# Dr. Alexander Katsevich

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## Dr. Alexander Katsevich

#### CV

#### FIELDS

Tomography, Radon transforms, Medical Imaging, Microlocal Analysis

#### DEGREES

Ph.D. in Mathematics, Kansas State University, 1994

M.S. in Applied Mathematics, Moscow Institute of Oil and Gas, 1988

#### ACADEMIC EXPERIENCE

Professor

Mathematics Department, University of Central Florida (UCF), August 2008 - present;

Associate Professor

Mathematics Department, University of Central Florida (UCF), August 2002 - July 2008;

Assistant Professor

Mathematics Department, UCF, August 1996 - July 2002;

PostDoc Fellow

Computing, Information, and Communications Division, Los Alamos National Laboratory. May 31, 1994 - July 1996;

Research Assistant

Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation of the USSR

Academy of Sciences (IZMIRAN), 1988-90

#### INVITED PROFESSOR POSITION

University of Saint-Etienne, France. Summer 2009.

#### CONFERENCE ORGANIZING

Organizer of the special session on "Medical Imaging and Tomography" of the 4^{th} International conference "Sampling Theory and Applications" (SampTA 2001). UCF, May 13-17, 2001.

Member of the scientific committee of "The VIIIth International Conference on Fully 3D

Reconstruction in Radiology and Nuclear Medicine". Salt Lake City, Utah. July 6-9, 2005

Organizer of the minisymposium "Efficient Image Reconstruction in Cone Beam Computer

Tomography" SIAM Conference on Imaging Sciences, Minneapolis, Minnesota, May 15-17,

2006.

Organizer of the minisymposium "Wave Propagation and Tomography" at the 32nd SIAM Southeastern-Atlantic Section Conference (SIAM-SEAS 2008). University of Central Florida, Orlando, FL. March 14-15, 2008.

#### PROFESSIONAL PUBLICATIONS

RESEARCH MONOGRAPH

"The Radon Transform and Local Tomography". CRC Press, 1996, 485 pp. (With A.G. Ramm).

#### AWARDS

1. Director's fellowship, Los Alamos National Laboratory, February 1995

2. Research Incentive Award, UCF, August 2001

3. Research Incentive Award, UCF, August 2006

4. Alexander von Humboldt Research Fellowship, May 2005-Aug. 2008.

5. Best paper in tomography Award. The IXth International Conference on Fully 3D Image

Reconstruction in Radiology and Nuclear Medicine. Lindau, Germany. July 2007

6. Alexander von Humboldt Research Fellowship, June, July 2012 and June 2013.

#### Publications

PAPERS

1. A. Katsevich and M.A. Frenkel. A method of interpolation of transient EM fields. In book: '*Methods for the solution of direct and inverse geoelectric problems',* IZMIRAN, Moscow, 1987, pp.78-90. In Russian.

2. M.S. Zhdanov, A. Katsevich, M.A. Frenkel. Interpolation method for transient electromagnetic fields. *Il Nuovo Cimento*, 1989, 12C, 5, pp.555-565.

3. A. Katsevich and M.A. Frenkel. Correlation method for the localization of geoelectric inhomogeneities. In the book: *'Direct and inverse problems of geoelectrics'*. NAUKA, Moscow, 1990, pp. 36-45. In Russian.

4. M.A. Frenkel and A. Katsevich. A method of physical approximation of electromagnetic field. *Geophysical Journal*, 1992, vol. 110, pp. 421-434.

5. A.G. Ramm and A. Katsevich. Inversion of incomplete Radon transform, *Appl. Math. Lett.,* Vol. 5, No. 2, pp. 41-46, 1992.

6. A. Katsevich and A.G. Ramm. FBP method for inversion of incomplete tomographic data, *Appl. Math. Lett.,* Vol. 5, No. 3, pp. 77-80, 1992.

7. A. Katsevich. Algorithm for recovering discontinuities of a function from its Radon transform, *Appl. Math. Lett*., Vol. 5, No. 4, pp. 73-75, 1992.

