Approximation and Reconstruction from Attenuated Radon Projections

2006/03/09 by Yuan Xu, Xu, Yuan, Oleg Tischenko +3
Computer Science · Medicine · #42A38 #42B08 #42B15 #Classical Analysis and ODEs (math.CA) #Digital Image Processing Techniques #FOS: Mathematics #Medical Image Segmentation Techniques #Medical Imaging Techniques and Applications #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.math/0603229

openalex publication_date 2006/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Attenuated Radon projections with respect to the weight function W_μ(x,y) = (1-x²-y²)^μ-1/2 are shown to be closely related to the orthogonal expansion in two variables with respect to W_μ. 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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