Efficient implementation of "optimal" algorithms in computerized tomography

Abstract

We describe three optimal algorithms for the reconstruction of a function in mathbb{R}^{2} from a finite number of line or strip integrals: Optimal recovery, Bayes estimate, Tikhonov-Phillips method. In the case of a rotationally invariant scanning geometry we show that the resulting linear system is a bloc-cyclic convolution. This observation leads to algorithms which are roughly as efficient as filtered backprojection which is one of the standard methods. The algorithms can be applied to the case of hollow and truncated projections. Numerical examples are given.