Collection Variational methods and optimization in imaging
Organizer(s)
Date(s)
18/04/2024
Blind Ptychography: Theory and Algorithm
Blind ptychography is a phase retrieval method using multiple coded diffraction patterns from different, overlapping parts of the unknown extended object illuminated with an unknown window function. As such blind ptychography is the inverse problem of simultaneous recovery of the object and the window function given the intensities of the windowed Fourier transform. We derive a general set of conditions under which the object and the window function can be uniquely determined up to a scaling factor and an affine phase factor. We also characterize all the other ambiguities inherent to the raster scan which consists of the shift positions of the standard windowed Fourier transform and propose an explicit remedy. Finally, we present a reconstruction algorithm based on the Douglas-Rachford Splitting with initialization informed by the uniqueness theory.
