# Simultaneous Phase Retrieval and Blind Deconvolution via Convex Programming

@article{Ahmed2019SimultaneousPR, title={Simultaneous Phase Retrieval and Blind Deconvolution via Convex Programming}, author={Ali Ahmed and Alireza Aghasi and Paul Hand}, journal={J. Mach. Learn. Res.}, year={2019}, volume={20}, pages={157:1-157:28} }

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…

## 3 Citations

### Non-Convex Recovery from Phaseless Low-Resolution Blind Deconvolution Measurements using Noisy Masked Patterns

- Mathematics, Computer Science2021 55th Asilomar Conference on Signals, Systems, and Computers
- 2021

A blind deconvolution algorithm for phaseless super-resolution (BliPhaSu) to minimize a non-convex least-squares objective function and shows that it converges linearly to a pair of true signals on expectation under a proper initialization that is based on spectral method.

### Class-Specific Blind Deconvolutional Phase Retrieval Under a Generative Prior

- MathematicsArXiv
- 2020

The proposed recovery algorithm strives to find a sharp image and a blur kernel in the range of the respective pre-generators that explain the forward measurement model and is able to reconstruct quality image estimates.

### Single-channel phaseless blind source separation

- Computer ScienceTelecommunication Systems
- 2022

A novel problem of blind source separation from observed magnitude-only measurements of their convolutive mixture in different communication systems is considered and a convex programming-based solution for joint recovery of the unknown channel and source signals is proposed.

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