  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.
