Derivation and analysis of a filtered backprojection algorithm for cone beam projection data

The authors address the problem of three-dimensional image reconstruction from cone beam projections. Modifying a result due to A.A. Kirillov (Soviet Math. Dokl., vol. 2, p.268-9, 1961), the authors derive an inversion formula for the case where the cone vertices form an unbounded curve. For the special case in which 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 L.A. Feldkamp et al. (1984). For this approximate inverse, the authors 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.