Computerized image reconstruction method and apparatus

A method for imaging an object, the method comprising:

• recording projection path information and energy loss information of a plurality of particles traversing an object;
• determining an estimated image based on the projection path information and the energy loss information sampled into a projection format, wherein the estimated image includes an active volume defined by an enclosure border;
• updating the estimated image by performing cost function minimization using one of an Adaptive-weighted Total Variation (AwTV) cost function, a Penalized Weighted Least-Squares (PWLS) cost function, and an Alpha-Divergence (α-D) cost function;
• updating the estimated image by performing an iterative updating algorithm corresponding to the cost function minimization;
• and
• when a difference between the updated estimated image and a previously estimated image is lower than a predetermined threshold, producing a final image based on the estimated image,
• wherein the one of the AwTV cost function, the PWLS cost function, and the α-D cost function is performed based on the estimated image, the recorded projection path information and energy loss information and a volumetric path.