1. A method for performing computed tomography, the method comprising: delivering a proton beam to an object, the proton beam comprising a plurality of protons; measuring, with one or more particle detectors, data for the plurality of protons that pass through the object, the measured data including information about first and second tracks for each of the protons, the first and second tracks corresponding to the proton's trajectories before and after its passage through the object, respectively, the measured data further including information about an interaction quantity of each proton resulting from its passage through the object; for each proton, calculating an estimated path corresponding to an actual path taken by the proton within the object based at least in part on the first and second tracks, the estimated path providing an estimate of the actual path; arranging the interaction quantities and the estimated paths of the protons such that the passages of the protons through the object is represented as a system of linear equations Ax=b where x is a discrete object vector representing an object parameter distribution such that each element of the vector x represents a value of the object parameter distribution at a voxel in the object, b is a vector that represents the interaction quantities of the protons resulting from interactions along their respective paths in the object, and A is a matrix that operates on the vector x to yield the vector b, the matrix A having information about the estimated paths of the protons in the object, an element of the matrix A corresponding to an estimated intersection length of a selected proton in a corresponding voxel, the estimated intersection length being calculated as a straight-line approximation of the estimated path of the selected proton in the corresponding voxel so as to account for non-linearity of the actual paths of the protons in the object and allow the system of linear equations to have a plurality of solutions; determining, using one or more computer processors, an initial solution for the system of linear equations, wherein the initial solution is one of the plurality of solutions; determining a superior solution different from the initial solution by iteratively performing the steps of: calculating a feasible solution by perturbing a vector representation x k of the object parameter distribution so as to yield a perturbed vector y k , the feasible solution being one of the plurality of solutions, wherein the initial solution is an initial vector representation x 0 ; designating the vector representation y k as the superior solution if the vector representation y k has a superior characteristic for a quantity associated with a reconstruction of the object parameter distribution than the vector representation x k ; and projecting the superior solution onto a hyperslab using a block-iterative projection algorithm set so as to yield a next vector representation x k+1 , wherein the measured data is divided into a plurality of blocks; calculating the object parameter distribution based on the superior solution; and generating a computed tomography image of the object based at least in part on the calculated object parameter distribution, wherein the quantity associated with the reconstruction of the object parameter distribution comprises a total variation of the reconstructed object parameter distribution, wherein the projecting is performed cyclically through all the blocks until all of the blocks are processed before proceeding to a next iteration.