The fast discrete Radon transform. I. Theory

An inversion scheme for reconstruction of images from projections based on the slope-intercept form of the discrete Radon transform is presented. A seminal algorithm for the forward and the inverse transforms proposed by G. Beylkin (1987) demonstrated poor dispersion characteristics for steep slopes...

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Bibliographic Details
Published in:IEEE transactions on image processing 1993-07, Vol.2 (3), p.382-400
Main Authors: Kelley, B.T., Madisetti, V.K.
Format: Article
Language:English
Subjects:
Application software
Applied sciences
Concurrent computing
Discrete transforms
Exact sciences and technology
Geophysics computing
Grid computing
Image processing
Image reconstruction
Information, signal and communications theory
Signal processing
Telecommunications and information theory
Time domain analysis
Tomography
Ultrasonic imaging
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Summary:An inversion scheme for reconstruction of images from projections based on the slope-intercept form of the discrete Radon transform is presented. A seminal algorithm for the forward and the inverse transforms proposed by G. Beylkin (1987) demonstrated poor dispersion characteristics for steep slopes and could not invert transforms based on nonlinear slope variations. By formulating the computation of a discrete computation of the continuous Radon transform formula, the authors explicitly derive fast generalized inversion methods that overcome the original shortcomings. The generalized forward (FRT) and inverse (IFRT) algorithms proposed are fast, eliminate interpolation calculations, and convert directly between a raster scan grid and a rectangular/polar grid in one step.< >
ISSN:1057-7149
1941-0042
DOI:10.1109/83.236530