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 $3le Nle 6$ and allows full parallelization of the TVS algorithm. Repeated perturbations per feasibility-seeking iterations reduced total variation (TV) and material dependent standard deviations for $3le Nle 6$. 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.
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