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  • Title: Shear-based fast hierarchical backprojection for parallel-beam tomography.
    Author: George AK, Bresler Y.
    Journal: IEEE Trans Med Imaging; 2007 Mar; 26(3):317-34. PubMed ID: 17354638.
    Abstract:
    We introduce a family of fast algorithms for 2-D parallel-beam tomographic backprojection. They aggregate the projections in a hierarchical structure involving the shearing and addition of sparsely sampled images. The algorithms achieve a computational cost of O(N(2) log P), when backprojecting an N x N pixel image from P projections. The algorithms provide a systematic means, guided by a Fourier-domain interpretation, to adjust and optimize the tradeoff between computational cost and accuracy. In an example with N = 512 and P = 1458 the algorithms provide high accuracy, with more than an order of magnitude reduction in operation counts.
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