  Ptychography is a popular imaging technique that combines diffractive imaging
with scanning microscopy. The technique consists of a coherent beam that is
scanned across an object in a series of overlapping positions, leading to
reliable and improved reconstructions. Ptychographic microscopes allow for
large fields to be imaged at high resolution at additional computational
expense. In this work, we explore the use of the fast Partial Fourier
Transforms (PFTs), which efficiently compute Fourier coefficients corresponding
to low frequencies. The core idea is to use the PFT in a plug-and-play manner
to warm-start existing ptychography algorithms such as the ptychographic
iterative engine (PIE). This approach reduces the computational budget required
to solve the ptychography problem. Our numerical results show that our scheme
accelerates the convergence of traditional solvers without sacrificing quality
of reconstruction.
