Provided herein is a computerized image reconstruction apparatus and method that includes recording projection path information and energy loss information of a plurality of particles traversing an object being imaged and determining an estimated image of the object based on the projection path information and the energy loss information sampled into a projection format. The estimated image includes an active volume defined by an enclosure border. Cost function minimization uses an Adaptive-weighted Total Variation cost function, a Penalized Weighted Least-Squares cost function, or an Alpha-Divergence cost function to update the estimated image. An iterative updating algorithm corresponding to the cost function updates the estimated image and produces a final image based on the estimated image according to a predetermined threshold.