Fourier-Domain Fixed Point Algorithms with Coded Diffraction Patterns

TL;DR

This paper introduces Fourier-domain fixed point algorithms, including FDM, for phase retrieval using coded diffraction patterns, demonstrating their ability to recover true solutions uniquely without object constraints.

Contribution

It proposes a new family of fixed point algorithms in the Fourier domain for phase retrieval, encompassing FHPR and FDR, with proven convergence to true solutions.

Findings

FDM yields a unique fixed point for generic complex objects.

Proper projection back to the object domain recovers the true solution.

Algorithms work without object constraints, up to a global phase.

Abstract

Fourier-domain Difference Map (FDM) for phase retrieval with two oversampled coded diffraction patterns are proposed. FDM is a 3-parameter family of fixed point algorithms including Fourier-domain Hybrid-Projection-Reflection (FHPR) and Douglas-Rachford (FDR) algorithm. For generic complex objects without any object constraint, FDM yields a unique fixed point, after proper projection back to the object domain, which is the true solution to the phase retrieval problem up to a global phase factor.