Convolution Algorithms for Arbitrary Projection Angles

Abstract

The point response function ψ of a convolution algorithm for reconstructing a function from a finite set of its projections is the sum of the back-projections of the filters used. An effective method is given for choosing the filters so that ψ is as close as possible to a specified point response ϕ. The weighted mean square error in approximating ϕ by ψ goes to 0 as the number of projection angles goes to infinity, independent of their placement. Compensation for additive noise in the projections is discussed and numerical results are presented.