An optimal technique for tomographic image reconstruction from curved ray projections

This paper extends the constrained optimisation image reconstruction techniques to curved-ray projections for a number of scanning systems and for 2-D and 3-D reconstructions. The work presented is general in that it includes the previous results on parallel-ray and divergent-ray geometries as special cases. Treating the problem in Hilbert space a general cost function is optimised and the solution is applied to a number of practical criteria. This has led to a convergent iterative algorithm which evaluates the associated Lagrange multiplier functions and establishes the reconstruction for all scanning geometries. Further a generalised Projection Slice Theorem is introduced based on a new Projection Transform.