A method of reconstructing a 3-dimensional image in a proton transmission computerized tomography (CT) apparatus is disclosed. The method comprises the creation of a reconstruction matrix. The matrix is created by directing a plurality of particles to traverse the object; and for each particle, measuring the trajectory and energy of each particle before and after it has traversed the object; for each particle, calculating the water-equivalent path length within the object; and for each particle, calculating the positions at which it entered and exited the object; and adding the water-equivalent path length, entry and exit positions to the reconstruction matrix. This procedure is repeated from a plurality of angular positions surrounding an object to be imaged. Then, a spatially varying 2-dimensional filter function is applied to the reconstruction matrix. Subsequently, a correction factor is applied to the filtered reconstruction matrix to at least partially correct for the finite extent of the matrix.