01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
06.03.1950
E-mail:
,
Keywords:
tensor tomography; refraction; anisotropy; integral geometry; inverse problem; integral equation; elliptic system; solenoidal field; approximation; interpolation; numerical simulation.
Subject:
The constructive methods and algorithms of reconstruction of a solenoidal part of the tensor field, given in domains with Euclidean or Riemannian metrics, by its ray transform are developed (some part of the work has been done together with V. A. Sharafutdinov, I. G. Kashina, M. A. Bezuglova, S. B. Sorokin). The finite difference approximations of covariant derivative and some other geometrical objects and operators, with conservation of main geometrical properties, are constructed in the domains with a given Riemannian metric. The polynomial approximations of solenoidal and potential tensor fields are investigated. For a refracted medium with an arbitrary absorption the numerical solution to the emission tomography problem is suggested (with V. A. Sharafutdinov, A. G. Kleshchev). The influence of refraction to the accuracy of the solution for the problem is investigated (with R. Dietz, A. K. Louis, T. Schuster). In the spaces of distributions with compact support the examples of distributions, that have vanishing images in the arbitrary given finite set of points of $R^{n}$, are constructed. For the problem of reconstruction of the optical surfaces of some types the questions of uniqueness are considered, and the constructive methods and algorithms are created, if two or three images of the surface are given.
Biography
Graduated from Faculty of Mathematics and Mechanics of Novosibirsk State University (NSU) in 1973 (department of numerical mathematics). Ph.D. thesis was defended in 1986. A list of my works contains more than 40 titles.
Main publications:
Derevtsov E. Yu. Ghost distributions in the cone-beam tomography // J. Inverse Ill-posed Problems, 1997, 5(5), 411–426.
Derevtsov E. Yu., Kleshchev A. G., Sharafutdinov V. A. Numerical solution of the emission 2D-tomography problem for a medium with absorption and refraction // J. Inverse Ill-posed Problems, 1999, 7(1), 83–103.
Derevtsov E. Yu., Dietz R., Louis A. K., Schuster Th. Influence of refraction to the accuracy of a solution for the 2D-emission tomography problem // J. Inverse Ill-posed Problems, 2000, 8(2), 161–191.
E. Yu. Derevtsov, S. V. Maltseva, “Recovery of a vector field in the cylinder by its jointly known NMR images and ray transforms”, Sib. Èlektron. Mat. Izv., 18:1 (2021), 86–103
3.
Yu. E. Anikonov, V. V. Bogdanov, Yu. S. Volkov, E. Yu. Derevtsov, “On the determination of the velocity and elastic parameters of the focal zone medium from the earthquake hodographs”, Sib. Zh. Ind. Mat., 24:4 (2021), 5–24
E. Yu. Derevtsov, “On the angular moment operators of attenuated ray transforms of scalar 3D-fields”, Sib. Zh. Ind. Mat., 23:2 (2020), 51–62; J. Appl. Industr. Math., 14:2 (2020), 256–264
2018
5.
E. Yu. Derevtsov, S. V. Maltseva, I. E. Svetov, “Determination of discontinuities of a function in a domain with refraction from its attenuated ray transform”, Sib. Zh. Ind. Mat., 21:4 (2018), 51–74; J. Appl. Industr. Math., 12:4 (2018), 619–641
E. Yu. Derevtsov, “On generalization of exponential ray transform in tomography”, Sib. J. Pure and Appl. Math., 18:4 (2018), 29–42; J. Math. Sci., 253:3 (2021), 369–381
E. Yu. Derevtsov, S. V. Mal'tseva, I. E. Svetov, “Mathematical models and algorithms for reconstruction of singular support of functions and vector fields by tomographic data”, Eurasian Journal of Mathematical and Computer Applications, 3:4 (2015), 4–44
8.
E. Yu. Derevtsov, I. E. Svetov, “Tomography of tensor fields in the plane”, Eurasian Journal of Mathematical and Computer Applications, 3:2 (2015), 25–69
9.
E. Yu. Derevtsov, “A difference approximation of the covariant derivative and other operators and geometric objects given in a Riemannian domain”, Sib. Èlektron. Mat. Izv., 12 (2015), 973–990
10.
E. Yu. Derevtsov, “Numerical solution of a problem of refractive tomography in a tube domain”, Sib. Zh. Ind. Mat., 18:4 (2015), 30–41
E. Yu. Derevtsov, S. V. Maltseva, “Reconstruction of a singular support of a tensor field given in refractive medium by its ray transform”, Sib. Zh. Ind. Mat., 18:3 (2015), 11–25; J. Appl. Industr. Math., 9:4 (2015), 447–460
E. Yu. Derevtsov, S. V. Maltseva, I. E. Svetov, “A numerical inversion of the ray transform operator in refraction tomography”, Sib. Èlektron. Mat. Izv., 11 (2014), 833–856
E. Yu. Derevtsov, S. V. Maltseva, I. E. Svetov, “Approximate recovery of a function given in a domain with low refraction from the ray integrals of the function”, Sib. Zh. Ind. Mat., 17:4 (2014), 48–59; J. Appl. Industr. Math., 9:1 (2015), 36–46
E. Yu. Derevtsov, A. P. Polyakova, “An Application of the SVD-Method to the Problem of Integral Geometry of 2-Tensor Fields”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 12:3 (2012), 73–94; J. Math. Sci., 202:1 (2014), 50–71
E. Yu. Derevtsov, V. V. Pickalov, “Reconstruction of vector fields and their singularities from ray transforms”, Sib. Zh. Vychisl. Mat., 14:1 (2011), 29–46; Num. Anal. Appl., 4:1 (2011), 21–35
Yu. E. Anikonov, Yu. S. Volkov, S. B. Gorshkalev, E. Yu. Derevtsov, S. V. Maltseva, “Certain Criterion for the Horizontal Homogeneity of a Medium in Inverse Kinematic Problem of Seismics”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 11:3 (2011), 3–19; J. Math. Sci., 195:6 (2013), 741–753
E. Yu. Derevtsov, “Some approaches to a reconstruction of a singular support of scalar, vector and tensor fields by their known tomographic data”, Sib. Èlektron. Mat. Izv., 5 (2008), 632–646
E. Yu. Derevtsov, I. E. Svetov, Yu. S. Volkov, “Использование $B$-сплайнов в задаче эмиссионной $2D$-томографии в рефрагирующей среде”, Sib. Zh. Ind. Mat., 11:3 (2008), 45–60
Yu. E. Anikonov, V. V. Bogdanov, E. Yu. Derevtsov, V. L. Miroshnichenko, N. A. Sapozhnikova, “Numerical solution of an inverse kinematic seismic problem with internal sources”, Sib. Zh. Ind. Mat., 9:4 (2006), 3–26
E. Yu. Derevtsov, I. G. Kashina, “Approximate solution of the problem of the reconstruction of a tensor field of valence two using polynomial bases”, Sib. Zh. Ind. Mat., 5:1 (2002), 39–62
E. Yu. Derevtsov, I. G. Kashina, “Numerical solution to the vector tomography problem using polynomial basis”, Sib. Zh. Vychisl. Mat., 5:3 (2002), 233–254
M. M. Lavrent'ev, E. Yu. Derevtsov, V. A. Sharafutdinov, “On the determination of an optical body in a homogeneous medium from its images”, Dokl. Akad. Nauk SSSR, 260:4 (1981), 799–803
Contact us: