Two dimensional noise reconstruction in proton computed tomography using distance-driven filtered back-projection of simulated projections.

We present a formalism for two dimensional (2D) noise reconstruction in proton computed tomography (pCT). This is necessary for the application of fluence modulated pCT (FMpCT) since it permits image noise prescription and the corresponding proton fuence optimization. We aimed at extending previously published formalisms to account for the impact of multiple Coulomb scattering (MCS) on projection noise, and the use of filtered back projection (FBP) reconstruction along \hl{curved paths} with distance driven binning (DDB). 
 
 2D noise reconstruction for a beam of protons with parallel initial momentum vectors, and for projections binned both at the rear tracker and with DDB, was established. Monte Carlo (MC) simulations of pCT scans of a water cylinder were employed to generate pCT projections and to calculate their noise for use in 2D noise reconstruction. These were compared to results from an analytical model accounting for MCS for rear tracker binning as well as against the previously published central pixel model which ignores MCS. Image noise reconstructed with the formalism for rear tracker binning and DDB were compared to MC results using annular regions of interest (ROIs).
 
 Agreement better than 8\% was obtained between the noise of projections calculated with MC simulation and our model. Noise from annular ROIs agreed with our noise reconstructions for rear tracker binning and DDB. The central pixel model ignoring MCS underestimated projection and thus image noise by up to 40\% towards the object's edge. 
 
 The use of DDB decreased the image noise towards the object's edge when compared to rear tracker binning and yielded more uniform noise throughout the image. MCS should not be neglected when predicting image noise for pixels away from the center of an object in a pCT scan due to the increasing influence of the gradient of the object's hull closer to the edges.