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. As in the resulting measurements the phase information is lost, ptychography gives rise to solving a phase retrieval problem. In this talk, we consider ptychographic measurements corrupted with a shift-invariant background signal. We develop a reconstruction algorithm for so-called phase objects that do not absorb the light but only scatter it. 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 system. Background noise 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. By means of this reconstruction method, we establish a uniqueness result for almost every phase object. The talk is based on joint work with Oleh Melnyk.