A technique for simplifying the processing of tomographic imagery (e.g., CT and PET) via statistical smoothing is disclosed. An image smoothness criterion is imposed in the projection domain while identifying data that matches observed data within a desired tolerance. The present invention thus amounts to a computation entirely in the projection domain. As a result, the standard (and somewhat expensive) practice of numerically iterating between the image and projection domains is avoided. Also, the fundamental system of equations having on the order of m p unknowns is decoupled into p independent systems of m unknowns each, where there are p projections of m measurements each. The present invention thus provides a processing technique defined in a single domain, which may be carried out via parallel processing.