  Recent work in CT imaging has seen increased interest in the use of total
variation (TV) and related penalties to regularize problems involving
reconstruction from undersampled or incomplete data. Superiorization is a
recently proposed heuristic which provides an automatic procedure to
"superiorize" an iterative reconstruction algorithm with respect to a chosen
objective function, such as TV. Under certain conditions, the superiorized
algorithm is guaranteed to find a solution that is as satisfactory as any found
by the original algorithm with respect to satisfying the constraints of the
problem; this solution is also expected to be superior with respect to the
chosen objective.
  Most work on superiorization has used reconstruction algorithms which assume
a linear measurement model, which in the case of CT corresponds to data
generated from a monoenergetic X-ray beam. Many CT systems generate X-rays from
a polyenergetic spectrum, however, in which the measured data represent an
integral of object attenuation over all energies in the spectrum. This
inconsistency with the linear model produces the well-known beam hardening
artifacts, which impair analysis of CT images.
  In this work we superiorize an iterative algorithm for reconstruction from
polyenergetic data, using both TV and an anisotropic TV (ATV) penalty. We apply
the superiorized algorithm in numerical phantom experiments modeling both
sparse-view and limited-angle scenarios. In our experiments, the superiorized
algorithm successfully finds solutions which are as constraints-compatible as
those found by the original algorithm, with significantly reduced TV and ATV
values. The superiorized algorithm thus produces images with greatly reduced
sparse-view and limited angle artifacts, which are also largely free of the
beam hardening artifacts that would be present if a superiorized version of a
monoenergetic algorithm were used.
