  Proton radiography combined with X-ray computed tomography (CT) has been
proposed to obtain a patient-specific calibration curve and reduce range
uncertainties in cancer treatment with charged particles. The main aim of this
study was to identify the optimal charged particle for the generation of the
radiographies and to determine the optimal number of projections necessary to
obtain minimal range errors. Three charged particles were considered to
generate the radiographies: proton (p-rad), helium ions ({\alpha}-rad) and
carbon ions (c-rad). The problem formulation was viewed as a least square
optimization, argmin_x (||Ax -b||_2^2 ), where the projection matrix A
represents the cumulative path crossed by each particle in each material, b is
the charged particle list-mode radiography expressed as the crossed water
equivalent thickness (WET) and x is the relative stopping power (RSP) map to be
optimized. The charged particle radiographies were simulated using the Geant4
Monte Carlo (MC) toolkit and an anthropomorphic adult head phantom. A was
determined by calculating the particles trajectory through the X-ray CT
employing a convex hull detection combined with a cubic spline path. For all
particle types, the impact of using multiple projections was assessed (from 1
to 6 projections). In this study, tissue segmentation methods were also
investigated in terms of achievable accuracy. The best results (mean RSP error
below 0.7% and range errors below 1 mm) were obtained for a-rad when 3
projections were used. The dose delivered to the phantom by a single
{\alpha}-rad was 8 \muGy, lower than the dose of X-ray radiography.
