Projections, reconstructions and orthogonal functions

AbstractThe techniques used for reconstructing an object from its projections are set up within a general mathematical framework. We show that the simplest version of the problem involves choosing a generator for two sets of orthogonal functions, and we also give the general theory. We illustrate the power of the method by considering in detail four examples of special projections. We have done these calculations to tie together with a general theory the many different choices of orthogonal polynomial that have been used by various investigators in the problem of projection and reconstruction and to show, by specific illustration, the interconnection of these various functions