1. A method for performing computed tomography, the method comprising: obtaining measured data for a plurality of protons that pass through an 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, estimating a path taken by the proton within the object based at least in part on the first and second tracks; arranging the interaction quantities and the estimated paths of the protons such that the passages of the protons through the object is represented as or representable as a system of equations Ax=b where x is a distribution of a parameter associated with the object, b represents the interaction quantities of the protons resulting from interactions along their respective paths in the object, and A is an operator that operates on x to yield b, the operator A having information about the estimated paths of the protons in the object, the system of equations configured so as to have a plurality of solutions; estimating an initial solution for the system of equations; seeking one or more feasible solutions among the plurality of solutions, each feasible solution obtained by perturbing an existing solution and having a superior characteristic for a quantity associated with a reconstruction of the object parameter distribution than another solution obtained without the perturbation of the existing solution; and calculating the object parameter distribution based on a selected one of the one or more feasible solutions.