We prove that if the two signals belong to known random subspaces of dimensions $k$ and $n$, then they can be recovered up to the inherent scaling ambiguity with $m >> (k+n) \log^2 m$ phaseless measurements. Our method provides the first theoretical recovery guarantee for this problem by a computationally efficient algorithm and does not require a solution estimate to be computed for initialization. Our proof is based Rademacher complexity estimates. Additionally, we provide an ADMM implementation of the method and provide numerical experiments that verify the theory.
Keywords: Information Theory · Convex Optimization · Signal Processing

Author Information

Ali Ahmed (Information Technology University)
Alireza Aghasi (Institute for Insight)
Paul Hand (Northeastern University)

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