TY - JOUR
T1 - A Hankel Transform Approach to Tomographic Image Reconstruction
AU - Higgins, William E.
AU - Munson, David C.
N1 - Funding Information:
Manuscript received August 18, 1986; revised September 25, 1987. This work was supported by the Joint Services Electronics Program under Con- tract N00014-79-(2-0424 and by a fellowship from the Shell Oil Company. W. E. Higgins is with the Biodynamics Research Unit, Mayo Clinic, Rochester, MN 55905. D. C. Munson, Jr. is with the Coordinated Science Laboratory and the Department of Electrical and Computer Engineering, University of Illinois, Urbana, IL 61801. IEEE Log Number 8718245.
PY - 1988/3
Y1 - 1988/3
N2 - We develop a relatively unexplored algorithm for reconstructing a two-dimensional image from a finite set of its sampled projections. The algorithm, which we refer to as the Hankel-transform reconstruction (HTR) algorithm, is polar-coordinate based. The algorithm expands the polar-form Fourier transform F(r, θ) of an image into a Fourier series in θ; calculates the appropriately ordered Hankel transform of the coefficients of this series, giving the coefficients for the Fourier series of the polar-form image f(p, Φ); resolves this series, giving a polar-form reconstruction; and finally, if desired, interpolates this reconstruction to a rectilinear grid. We outline the HTR algorithm and show that its performance can compare favorably to the popular convolution-backprojection algorithm.
AB - We develop a relatively unexplored algorithm for reconstructing a two-dimensional image from a finite set of its sampled projections. The algorithm, which we refer to as the Hankel-transform reconstruction (HTR) algorithm, is polar-coordinate based. The algorithm expands the polar-form Fourier transform F(r, θ) of an image into a Fourier series in θ; calculates the appropriately ordered Hankel transform of the coefficients of this series, giving the coefficients for the Fourier series of the polar-form image f(p, Φ); resolves this series, giving a polar-form reconstruction; and finally, if desired, interpolates this reconstruction to a rectilinear grid. We outline the HTR algorithm and show that its performance can compare favorably to the popular convolution-backprojection algorithm.
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U2 - 10.1109/42.3929
DO - 10.1109/42.3929
M3 - Article
C2 - 18230454
AN - SCOPUS:0023984231
SN - 0278-0062
VL - 7
SP - 59
EP - 72
JO - IEEE transactions on medical imaging
JF - IEEE transactions on medical imaging
IS - 1
ER -