Approximation and Reconstruction from Attenuated Radon Projections

Details Approximation and Reconstruction from Attenuated Radon Projections Approximation and Reconstruction from Attenuated Radon Projections

2006-03-09

arxiv.org/abs/math/0603229v1

Mathematics

Numerical Analysis

25 pages, 3 figures

Scientific paper

Attenuated Radon projections with respect to the weight function $W_\mu(x,y) = (1-x^2-y^2)^{\mu-1/2}$ are shown to be closely related to the orthogonal expansion in two variables with respect to $W_\mu$. 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.

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