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Measurements achieved with ptychographic imaging are a special case ofdiffraction measurements. They are generated by illuminating small parts of asample with, e.g., a focused X-ray beam. By shifting the sample, a set offar-field diffraction patterns of the whole sample are then obtained. From amathematical point of view those measurements are the squared modulus of thewindowed Fourier transform of the sample. Thus, we have a phase retrievalproblem for local Fourier measurements. A direct solver for this problem wasintroduced by Iwen, Viswanathan and Wang in 2016 and improved by Iwen,Preskitt, Saab and Viswanathan in 2018. Motivated by the applied perspective ofptychographic imaging, we present a generalization of this method and comparethe different versions in numerical experiments. The new method proposed hereinturns out to be more stable, particularly in the case of missing data.

A direct solver for the phase retrieval problem in ptychographic imaging