Incremental algorithm-a new fast backprojection scheme for parallel beam geometries

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Abstract
A fast backprojection scheme for parallel beam geometries is proposed. Known as the incremental algorithm, it performs backprojection on a ray-by-ray (beam-by-beam) basis rather than the pixel-by-pixel backprojection in the conventional algorithm. By restructuring a conventional backprojection algorithm, the interdependency of pixel computations (position and value) is transformed to a set of incremental relations for a beam, where a beam is a set of pixels enclosed by two adjacent rays in 2-D computed tomography (CT), and a set of voxels enclosed by four adjacent rays in 3-D CT. To minimize the overhead of searching for the next pixels, a searching flow technique has been developed to implement the first-order and second-order incremental relations for 2-D and 3-D CTs, respectively. The values of all the pixels in each beam (except the first pixel) are computed with additions only, the key idea of the proposed backprojection scheme. The incremental algorithm has been implemented on two different machines and compared to B.F. Shepp and L.A. Logan's (1974) algorithm. The present implementation results show the superiority of this approach over the conventional algorithm.