Blind Ptychography by Douglas-Rachford Splitting

TL;DR

This paper introduces AMDRS, a globally convergent algorithm for blind ptychography based on Douglas-Rachford splitting, which effectively recovers both object and probe using boundary conditions and noise modeling.

Contribution

The paper presents a novel blind ptychography algorithm, AMDRS, with proven global convergence and geometric rate, incorporating boundary conditions and noise considerations.

Findings

AMDRS converges globally and geometrically.

Enforcing boundary conditions improves convergence rate.

Bright-field boundary condition removes linear phase ambiguity.

Abstract

Blind ptychography is the scanning version of coherent diffractive imaging which seeks to recover both the object and the probe simultaneously. Based on alternating minimization by Douglas-Rachford splitting, AMDRS is a blind ptychographic algorithm informed by the uniqueness theory, the Poisson noise model and the stability analysis. Enhanced by the initialization method and the use of a randomly phased mask, AMDRS converges globally and geometrically. Three boundary conditions are considered in the simulations: periodic, dark-field and bright-field boundary conditions. The dark-field boundary condition is suited for isolated objects while the bright-field boundary condition is for non-isolated objects. The periodic boundary condition is a mathematically convenient reference point. Depending on the avail- ability of the boundary prior the dark-field and the bright-field boundary conditions may or may not be enforced in the reconstruction. Not surprisingly, enforcing the boundary condition improves the rate of convergence, sometimes in a significant way. Enforcing the bright-field condition in the reconstruction can also remove the linear phase ambiguity.