  Multi-scale 3D characterization is widely used by materials scientists to
further their understanding of the relationships between microscopic structure
and macroscopic function. Scientific computed tomography (CT) instruments are
one of the most popular choices for 3D non-destructive characterization of
materials at length scales ranging from the angstrom-scale to the micron-scale.
These instruments typically have a source of radiation that interacts with the
sample to be studied and a detector assembly to capture the result of this
interaction. A collection of such high-resolution measurements are made by
re-orienting the sample which is mounted on a specially designed stage/holder
after which reconstruction algorithms are used to produce the final 3D volume
of interest. The end goal of scientific CT scans include determining the
morphology,chemical composition or dynamic behavior of materials when subjected
to external stimuli. In this article, we will present an overview of recent
advances in reconstruction algorithms that have enabled significant
improvements in the performance of scientific CT instruments - enabling faster,
more accurate and novel imaging capabilities. In the first part, we will focus
on model-based image reconstruction algorithms that formulate the inversion as
solving a high-dimensional optimization problem involving a data-fidelity term
and a regularization term. In the last part of the article, we will present an
overview of recent approaches using deep-learning based algorithms for
improving scientific CT instruments.
