A FAST APPROXIMATION ALGORITHM FOR 3D IMAGE RECONSTRUCTION

Abstract

In this paper we present a fast algorithm for the computation of plannar projections of a 3D image (i.e., the three-dimensional Radon Transform, or 3DRT) and the inverse problem of reconstruction a 3D image from its projections. For an N*N*N image I(x,y,z), it would generally require O(N^5) time to compute the projections of N^3 different planes, since each plane contains about N^2 sample points from I(x,y,z). Reconstruction of an N*N*N image from N^3 projections also would usually take O(N^5) time. Our fast approximate algorithm performs planar projection and backprojection in only O(N^3log N) time.