Faster tomographic fan-beam back-projection using Cartesian axes pre-projection

The convolution back-projection algorithm is the most common method for reconstructing images from complete sets of fan-beam projections. For each pixel and for every projection, the interception point on the detector array must be determined and a weighted value from the appropriate point on the filtered back projection added. Thus the number of operations required is of order n(2)p, where it is the number of points per projection, and p the number of projections. This can mean a considerable computation time: even with modern, fast computer workstations. The complexity of each pixel operation (weighting and geometric computations) is reduced if the projection is first pre-projected onto one or other of the Cartesian axes. This has been demonstrated to reduce the computational time by a factor of 2, with no loss of accuracy, when compared with a highly optimised implementation of the conventional fan-beam back-projection algorithm. (C) 1998 Elsevier Science B.V. All rights reserved.