title: Shear-based fast hierarchical backprojection for parallel-beam tomography.
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.
authors.affiliation: Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. akgeorge@uiuc.edu
authors.forename: Ashvin K
authors.initials: AK
authors.lastname: George
authors.forename: Yoram
authors.initials: Y
authors.lastname: Bresler
mesh_terms: D000465:Algorithms; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D019047:Phantoms, Imaging; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D014054:Tomography / Q000295:instrumentation / Q000379:methods*