Blind Ptychography by Douglas-Rachford Splitting
This work addresses a specific computational imaging problem for researchers in optics and microscopy, presenting an incremental improvement in algorithm design with theoretical grounding.
The authors tackled the problem of blind ptychography, which involves recovering both an object and a probe from scanning coherent diffractive imaging data, by proposing the AMDRS algorithm based on Douglas-Rachford splitting. They demonstrated that AMDRS converges globally and geometrically, with improved convergence rates when enforcing boundary conditions such as dark-field or bright-field, and it can remove linear phase ambiguity in some cases.
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.