Abstract
CT 2(pi) helical weighting algorithms do not lend themselves to fast reconstruction: the weight distributions present a line of discontinuity across the sinogram which defines two separate regions and associated weight expressions. Accordingly, reconstruction of P image planes requires P weightings and filterings of all projections. This paper shows that, by generalizing the concept of the interpolation/extrapolation function to that of distance function, and by selecting particular classes of such functions, the sinogram discontinuity can be eliminated. By imposing specific necessary conditions, single analytical expressions across the entire 2(pi) sinogram are obtained. Decomposition of these particular 'single' functions leads to exact or approximate fast two-filtering algorithms, for which a given projection needs to be filtered only two times for an arbitrary number P of reconstruction planes. Further, another generalization of the concept of helical weighting leads to 'single' weighting functions that depend only on the sum of the projection- and fan-angles. Accordingly, after rebinning the fan-beam projections to parallel projections, weighting commutes with filtering, and reconstruction of an arbitrary number P of image planes requires only one filtering per projection.
