1,018 research outputs found
Fast OPED algorithm for reconstruction of images from Radon data
A fast implementation of the OPED algorithm, a reconstruction algorithm for
Radon data introduced recently, is proposed and tested. The new implementation
uses FFT for discrete sine transform and an interpolation step. The convergence
of the fast implementation is proved under the condition that the function is
mildly smooth. The numerical test shows that the accuracy of the OPED algorithm
changes little when the fast implementation is used.Comment: 13 page
OPED reconstruction algorithm for limited angle problem
The structure of the reconstruction algorithm OPED permits a natural way to
generate additional data, while still preserving the essential feature of the
algorithm. This provides a method for image reconstruction for limited angel
problems. In stead of completing the set of data, the set of discrete sine
transforms of the data is completed. This is achieved by solving systems of
linear equations that have, upon choosing appropriate parameters, positive
definite coefficient matrices. Numerical examples are presented.Comment: 17 page
Approximation and Reconstruction from Attenuated Radon Projections
Attenuated Radon projections with respect to the weight function are shown to be closely related to the orthogonal
expansion in two variables with respect to . This leads to an algorithm
for reconstructing two dimensional functions (images) from attenuated Radon
projections. Similar results are established for reconstructing functions on
the sphere from projections described by integrals over circles on the sphere,
and for reconstructing functions on the three-dimensional ball and cylinder
domains.Comment: 25 pages, 3 figure
Reconstruction from Radon projections and orthogonal expansion on a ball
The relation between Radon transform and orthogonal expansions of a function
on the unit ball in \RR^d is exploited. A compact formula for the partial
sums of the expansion is given in terms of the Radon transform, which leads to
algorithms for image reconstruction from Radon data. The relation between
orthogonal expansion and the singular value decomposition of the Radon
transform is also exploited.Comment: 15 page
Thermoacoustic tomography with detectors on an open curve: an efficient reconstruction algorithm
Practical applications of thermoacoustic tomography require numerical
inversion of the spherical mean Radon transform with the centers of integration
spheres occupying an open surface. Solution of this problem is needed (both in
2-D and 3-D) because frequently the region of interest cannot be completely
surrounded by the detectors, as it happens, for example, in breast imaging. We
present an efficient numerical algorithm for solving this problem in 2-D
(similar methods are applicable in the 3-D case). Our method is based on the
numerical approximation of plane waves by certain single layer potentials
related to the acquisition geometry. After the densities of these potentials
have been precomputed, each subsequent image reconstruction has the complexity
of the regular filtration backprojection algorithm for the classical Radon
transform. The peformance of the method is demonstrated in several numerical
examples: one can see that the algorithm produces very accurate reconstructions
if the data are accurate and sufficiently well sampled, on the other hand, it
is sufficiently stable with respect to noise in the data
Hierarchical reconstruction using geometry and sinogram restoration
"IP Editors' Information Classification Scheme (EDICS): 2.3."Includes bibliographical references (p. 30-32).Supported by the National Science Foundation. MIP-9015281 Supported by the Office of Naval Research. N00014-91-J-1004 Supported by the U.S. Army Research Office. DAAL03-86-K-0171 Supported by a U.S. Army Research Office Fellowship.Jerry L. Prince and Alan S. Willsky
Reconstruction from projections based on detection and estimation of objects
Includes bibliographies.Caption title. "13 July 1983."National Science Foundation grant ECS-8012668David J. Rossi, Alan S. Willsky.pt.1. Performance analysis--pt.2. Robustness analysis
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