Approximate methods for phase retrieval via gauge duality
Optimization and Control
2020-06-02 v1
Abstract
We consider the problem of finding a low rank symmetric matrix satisfying a system of linear equations, as appears in phase retrieval. In particular, we solve the gauge dual formulation, but use a fast approximation of the spectral computations to achieve a noisy solution estimate. This estimate is then used as the initialization of an alternating gradient descent scheme over a nonconvex rank-1 matrix factorization formulation. Numerical results on small problems show consistent recovery, with very low computational cost.
Cite
@article{arxiv.2006.01014,
title = {Approximate methods for phase retrieval via gauge duality},
author = {Ron Estrin and Yifan Sun and Halyun Jeong and Michael Friedlander},
journal= {arXiv preprint arXiv:2006.01014},
year = {2020}
}