8. A. Katsevich and A.G. Ramm. Multidimensional algorithm for finding discontinuities of signals from noisy discrete data. "Multidimensional inverse problems", Special issue of the Journal "*Mathematical and Computer Modelling*"*.* Vol. 18, No. 1, pp. 89-107, 1993.

9. A. Katsevich and A.G. Ramm. Consistency of Rank Tests against Some General Alternatives "*Mathematical and Computer Modelling*". Vol. 18, No. 12, pp. 49-55, 1993.

10. A. Katsevich and A.G. Ramm. Nonparametric estimation of the singularities of a signal from noisy measurements. *Proceedings of the AMS*. Vol. 120, No. 8, pp. 1221-1234, 1994.

11. A. Katsevich and A.G. Ramm. A method for finding discontinuities of functions from the tomographic data. In book "*Tomography, impedance imaging, and integral geometry*"*. Lectures in Applied Mathematics*, Vol. 30, pp. 115-123. Amer. Math. Soc., NY, 1994.

12. A. Katsevich and A.G. Ramm. Some mathematical results in signal and image processing. *Doklady, Russian Academy of Sciences*. Vol. 339, No. 1, pp. 11-14, 1995.

13. A. Katsevich. Kernel estimation of the singularities of a signal. *PanAmerican Mathematical Journal*, Vol. 5, No. 1, 1995, pp. 1-11.

14. A. Katsevich and A.G. Ramm. Finding singular support of a function from its tomographic data. *Proceedings of the Japan Academy, Series A: Mathematical Sciences*. Vol. 71, No. 3, pp. 62-67, 1995.

15. V. Faber, A. Katsevich, and A.G. Ramm. Inversion of cone-beam data and helical tomography. *Journal of Inverse and Ill-Posed Problems*, Vol. 3, No. 6, pp. 429 - 445, 1995.

16. A. Katsevich and A.G. Ramm. Asymptotics of PDO (pseudodifferential operators) on discontinuous functions near singular support. *Applicable Analysis*, Vol. 58, No. 3-4, pp. 383-390, 1995.

17. A. Katsevich and A.G. Ramm. New methods for finding values of the jumps of a function from its local tomographic data. *Inverse Problems*, Vol. 11, No. 5, pp. 1005-1023, 1995.

18. A. Katsevich and A.G. Ramm. Pseudolocal tomography. *SIAM**J. Appl. Math*, Vol. 56, No. 1, pp. 167-191, 1996.

19. A. Katsevich and A.G. Ramm. Approximate inverse geophysical scattering on a small body. *SIAM**J. Appl. Math*, Vol. 56, No. 1, pp. 192-218, 1996.

20. A. Katsevich and A.G. Ramm. Consistency of a rank test against general alternatives of change points (surfaces) and continuous trend. *Acta Applicandae Mathematicae*, Vol. 42, No. 2, pp. 105-137, 1996.

21. A. Katsevich and A.G. Ramm. Approximate solution to inverse scattering problem for potentials with small support. *Mathematical Methods in the Applied Sciences*, Vol. 19, pp. 1121-1134, 1996.

22. A. Katsevich and A.G. Ramm. Finding jumps of a function using local tomography. *PanAmerican Mathematical Journal*, Vol. 6, No. 2, pp. 1-21, 1996.

23. A. Katsevich. Local reconstructions in exponential tomography. *Journal of Mathematical Analysis and Applications*, Vol. 199, pp. 425-444, 1996.

24. A. Katsevich. Local tomography for the generalized Radon transform. *SIAM**J. Appl. Math*, Vol. 57, No. 4, 1997, pp. 1128-1162

25. A. Katsevich. Range of the Radon transform on functions which do not decay fast at infinity. *SIAM**J. on Math. Analysis*, Vol. 28, No. 4, pp. 852-866, 1997.

26. A. Katsevich. Local tomography for the limited-angle problem. *Journal of Mathematical Analysis and Applications*, Vol. 213, pp. 160-182, 1997.

27. A. Katsevich. Local tomography with non-smooth attenuation II. In book "*Inverse Problems, Tomography, and Image Processing*" (A. G. Ramm, editor), pp. 73-86, 1998, Plenum, New York.

