Phase Retrieval from Local Measurements: Improved Robustness via Eigenvector-Based Angular Synchronization
For researchers in signal processing and imaging, this provides a more robust and efficient phase retrieval algorithm with theoretical guarantees.
The paper improves a phase retrieval method using correlation-based measurements with compactly supported masks, achieving more robust and faster recovery via eigenvector-based angular synchronization. Numerical experiments show it outperforms competing approaches on large problems.
We improve a phase retrieval approach that uses correlation-based measurements with compactly supported measurement masks [27]. The improved 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 from [27] are improved as a result for the new and more robust reconstruction approach proposed herein. 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.