Techniques in Iterative Proton CT Image Reconstruction

Scott Penfold, Yair Censor

Research output: Contribution to journalArticlepeer-review


This is a review paper on some of the physics, modeling, and iterative algorithms in proton computed tomography (pCT) image reconstruction. The primary challenge in pCT image reconstruction lies in the degraded spatial resolution resulting from multiple Coulomb scattering within the imaged object. Analytical models such as the most likely path have been proposed to predict the scattered trajectory from measurements of individual proton location and direction before and after the object. Iterative algorithms provide a flexible tool with which to incorporate these models into image reconstruction. The modeling leads to a large and sparse linear system of equations that can efficiently be solved by projection methods-based iterative algorithms. Such algorithms perform projections of the iterates onto the hyperlanes that are represented by the linear equations of the system. They perform these projections in possibly various algorithmic structures, such as block-iterative projections, string-averaging projections. These algorithmic schemes allow flexibility of choosing blocks, strings, and other parameters. They also cater for parallel implementations which are apt to further save clock time in computations. Experimental results are presented which compare some of those algorithmic options.

Original languageEnglish
Article number19
JournalSensing and Imaging
Issue number1
StatePublished - 1 Nov 2015

Bibliographical note

Funding Information:
The authors would like to thank Reinhard Schulte for his devoted guidance, insightful collaboration and for the encouragement to undertake the writing of this review paper. The authors also thank Dan Gordon for reading and constructively commenting on an earlier version of the paper. We thank three anonymous referees for their reviews which helped us improve the paper. The work of Y.C. was partially supported by the United States-Israel Binational Science Foundation (BSF) Grant Number 2013003.

Publisher Copyright:
© 2015, Springer Science+Business Media New York.


  • Block-iterative projections
  • Most-likely path
  • Multiple Coulomb scattering
  • Projection methods
  • Proton computed tomography
  • String-averaging projections
  • Superiorization

ASJC Scopus subject areas

  • Instrumentation
  • Electrical and Electronic Engineering


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