  Ultra-thin multimode optical fiber imaging promises next-generation medical
endoscopes reaching high image resolution for deep tissues. However, current
technology suffers from severe optical distortion, as the fiber's calibration
is sensitive to bending and temperature and thus requires in vivo
re-measurement with access to a single end only. We present a neural network
(NN)-based approach to reconstruct the fiber's transmission matrix (TM) based
on multi-wavelength reflection-mode measurements. We train two different NN
architectures via a custom loss function insensitive to global
phase-degeneracy: a fully connected NN and convolutional U-Net. We reconstruct
the 64 $\times$ 64 complex-valued fiber TMs through a simulated single-ended
optical fiber with $\leq$ 4\% error and cross-validate on experimentally
measured TMs, demonstrating both wide-field and confocal scanning image
reconstruction with small error. Our TM recovery approach is 4500 times faster,
is more robust to fiber perturbation during characterization, and operates with
non-square TMs.
