  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 (MLP) 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 (BIP), string-averaging projections (SAP). 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.
