A computerized tomography apparatus and program for obtaining a cross-sectional image corresponding to projections are provided in which, for a temporary cross-sectional image f(x, y) obtained in some manner, an evaluation function E is defined which includes differences between projections calculated from f(x, y) and measured projections, and f(x, y) is changed in a manner which substantially decreases E. The computerized tomography apparatus and program are characterized in which a back projection operation, which is required by conventional computerized tomography, is not essentially required. The computerized tomography apparatus and program are particularly effective in removal or reduction of metal artifacts, aliasing artifacts and the like.