衰减Radon投影的逼近与重建
Approximation and Reconstruction from Attenuated Radon Projections
AI总结：
本文揭示了加权函数W_μ下的衰减Radon投影与双变量正交展开的紧密联系，并据此提出了从衰减Radon投影重建二维函数（图像）的算法，同时将类似结果推广到球面、三维球体和圆柱域上的函数重建。
摘要：
对于权重函数$W_μ(x,y) = (1-x^2-y^2)^{μ-1/2}$，衰减Radon投影被证明与关于$W_μ$的双变量正交展开密切相关。这导致了一种从衰减Radon投影重建二维函数（图像）的算法。对于由球面上的圆积分描述的投影重建球面函数，以及三维球体和圆柱域上的函数重建，也建立了类似的结果。
英文摘要：
Attenuated Radon projections with respect to the weight function $W_μ(x,y) = (1-x^2-y^2)^{μ-1/2}$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
