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

Blake Schultze, Yair Censor, Paniz Karbasi, Keith E. Schubert, Reinhard W. Schulte

Research output: Contribution to journalArticlepeer-review


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 paper 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 , effectively equal 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 feasibility-seeking with a larger relaxation parameter λthan previously used, without the corresponding increases in standard deviations experienced with the original TVS algorithm. This paper 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.

Original languageEnglish
Article number8692608
Pages (from-to)294-307
Number of pages14
JournalIEEE Transactions on Medical Imaging
Issue number2
StatePublished - Feb 2020

Bibliographical note

Publisher Copyright:
© 1982-2012 IEEE.


  • Feasibility-seeking algorithms
  • image reconstruction
  • perturbations
  • proton computed tomography (pCT)
  • superiorization
  • total variation superiorization (TVS)
  • Protons
  • Humans
  • Head/diagnostic imaging
  • Algorithms
  • Image Processing, Computer-Assisted/methods
  • Tomography/methods
  • Phantoms, Imaging

ASJC Scopus subject areas

  • Software
  • Radiological and Ultrasound Technology
  • Electrical and Electronic Engineering
  • Computer Science Applications


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