Fourier ptychography (FP) is a recently proposed computational imaging
technique for high space-bandwidth product imaging. In real setups such as
endoscope and transmission electron microscope, the common sample motion
largely degrades the FP reconstruction and limits its practicability. In this
paper, we propose a novel FP reconstruction method to efficiently correct for
unknown sample motion. Specifically, we adaptively update the sample's Fourier
spectrum from low spatial-frequency regions towards high spatial-frequency
ones, with an additional motion recovery and phase-offset compensation
procedure for each sub-spectrum. Benefiting from the phase retrieval redundancy
theory, the required large overlap between adjacent sub-spectra offers an
accurate guide for successful motion recovery. Experimental results on both
simulated data and real captured data show that the proposed method can correct
for unknown sample motion with its standard deviation being up to 10% of the
field-of-view scale. We have released our source code for non-commercial use,
and it may find wide applications in related FP platforms such as endoscopy and
transmission electron microscopy
