DERIVATION AND ANALYSIS OF A FILTERED BACKPROJECTION ALGORITHM FOR CONE BEAM PROJECTION DATA

In this paper we address the problem of three-dimensional image reconstruction from cone beam projections. Modifying a result due to Kirillov, we derive an inversion formula for the case where the cone vertices form an unbounded curve. For the special case where the cone vertices form a circle, an approximate reconstruction formula is developed and shown to be essentially equivalent to the 'practical cone-beam algorithm' of Feldkamp et al. For this approximate inverse, we derive the resulting spatially varying point spread function, examine the effect of bandlimiting due to sampling and compare the resulting image quality as a function of the radius of the circle formed by the cone vertices.