1,432 research outputs found
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
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
A new approach to the reconstruction of images from Radon projections
A new approach is proposed for reconstruction of images from Radon
projections. Based on Fourier expansions in orthogonal polynomials of two and
three variables, instead of Fourier transforms, the approach provides a new
algorithm for the computed tomography. The convergence of the algorithm is
established under mild assumptions.Comment: 28 pages, accepted by Adv. in Applied Mat
Inversion of noisy Radon transform by SVD based needlet
A linear method for inverting noisy observations of the Radon transform is
developed based on decomposition systems (needlets) with rapidly decaying
elements induced by the Radon transform SVD basis. Upper bounds of the risk of
the estimator are established in () norms for functions
with Besov space smoothness. A practical implementation of the method is given
and several examples are discussed
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