Total variation superiorization schemes in proton computed tomography image reconstruction

S. N. Penfold, R. W. Schulte, Y. Censor, A. B. Rosenfeld

Research output: Contribution to journalArticlepeer-review


Purpose: Iterative projection reconstruction algorithms are currently the preferred reconstruction method in proton computed tomography (pCT). However, due to inconsistencies in the measured data arising from proton energy straggling and multiple Coulomb scattering, the noise in the reconstructed image increases with successive iterations. In the current work, the authors investigated the use of total variation superiorization (TVS) schemes that can be applied as an algorithmic add-on to perturbation-resilient iterative projection algorithms for pCT image reconstruction. Methods: The block-iterative diagonally relaxed orthogonal projections (DROP) algorithm was used for reconstructing GEANT4 Monte Carlo simulated pCT data sets. Two TVS schemes added on to DROP were investigated; the first carried out the superiorization steps once per cycle and the second once per block. Simplifications of these schemes, involving the elimination of the computationally expensive feasibility proximity checking step of the TVS framework, were also investigated. The modulation transfer function and contrast discrimination function were used to quantify spatial and density resolution, respectively. Results: With both TVS schemes, superior spatial and density resolution was achieved compared to the standard DROP algorithm. Eliminating the feasibility proximity check improved the image quality, in particular image noise, in the once-per-block superiorization, while also halving image reconstruction time. Overall, the greatest image quality was observed when carrying out the superiorization once per block and eliminating the feasibility proximity check. Conclusions: The low-contrast imaging made possible with TVS holds a promise for its incorporation into future pCT studies.

Original languageEnglish
Pages (from-to)5887-5895
Number of pages9
JournalMedical Physics
Issue number11
StatePublished - Nov 2010

Bibliographical note

Funding Information:
The authors thank the anonymous referees for their constructive comments. The first author was supported in part by Grant No. 08/RSA/1-02 from the Cancer Institute New South Wales and the Department of Radiation Medicine at Loma Linda University Medical Center, California. Yair Censor was supported by NIH Grant No. R01HL070472 administered by the National Heart, Lung, and Blood Institute. The authors would like to thank Gabor Herman and Ran Davidi from the Graduate Center of the City University of New York for their valuable advice on superiorization schemes.


  • iterative projection methods
  • proton computed tomography
  • superiorization
  • total variation

ASJC Scopus subject areas

  • Biophysics
  • Radiology Nuclear Medicine and imaging


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