Disclosed are systems, devices and methodologies relating to proton computed tomography. In some implementations, detection of protons can yield track information before and after an object for each proton so as to allow determination of a likely path of each proton within the object. Further, measurement of energy loss experienced by each proton allows determination that a given likely path results in a given energy loss. A collection of such data allows characterization of the object. In the context of energy loss, such a characterization can include an image map of relative stopping power of the object. Various reconstruction methodologies for obtaining such an image, including but not limited to superiorization of a merit function such as total variation, are disclosed. In some implementations, various forms of total variation superiorization methodology can yield excellent results while being computationally efficient and with reduced computing time. In some implementations, such a methodology can result in high quality proton CT images using relatively low dose of protons.
