1. A method for performing intensity-modulated ion therapy, the method comprising: one or more hardware processors configured to perform the steps of: generating a representation of a patient by: for a plurality of ions, estimating a path taken by each ion within the patient based at least in part on trajectories determined from measured data; determining a system of equations of the form Ax=b where x represents a distribution parameter associated with the patient, b represents interaction quantities of the plurality of ions resulting from interactions within the patient, and A represents an operator that operates on x to yield b, the operating having information about the estimated paths of the plurality of ions in the patient; determining one or more feasible solutions to the system of equations by perturbing an estimated initial solution to determine whether the perturbation yields a superior reconstruction than a non-perturbed solution; and calculating the distribution parameter associated with the patient; identifying a volume of interest from the representation of the patient, the volume of interest divided into a total number of voxels ordered according to distance to a feature of interest; defining a plurality of sub-volumes wherein a sub-volume comprises a number of consecutive ordered voxels, wherein a ratio of the number consecutive ordered voxels comprising the sub-volume to the total number of voxels is approximately equal to a target fractional value for the sub-volume; and generating an ion treatment plan that satisfies dose constraints for each of the plurality of sub-volumes.