  Limited-angle tomography of strongly scattering quasi-transparent objects is
a challenging, highly ill-posed problem with practical implications in medical
and biological imaging, manufacturing, automation, and environmental and food
security. Regularizing priors are necessary to reduce artifacts by improving
the condition of such problems. Recently, it was shown that one effective way
to learn the priors for strongly scattering yet highly structured 3D objects,
e.g. layered and Manhattan, is by a static neural network [Goy et al, Proc.
Natl. Acad. Sci. 116, 19848-19856 (2019)]. Here, we present a radically
different approach where the collection of raw images from multiple angles is
viewed analogously to a dynamical system driven by the object-dependent forward
scattering operator. The sequence index in angle of illumination plays the role
of discrete time in the dynamical system analogy. Thus, the imaging problem
turns into a problem of nonlinear system identification, which also suggests
dynamical learning as better fit to regularize the reconstructions. We devised
a recurrent neural network (RNN) architecture with a novel split-convolutional
gated recurrent unit (SC-GRU) as the fundamental building block. Through
comprehensive comparison of several quantitative metrics, we show that the
dynamic method improves upon previous static approaches with fewer artifacts
and better overall reconstruction fidelity.
