  Objective: Proton therapy is a emerging method against cancer. One of the
main development is to increase the accuracy of the Bragg-peak position
calculation, which requires more precise relative stopping power (RSP)
measurements. An excellent choice is the application of proton computed
tomography (pCT) systems which take the images under similar conditions to
treatment as they use the same irradiation device and hadron beam for imaging
and treatment. A key aim is to develop an accurate image reconstruction
algorithm for pCT systems to reach their maximal performance.
  Approach: An image reconstruction algorithm was developed in this work, which
is suitable to reconstruct pCT images from the energy, position and direction
measurement of individual protons. The flexibility of an iterative image
reconstruction algorithm was utilised to appropriately model the trajectory of
protons. Monte Carlo (MC) simulations of a Derenzo and a CTP404 phantom was
used to test the accuracy of the image reconstruction.
  Main results: The Richardson-Lucy algorithm was applied first and
successfully for pCT image reconstruction. Probability density based approach
was applied for interaction (system) matrix generation, which is an advanced
approach to consider the uncertain path of the protons in the patient.
  Significance: The track of protons are scattered when they travel through
material at the hadron therapy energies. This property limits the achievable
spatial resolution, especially for single-sided pCT setups investigated in this
study. The main motivation of the presented research is to test new approaches
for the image reconstruction, focusing on the achieved spatial- and density
resolution and the image noise. Realistic imaging setup were simulated with
reasonably low proton statistics, to achieve results, which is likely to be
reproducible in clinical environment.
