Fast Phase Retrieval from Localized Time-Frequency Measurements

Series: 
Applied and Computational Mathematics Seminar
Monday, March 26, 2018 - 1:55pm
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Michigan State University
,  
Organizer: 
We propose a general phase retrieval approach that uses correlation-based measurements with compactly supported measurement masks. The algorithm admits deterministic measurement constructions together with a robust, fast recovery algorithm that consists of solving a system of linear equations in a lifted space, followed by finding an eigenvector (e.g., via an inverse power iteration). Theoretical reconstruction error guarantees are presented. Numerical experiments demonstrate robustness and computational efficiency that outperforms competing approaches on large problems. Finally, we show that this approach also trivially extends to phase retrieval problems based on windowed Fourier measurements.