Reconstruction of 2-tensor fields, given in a unit circle, by their ray transforms based on LSM with B-splines

I. E. Svetov1,2, A. P. Polyakova2
1Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
2Novosibirsk State University, Novosibirsk, Russia

Tóm tắt

Từ khóa


Tài liệu tham khảo

Romanov, V.G., Obratnye zadachi matematicheskoi fiziki (Inverse Problems of Mathematical Physics), Moscow: Nauka, 1984.

Romanov, V.G., Integral Geometry on Geodesics of the Isotropic Riemann Metrix, Dokl. Ak. Nauk SSSR, 1978, vol. 241, no. 2, pp. 290–293.

Sharafutdinov, V.A., Integral Geometry of Tensor Fields, Utrecht: VSP, 1994.

Derevtsov, E.Yu., Kleshchev, A.G., and Sharafutdinov, V.A., Numerical Solution of the Emission 2DTomography Problem for a Medium with Absorption and Refraction, J. Inv. Ill-Posed Probl., 1999, vol. 7, no. 1, pp. 83–103.

Derevtsov, E.Yu., Svetov, I.E., and Volkov, Yu.S., Application of B-Splines in the Problem of Emission 2DTomography in a RefractiveMedium, Sib. Zh. Industr. Mat., 2008, vol. 11, no. 3(35), pp. 45–60.

Derevtsov, E.Yu. and Kashina, I.G., Approximate Solution of the Vector Tomography Problemwith theUse of Polynomial Bases, Preprint of Sobolev Inst.Math., Sib. Branch, Russ. Acad. Sci., Novosibirsk, 2000, no. 74.

Derevtsov, E.Yu., Svetov, I.E., Volkov, Yu.S., and Schuster, T., Numerical B-Spline Solution of Emission and Vector 2D-Tomography Problems for Media with Absorption and Refraction, Proc. 2008 IEEE Region 8 Int. Conf. on Computational Technologies in Electrical and Electronics Engineering SIBIRCON-08, Novosibirsk, Russia, 2008, pp. 212–217.

Derevtsov, E.Yu. and Kashina, I.G., Approximate Solution of the Problem of Two-Tensor Field Reconstruction with the Use of Polynomial Bases, Sib. Zh. Industr. Mat., 2002, vol. 5, no. 1(9), pp. 39–62.

Zav’yalov, Yu.S., Kvasov, B.I., and Miroshnichenko, V.L., Metody splain-funktsii (Methods of Spline Functions), Moscow: Nauka, 1980.

Natterer, F., The Mathematics of Computerized Tomography, New York: Wiley, 1986.

Derevtsov, E.Yu., Dietz, R., Louis, A.K., and Schuster, T., Influence of Refraction to the Accuracy of a Solution for the 2D-Emission Tomography Problem, J. Inv. Ill-Posed Probl., 2000, vol. 8, no. 2, pp. 161–191.

Statistical Methods for Digital Computers, Enslein, K., Ralston, A., and Wilf, H.S., Eds., New York: Wiley, 1977.