Back Projection Speed Improvement for 3-D Reconstruction

The Fourier convolution algorithm has been used to reconstruct a 3-D density function. The method involves a particular choice of weighting function to convolve with projection data sets scanned through various angles from 0 to π. The convolved data are then back projected to obtain a 2-D image. A 3-D reconstruction is obtained as a stack of 2-D images. Because the new tomographic machines have much finer resolution, the number or projection data to be processed is considerably more than with the early models. The amount of data to be processed makes critical the need for improvements in both the speed as well as the accuracy. A first step toward speed improvement is to use a finite field transform to perform the convolutions. This was shown previously by the authors to be, in fact, a worthwhile effort. Another and most time-consuming part of the reconstruction algorithm is the so-called back-projection algorithm. The purpose of this paper is to present a method for speeding-up the back-projection algorithm by cutting down the computational time by a factor of two.