• Corpus ID: 139105193

# 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}
}
• Published 26 April 2019
• Computer Science, Mathematics
• 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… 3 Citations ## Figures from this paper • Mathematics, Computer Science 2021 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. • Mathematics ArXiv • 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. • Computer Science Telecommunication 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. ## References SHOWING 1-10 OF 36 REFERENCES • Computer Science IEEE Transactions on Information Theory • 2014 It is proved that, for “generic” signals, the program can deconvolve w and x exactly when the maximum of N and K is almost on the order of L, and it is shown that if x is drawn from a random sub space of dimension N, and w is a vector in a subspace of dimension K whose basis vectors are spread out in the frequency domain, then nuclear norm minimization recovers wx* without error. • Mathematics 2017 51st Asilomar Conference on Signals, Systems, and Computers • 2017 The convex program BranchHull is introduced, which is posed in the natural parameter space and does not require an approximate solution or initialization in order to be stated or solved on the bilinear inverse problem of recovering two vectors in RL from their entrywise product. • Computer Science IEEE Transactions on Information Theory • 2018 This work formulate phase retrieval as a convex optimization problem, which it is shown that the dual problem to PhaseMax is basis pursuit, which implies that the phase retrieval can be performed using algorithms initially designed for sparse signal recovery. • Computer Science AISTATS • 2017 A flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal to avoid the prohibitive computational cost associated with "lifting" and semidefinite programming and compete with recently developed non-convex techniques for phase retrieval. • Computer Science ICML • 2019 A method based on nonconvex optimization is proposed, which under certain conditions recovers the target short and sparse signals, up to a signed shift symmetry which is intrinsic to this model. • Computer Science NeurIPS • 2018 The introduced$\ell_1\$-BranchHull, which is a convex program posed in the natural parameter space and does not require an approximate solution or initialization in order to be stated or solved, and an ADMM implementation of these variants are provided.
• Computer Science, Mathematics
ArXiv
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We consider the problem of estimating a solution to (random) systems of equations that involve convex nonlinearities which has applications in machine learning and signal processing. Conventional
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We obtain bounds on estimation error rates for regularization procedures of the form \begin{equation*} \hat f \in {\rm argmin}_{f\in F}\left(\frac{1}{N}\sum_{i=1}^N\left(Y_i-f(X_i)\right)^2+\lambda
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A nonlinear programming algorithm for solving semidefinite programs (SDPs) in standard form that replaces the symmetric, positive semideFinite variable X with a rectangular variable R according to the factorization X=RRT.