28. A. Katsevich. Local tomography with non-smooth attenuation. *Transactions of the American Mathematical Society*, Vol. 351, pp. 1947-1974, 1999.

29. A. Katsevich. Asymptotics of pseudodifferential operators acting on functions with corner singularities. *Applicable Analysis*, Vol. 72, pp. 229-252, 1999.

30. A. Katsevich. Cone beam local tomography. *SIAM* *J. Appl. Math*. Vol. 59, pp. 2224--2246 (1999).

31. A. Katsevich. Analysis of artifacts in local tomography with non-smooth attenuation. *Contemporary Mathematics, Amer. Math. Soc*. Vol. 251, pp.339-370 (2000).

32. A. Katsevich. On quasi-local inversion of spiral CT data. *Mathematical Methods in the Applied Sciences*. Vol. 23, pp. 271-297 (2000).

33. A. Katsevich. New range theorems for the dual Radon transform. *Transactions of the American Mathematical Society*, Vol. 353, pp. 1089-1102 (2001).

34. A. Katsevich. Range theorems for the Radon transform and its dual. *Contemporary Mathematics, Amer. Math. Soc.*, Vol. 278, pp. 167-191 (2001).

35. A. Katsevich. Micro-local analysis of an FBP algorithm for truncated spiral cone beam data. *The Journal of Fourier Analysis and Applications*, Vol. 8, pp. 407-425 (2002).

36. A. Katsevich. Theoretically exact FBP-type inversion algorithm for spiral CT. *SIAM J. Appl. Math.*, Vol. 62, pp. 2012-2026 (2002).

37. A. Katsevich. Analysis of an exact algorithm for spiral cone beam CT. *Physics in Medicine and Biology*, Vol. 47, pp. 2583-2597 (2002)

38. A. Katsevich. A general scheme for constructing inversion algorithms for cone beam CT, *International Journal of Mathematics and Mathematical Sciences*, Vol. 21, pp. 1305-1321 (2003).

39. A. Katsevich. Improved exact filtered back-projection algorithm for spiral CT. *Advances in Applied Mathematics,* Vol. 32, pp. 681-697 (2004).

40. A. Katsevich and G. Lauritsch.. Filtered back-projection algorithms for spiral cone beam CT. In book: *Sampling, Wavelets, and Tomography*. (A. Zayed and J. Benedetto, editors), pp. 255-287, 2003, Birkhauser, Boston.

41. A. Katsevich. On two versions of a 3p algorithm for spiral CT. *Physics in Medicine and Biology*, Vol. 49, pp. 2129 - 2143 (2004).

42. A. Katsevich, S. Basu, and J. Hsieh. Exact filtered backprojection reconstruction for dynamic pitch helical cone beam computed tomography. *Physics in Medicine and Biology*, Vol. 49, pp. 3089 - 3103 (2004).

43. A. Katsevich. Image reconstruction for the circle and line trajectory. *Physics in Medicine and Biology*, Vol. 49, pp. 5059 - 5072 (2004). - Institute of Physics (IoP) Select article.

Articles for IoP Select are chosen by IoP editors "for their novelty, significance and potential impact on future research".

44. A. Katsevich. An inversion formula for the dual horocyclic Radon Transform on the hyperbolic plane. *Mathematische Nachrichten*, Vol. 278, pp. 437 - 450 (2005).

45. A. Katsevich. Stability estimates for helical CT. *Journal of Fourier Analysis and* Applications, Vol. 11, no. 1, pp. 85 - 105 (2005).

46. A. Katsevich. Image reconstruction for the circle and arc trajectory. *Physics in Medicine and Biology*, Vol. 50, pp. 2249 - 2265 (2005).

47. A. Katsevich and A. Zamyatin. Analysis of a family of exact inversion formulas for cone beam CT. *Contemporary Mathematics, Amer. Math. Soc.* Vol. 405, pp. 59 -74 (2006).

48. A. Katsevich. 3PI algorithms for helical computer tomography. *Advances in Applied Mathematics,* Vol. 36, pp. 213 - 250 (2006).

