Title :
Numerical B-spline solution of emission and vector 2D-tomography problems for media with absorption and refraction
Author :
Derevtsov, E.Yu. ; Svetov, I.E. ; Volkov, Yu.S. ; Schuster, T.
Author_Institution :
Sobolev Inst. of Math., Novosibirsk
Abstract :
A method of numerical solution for the tomography problems setting in a with medium with refraction and absorption is suggested. Namely, scalar or vector field by its ray transform calculated along geodesics of a Riemannian metric is reconstructed. The approximation of the solution is determined with usage of the least squares method. As bases we use the local bases of scalar and vector fields constructed by means of two-dimensional B-splines. Influence (on accuracy of reconstruction) such factors as smoothness of the required fields, curvature of the metrics and character of change of absorption coefficient, degree of digitization of data, an order and quantity of bases B-splines, various ways of construction of the local bases was numerically investigated.
Keywords :
absorbing media; differential geometry; electromagnetic wave absorption; electromagnetic wave refraction; emission tomography; image reconstruction; least squares approximations; splines (mathematics); tomography; vectors; Riemannian metric; absorption coefficient; absorption medium; degree of digitization; emission tomography; geodesics; least squares method; numerical B-spline solution; ray transform; reconstruction accuracy; refraction medium; vector 2D-tomography problems; Absorption; Biological system modeling; Blood flow; Least squares approximation; Least squares methods; Region 8; Spline; Tensile stress; Tomography; Tumors;
Conference_Titel :
Computational Technologies in Electrical and Electronics Engineering, 2008. SIBIRCON 2008. IEEE Region 8 International Conference on
Conference_Location :
Novosibirsk
Print_ISBN :
978-1-4244-2133-6
Electronic_ISBN :
978-1-4244-2134-3
DOI :
10.1109/SIBIRCON.2008.4602618
