Shear-Based Fast Hierarchical Backprojection for Parallel-Beam Tomography

Author

George, Ashvin K. ; Bresler, Yoram

Author_Institution

Coordinated Sci. Lab., Illinois Univ., Urbana, IL

Volume

26

Issue

3

fYear

2007

fDate

3/1/2007 12:00:00 AM

Firstpage

317

Lastpage

334

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(N²logP), when backprojecting an NtimesN 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

Keywords

Fourier transforms; computerised tomography; medical image processing; 2-D parallel-beam tomographic backprojection; Fourier-domain interpretation; parallel-beam tomography; shear-based fast hierarchical backprojection; Aggregates; Biomedical imaging; Computational efficiency; Computed tomography; Image reconstruction; Iterative algorithms; Magnetic resonance imaging; Positron emission tomography; Reconstruction algorithms; Shearing; Backprojection; fast algorithm; image shear; radon transform; spline interpolation; tomography; Algorithms; Image Enhancement; Image Interpretation, Computer-Assisted; Imaging, Three-Dimensional; Phantoms, Imaging; Reproducibility of Results; Sensitivity and Specificity; Tomography;

fLanguage

English

Journal_Title

Medical Imaging, IEEE Transactions on

Publisher

ieee

ISSN

0278-0062

Type

jour

DOI

10.1109/TMI.2006.887370

Filename

4114553