Numerical solution of the emission 2D-tomography problem for a medium with absorption and refraction
Numerical solution of the emission 2D-tomography problem for a medium with absorption and refraction
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具有吸收和折射介质的发射二维断层扫描问题的数值求解
DOI：
10.1515/jiip.1999.7.1.83
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发表时间：
1999
影响因子：
0.3
通讯作者：
V. Sharafutdinov
中科院分区：
文献类型：
--
作者：
E. Derevtsov;A. G. Kleshchev;V. Sharafutdinov
本文提出了一种求解二维折射介质中任意变化吸收的发射层析成像问题的数值方法。通过沿已知黎曼度量的测地线的指数射线变换重建源分布。近似解由最小二乘法确定，并通过最佳逼近收敛到精确解。多项式序列被用作基本函数。沿着求解发射层析成像问题的方法，我们首先提出了重建吸收系数近似值的数值方法，然后提出了重建源函数的数值方法。数值模拟验证了该算法的有效性，并对Sobolev空间的源函数进行了重构。
We suggest a numerical method for the solving emission tomography problem in a refracting 2D-media with an arbitrary varying absorption. The source distribution is reconstructed by its exponential ray transform along the geodesic lines of a known Riemannian metric. The approximate solution is determined by the least squares method and converges to the exact solution by meaning of the best approximation. The sequence of polynomials are used as the basic functions. Along with the method of a solution to the emission tomography problem we suggest the numerical method for reconstruction of the approximation of the absorption coefficient at first and then the reconstruction of the source function as well. Numerical simulations verify an efficiency of the algorithm and show good results of the reconstruction of source functions belonging to Sobolev's spaces.