49. A. Katsevich, K. Taguchi, and A. Zamyatin. Formulation of four Katsevich algorithms in native geometry. *IEEE Transactions on Medical Imaging*. Vol. 25, pp. 855 - 868 (2006).

50. A. Katsevich. Improved cone beam local tomography. *Inverse Problems*, Vol. 22, pp. 627 - 643 (2006).

This article has been selected by the Editorial Board for the 2006 highlights.

51. M. Kapralov and A. Katsevich. A one-PI algorithm for helical trajectories that violate the convexity condition. *Inverse Problems*. Vol. 22, pp. 2123 - 2143 (2006). - Institute of Physics (IoP) Select article.

Articles for IoP Select are chosen by IoP editors "for their novelty, significance and potential impact on future research".

52. A. Katsevich and M. Kapralov. Filtered backprojection inversion of the cone beam transform for a general class of curves. *SIAM* *J. Appl. Math.* Vol. 68, pp. 334-353 (2007).

53. A. Katsevich. Image reconstruction for a general circle-plus trajectory. *Inverse Problems*. Vol. 23, pp. 2223 - 2230 (2007).

54. A. Katsevich. Motion compensated local tomography. *Inverse Problems*. Vol. 24 (2008). Article id 045012 (21pp)

55. A. Katsevich and F. Natterer. Ultrasound tomography with sources on a line. "*Mathematical Methods in Biomedical Imaging and Intensity-Modulated Radiation Therapy (IMRT)*", Y. Censor, M. Jiang and A.K. Louis, Editors, Edizioni della Normale, Pisa, Italy, 2008.

56. A. Zamyatin, A. Katsevich, and B. S. Chiang. Exact image reconstruction for circle and line trajectory with gantry tilt. *Physics in Medicine and Biology*. Vol. 53, pp. N423 - N435 (2008).

57. M. Kapralov and A. Katsevich. On the study of 1PI algorithms for a general class of curves. *SIAM* *Journal on Imaging Sciences*. Vol. 1, pp. 418 - 459 (2008).

58. A. Katsevich, A. Zamyatin,and M. Silver. Optimized reconstruction algorithm for helical CT with fractional pitch between 1PI and 3PI. *IEEE Transactions on Medical Imaging*. Vol. 28, pp. 982 - 990 (2009).

59. A. Katsevich. An approach to motion compensation in tomography. In volume: *Biomedical Mathematics: Promising Directions in Imaging, Therapy Planning and Inverse Problems*, Yair Censor, Ming Jiang and Ge Wang (Editors), Medical Physics Publishing, Madison, Wisconsin, pp. 221 - 242 (2010).

60. Y. Lu, A. Katsevich, J. Zhao, H. Yu, and G. Wang. Fast Exact/Quasi-Exact FBP Algorithms for Triple-Source Helical Cone-Beam CT. *IEEE Transactions on Medical Imaging* Vol. 29, pp. 756 - 770 (2010).

61. A. Katsevich. An accurate approximate algorithm for motion compensation in two- dimensional tomography. *Inverse Problems*. Vol. 26, article id 065007 (2010).

62. A. Katsevich. Singular value decomposition for the truncated Hilbert transform. *Inverse Problems*. Vol. 26, article id 115011, 12pp (2010).

63. A. Katsevich, M. Silver, and A. Zamyatin. Local tomography and the motion estimation problem. *SIAM* *Journal on Imaging Sciences*. Vol. 4, pp. 200 - 219 (2011).

64. A. Katsevich. A note on computing the derivative at constant direction. *Physics in Medicine and Biology*. Vol. 56, pp. N53 - N61 (2011).

65. A. Katsevich. Singular value decomposition for the truncated Hilbert transform: part II. *Inverse Problems*. Vol. 27, article id 075006, 7pp (2011).

66. G. Wang, H. Yu, W. Cong, and A. Katsevich. Non-uniqueness and instability of

'ankylography'. *Nature*. Vol. 480 (2011).

67. M. Bertola, A. Katsevich, and A. Tovbis. Inversion formulae for the cosh-weighted Hilbert transform. *Proceedings of the AMS* (2012), to appear.