# Phase Retrieval Using Alternating Minimization in a Batch Setting

@article{Zhang2018PhaseRU,
title={Phase Retrieval Using Alternating Minimization in a Batch Setting},
author={Teng Zhang},
journal={2018 Information Theory and Applications Workshop (ITA)},
year={2018},
pages={1-17}
}
• Teng Zhang
• Published 25 June 2017
• Computer Science
• 2018 Information Theory and Applications Workshop (ITA)

### PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming

• Computer Science
ArXiv
• 2011
It is shown that in some instances, the combinatorial phase retrieval problem can be solved by convex programming techniques, and it is proved that the methodology is robust vis‐à‐vis additive noise.

### Phase recovery, MaxCut and complex semidefinite programming

• Computer Science
Math. Program.
• 2015
This work casts the phase retrieval problem as a non-convex quadratic program over a complex phase vector and formulates a tractable relaxation similar to the classical MaxCut semidefinite program.

### Optimal Rates of Convergence for Noisy Sparse Phase Retrieval via Thresholded Wirtinger Flow

• Computer Science
ArXiv
• 2015
A novel thresholded gradient descent algorithm is proposed and it is shown to adaptively achieve the minimax optimal rates of convergence over a wide range of sparsity levels when the a_j's are independent standard Gaussian random vectors, provided that the sample size is sufficiently large compared to the sparsity of \$x.

### Structured Signal Recovery From Quadratic Measurements: Breaking Sample Complexity Barriers via Nonconvex Optimization

The projected gradient descent, when initialized in a neighborhood of the desired signal, converges to the unknown signal at a linear rate and is proved to be the first provably tractable algorithm for this data-poor regime.

### Phase Retrieval Using Alternating Minimization

• Computer Science, Mathematics
IEEE Transactions on Signal Processing
• 2015
This work represents the first theoretical guarantee for alternating minimization (albeit with resampling) for any variant of phase retrieval problems in the non-convex setting.

### Phase Retrieval via Wirtinger Flow: Theory and Algorithms

• Computer Science
IEEE Transactions on Information Theory
• 2015
This paper develops a nonconvex formulation of the phase retrieval problem as well as a concrete solution algorithm that is shown to rigorously allow the exact retrieval of phase information from a nearly minimal number of random measurements.

### Phase Retrieval With Random Gaussian Sensing Vectors by Alternating Projections

It is conjecture that the classical algorithm of alternating projections (Gerchberg–Saxton) succeeds with high probability when no special initialization procedure is used, and it is conjectured that this result is still true when nospecial initialization process is used.