An Improved Method of Total Variation Superiorization Applied to Reconstruction in Proton Computed Tomography

Abstract

NOTE: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.Abstract-Previous work has shown 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 < α < 1. The structural change of excluding the TV reduction requirement check tended to have a beneficial effect for 3 ≤ N ≤ 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 ≤ N ≤ 6. The perturbation kernel α, equivalent to α = 0.5 in the original TVS algorithm, reduced TV and standard deviations as α was increased beyond α = 0.5, but negatively impacted reconstructed relative stopping power (RSP) values for α > 0.75. The reductions in TV and standard deviations allowed feasibilityseeking with a larger relaxation parameter λ 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.

An optimization algorithm for dose reduction with fluence‐modulated proton CT

“…Future work should also address the impact of iterative image reconstruction, which is frequently used for pCT imaging . In contrast to the direct filtered backprojection algorithm used in this study, iterative reconstruction employs a regularization method (typically total variation), which reduces noise and whose optimal weight depends on the object and the fluence level .…”

“…Future work should also address the impact of iterative image reconstruction, which is frequently used for pCT imaging. [44][45][46][47][48] In contrast to the direct filtered backprojection algorithm used in this study, iterative reconstruction employs a regularization method (typically total variation), which reduces noise and whose optimal weight depends on the object and the fluence level. 49 While most fluence modulation studies for x-ray CT have been performed using filtered backprojection, 20,21 a first study 23 investigated a joint optimization of the fluence field and a spatially varying regularization parameter in the iterative reconstruction.…”

The impact of secondary fragments on the image quality of helium ion imaging

“…The DROP-TVS algorithm was run for 8 iterations and using 40 reconstruction blocks to allow a comparison with the experimental pCT results presented in Giacometti et al (2017). A recent study (Schultze et al 2018) showed that a higher number of iterations would increase the spatial resolution and RSP accuracy, but would also enhance noise.…”

Comparison of regularized and superiorized methods for tomographic image reconstruction

“…While it is possible that our results could be improved upon with different choices for these two parameters, in practice it appears difficult to determine optimal values without extensive experimentation. A recent paper [37] suggests taking 3 ≤ N ≤ 6 and γ = 0.75 for a problem in proton computed tomography, but our own experiments indicated that it was necessary to take γ much closer to 1.0 to obtain good results in our experiments. Values as large as γ = 0.99995 have been used other studies [23].…”

“…The parameter γ controls the rate at which the perturbation size decreases. The values of γ and N are chosen empirically and may significantly affect the performance of the algorithm [37]. Small values of γ cause the size of the perturbations to decrease rapidly, such that the perturbations may have little effect after the first few iterations, while a value of γ close to one results in larger perturbations that may delay convergence to an ε-compatible solution.…”