  Traditional fluorescence microscopy is constrained by inherent trade-offs
among resolution, field-of-view, and system complexity. To navigate these
challenges, we introduce a simple and low-cost computational multi-aperture
miniature microscope, utilizing a microlens array for single-shot wide-field,
high-resolution imaging. Addressing the challenges posed by extensive view
multiplexing and non-local, shift-variant aberrations in this device, we
present SV-FourierNet, a novel multi-channel Fourier neural network.
SV-FourierNet facilitates high-resolution image reconstruction across the
entire imaging field through its learned global receptive field. We establish a
close relationship between the physical spatially-varying point-spread
functions and the network's learned effective receptive field. This ensures
that SV-FourierNet has effectively encapsulated the spatially-varying
aberrations in our system, and learned a physically meaningful function for
image reconstruction. Training of SV-FourierNet is conducted entirely on a
physics-based simulator. We showcase wide-field, high-resolution video
reconstructions on colonies of freely moving C. elegans and imaging of a mouse
brain section. Our computational multi-aperture miniature microscope, augmented
with SV-FourierNet, represents a major advancement in computational microscopy
and may find broad applications in biomedical research and other fields
requiring compact microscopy solutions.
