  Fourier Ptychography is a recently proposed imaging technique that yields
high-resolution images by computationally transcending the diffraction blur of
an optical system. At the crux of this method is the phase retrieval algorithm,
which is used for computationally stitching together low-resolution images
taken under varying illumination angles of a coherent light source. However,
the traditional iterative phase retrieval technique relies heavily on the
initialization and also need a good amount of overlap in the Fourier domain for
the successively captured low-resolution images, thus increasing the
acquisition time and data. We show that an auto-encoder based architecture can
be adaptively trained for phase retrieval under both low overlap, where
traditional techniques completely fail, and at higher levels of overlap. For
the low overlap case we show that a supervised deep learning technique using an
autoencoder generator is a good choice for solving the Fourier ptychography
problem. And for the high overlap case, we show that optimizing the generator
for reducing the forward model error is an appropriate choice. Using
simulations for the challenging case of uncorrelated phase and amplitude, we
show that our method outperforms many of the previously proposed Fourier
ptychography phase retrieval techniques.
