Phase retrieval from local measurements: Improved robustness via eigenvector-based angular synchronization

Abstract

Abstract We improve a phase retrieval approach that uses correlation-based measurements with compactly supported measurement masks [30] . Our approach 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 from [30] are improved as a result for the new and more robust reconstruction approach proposed herein. Numerical experiments demonstrate robustness and computational efficiency that compete with other approaches on large problems. Along the way, we show that this approach also trivially extends to phase retrieval problems based on windowed Fourier measurements.