Three-dimensional reconstruction from projections

Jelínek, Jiří, Segeth, Karel, and Overton, T. R.. "Three-dimensional reconstruction from projections." Aplikace matematiky 30.2 (1985): 92-109. <http://eudml.org/doc/15388>.

@article{Jelínek1985,
abstract = {Computerized tomograhphy is a technique for computation and visualization of density (i.e. X- or $\gamma $-ray absorption coefficients) distribution over a cross-sectional anatomic plane from a set of projections. Three-dimensional reconstruction may be obtained by using a system of parallel planes. For the reconstruction of the transverse section it is necessary to choose an appropriate method taking into account the geometry of the data collection, the noise in projection data, the amount of data, the computer power available, the accuracy required etc. In the paper the theory related to the convolution reconstruction methods is reviewed. The principal contribution consists in the exact mathematical treatment of Radon’s inverse transform based on the concepts of the regularization of a function and the generalized function. This approach naturally leads to the employment of the generalized Fourier transform. Reconstructions using simulated projection data are presented for both the parallel and divergent-ray collection geometries.},
author = {Jelínek, Jiří, Segeth, Karel, Overton, T. R.},
journal = {Aplikace matematiky},
keywords = {research survey; parallel beam; divergent beam; ill-posed problem; convolution reconstruction methods; computer tomography; Radon’s inverse transform; regularization; generalized Fourier transform; spatial filter; window functions; errors; research survey; parallel beam; divergent beam; ill-posed problem; convolution reconstruction methods; computer tomography; Radon's inverse transform; regularization; generalized Fourier transform; spatial filter; window functions; errors},
language = {eng},
number = {2},
pages = {92-109},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Three-dimensional reconstruction from projections},
url = {http://eudml.org/doc/15388},
volume = {30},
year = {1985},
}

TY - JOUR
AU - Jelínek, Jiří
AU - Segeth, Karel
AU - Overton, T. R.
TI - Three-dimensional reconstruction from projections
JO - Aplikace matematiky
PY - 1985
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 30
IS - 2
SP - 92
EP - 109
AB - Computerized tomograhphy is a technique for computation and visualization of density (i.e. X- or $\gamma $-ray absorption coefficients) distribution over a cross-sectional anatomic plane from a set of projections. Three-dimensional reconstruction may be obtained by using a system of parallel planes. For the reconstruction of the transverse section it is necessary to choose an appropriate method taking into account the geometry of the data collection, the noise in projection data, the amount of data, the computer power available, the accuracy required etc. In the paper the theory related to the convolution reconstruction methods is reviewed. The principal contribution consists in the exact mathematical treatment of Radon’s inverse transform based on the concepts of the regularization of a function and the generalized function. This approach naturally leads to the employment of the generalized Fourier transform. Reconstructions using simulated projection data are presented for both the parallel and divergent-ray collection geometries.
LA - eng
KW - research survey; parallel beam; divergent beam; ill-posed problem; convolution reconstruction methods; computer tomography; Radon’s inverse transform; regularization; generalized Fourier transform; spatial filter; window functions; errors; research survey; parallel beam; divergent beam; ill-posed problem; convolution reconstruction methods; computer tomography; Radon's inverse transform; regularization; generalized Fourier transform; spatial filter; window functions; errors
UR - http://eudml.org/doc/15388
ER -