• Corpus ID: 139105193

Simultaneous Phase Retrieval and Blind Deconvolution via Convex Programming

  title={Simultaneous Phase Retrieval and Blind Deconvolution via Convex Programming},
  author={Ali Ahmed and Alireza Aghasi and Paul Hand},
  journal={J. Mach. Learn. Res.},
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 \gg (k+n) \log^2… 

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