  Previous work showed that total variation superiorization (TVS) improves
reconstructed image quality in proton computed tomography (pCT). The structure
of the TVS algorithm has evolved since then and this work investigated if this
new algorithmic structure provides additional benefits to pCT image quality.
Structural and parametric changes introduced to the original TVS algorithm
included: (1) inclusion or exclusion of TV reduction requirement, (2) a
variable number, $N$, of TV perturbation steps per feasibility-seeking
iteration, and (3) introduction of a perturbation kernel $0<\alpha<1$. The
structural change of excluding the TV reduction requirement check tended to
have a beneficial effect for $3\le N\le 6$ and allows full parallelization of
the TVS algorithm. Repeated perturbations per feasibility-seeking iterations
reduced total variation (TV) and material dependent standard deviations for
$3\le N\le 6$. The perturbation kernel $\alpha$, equivalent to $\alpha=0.5$ in
the original TVS algorithm, reduced TV and standard deviations as $\alpha$ was
increased beyond $\alpha=0.5$, but negatively impacted reconstructed relative
stopping power (RSP) values for $\alpha>0.75$. The reductions in TV and
standard deviations allowed feasibility-seeking with a larger relaxation
parameter $\lambda$ than previously used, without the corresponding increases
in standard deviations experienced with the original TVS algorithm. This work
demonstrates that the modifications related to the evolution of the original
TVS algorithm provide benefits in terms of both pCT image quality and
computational efficiency for appropriately chosen parameter values.
