Background Removal for Ptychography via Wigner Distribution Deconvolution

Ptychography is a computational imaging technique that aims to reconstruct the object of interest from a set of diffraction patterns. Each of these is obtained by a localized illumination of the object, which is shifted after each illumination to cover its whole domain. Because in the resulting measurements the phase information is lost, ptychography gives rise to solving a phase retrieval problem. In this work, we consider ptychographic measurements contaminated by a background signal. Such a background is caused by imperfections in the experimental setup and appears as a signal that is added to the diffraction patterns. The background is assumed to be independent of the shift of the object, i.e., it is the same for all diffraction patterns. Two algorithms are provided, for arbitrary objects and for so-called phase objects that do not absorb the light but only scatter it. For the second type, a uniqueness of reconstruction is established for almost every object. Our approach is based on the Wigner distribution deconvolution, which lifts the object to a higher-dimensional matrix space where the recovery can be reformulated as a linear problem. The background only affects a few equations of the linear system that are therefore discarded. The lost information is then restored using redundancy in the higher-dimensional space.