  Scatter due to interaction of photons with the imaged object is a fundamental
problem in X-ray Computed Tomography (CT). It manifests as various artifacts in
the reconstruction, making its abatement or correction critical for image
quality. Despite success in specific settings, hardware-based methods require
modification in the hardware, or increase in the scan time or dose. This
accounts for the great interest in software-based methods, including
Monte-Carlo based scatter estimation, analytical-numerical, and kernel-based
methods, with data-driven learning-based approaches demonstrated recently. In
this work, two novel physics-inspired deep-learning-based methods, PhILSCAT and
OV-PhILSCAT, are proposed. The methods estimate and correct for the scatter in
the acquired projection measurements. Different from previous works, they
incorporate both an initial reconstruction of the object of interest and the
scatter-corrupted measurements related to it, and use a deep neural network
architecture and cost function, both specifically tailored to the problem.
Numerical experiments with data generated by Monte-Carlo simulations of the
imaging of phantoms reveal consistent improvement over a recent purely
projection-domain deep neural network scatter correction method.
