The nonsmooth landscape of phase retrieval
Abstract
We consider a popular nonsmooth formulation of the real phase retrieval problem. We show that under standard statistical assumptions a simple subgradient method converges linearly when initialized within a constant relative distance of an optimal solution. Seeking to understand the distribution of the stationary points of the problem, we complete the paper by proving that as the number of Gaussian measurements increases, the stationary points converge to a codimension two set, at a controlled rate. Experiments on image recovery problems illustrate the developed algorithm and theory.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 09, 2020
- Source ID
- 10.1093/imanum/drz031
Entities
People
- Courtney Paquette
- Damek Davis
- Dmitriy Drusvyatskiy
Organizations
- Air Force Office of Scientific Research
- Cornell University
- Division of Computing and Communication Foundations
- Lehigh University
- National Science Foundation
- University of Washington