Gaik Ambartsoumian

Research Interests

  • Computerized Tomography
  • Integral Geometry
  • Inverse Problems
  • Mathematical Problems of Imaging


Broken Rays, Cones, And Stars In Tomography.

Peer-Reviewed Publications

  1. Microlocal analysis of the generalized V-line transforms, (with V. Krishnan and E. T. Quinto) in preparation.
  2. Numerical implementation of inversion schemes for generalized V-line transforms of 2D vector fields, (with M. J. Latifi-Jebelli, and R. K. Mishra) in preparation.
  3. Inversion and symmetries of the star transform, (with M. J. Latifi-Jebelli) to appear in The Journal of Geometric Analysis 31 (2021), pp 11270-11291.
  4. Generalized V-line transforms in 2D vector tomography, (with M. J. Latifi-Jebelli, and R. K. Mishra) Inverse Problems 36 (2020), no. 10, 104002.
  5. Improved interior tomography reconstruction based on prior knowledge, (with L. Florescu and E. Bridges) American Institute of Physics Conference Proceedings, vol. 2302, 060002 (2020).
  6. Generalized Radon transforms and applications in tomography, (with E. T. Quinto) Inverse Problems 36 (2019), no. 2, 020301.
  7. Inversion of the star transform, (with M. J. Latifi-Jebelli) in Tomographic Inverse Problems: Theory and Applications, edited by M. Burger, B. Hahn and E. T. Quinto, Oberwolfach Reports, EMS, 2019.
  8. V-line and conical Radon transforms with applications in imaging, Chapter 7 in The Radon Transform: The First 100 Years and Beyond, edited by R. Ramlau and O. Scherzer, Radon Series on Computational and Applied Mathematics, De Gruyter, 2019.
  9. The V-line transform with some generalizations and cone differentiation, (with M. J. Latifi-Jebelli) Inverse Problems 35 (2019), no. 3, 034003.
  10. Singular FIOs in SAR imaging, II: transmitter and receiver at different speeds, (with R. Felea, V. Krishnan, C. Nolan, and E. T. Quinto) SIAM Journal on Mathematical Analysis, vol. 50 (1), 2018, pp 591-621.
  11. Image reconstruction from radially incomplete spherical Radon data, (with R. Gouia-Zarrad, V. Krishnan, and S. Roy) European Journal of Applied Mathematics, vol. 29 (2018), issue 3, pp 470-493.
  12. Numerical inversion of a broken ray transform arising in single scattering optical tomography, (with S. Roy) IEEE Transactions on Computational Imaging, vol. 2 (2016), issue 2, pp 166-173.
  13. Inversion of a class of circular and elliptical Radon transforms, (with V. Krishnan) Contemporary Mathematics, vol. 653 (2015), 13174.
  14. Microlocal analysis and imaging, (with R. Felea, V. Krishnan, C. Nolan, and E. T. Quinto) in Mathematics of Planet Earth, edited by H. Kaper and C. Rousseau, SIAM, 2015.
  15. Integral geometry and mathematical problems of image reconstruction, A chapter in Mathematical Models, Methods and Applications, edited by A.H. Siddiqi, P. Manchanda, and R. Bhardwaj, Industrial and Applied Mathematics Series, Springer, 2015.
  16. Exact inversion of the conical Radon transform with a fixed opening angle, (with R. Gouia-Zarrad) Inverse Problems 30 (2014), no. 4, 045007.
  17. Exterior/interior problem for the circular means transform with applications to intravascular imaging, (with L. Kunyansky) Inverse Problems and Imaging, 8, no. 2 (2014), pp 339-359.
  18. On the V-line Radon transform and its applications in imaging, (with R Gouia-Zarrad, and S. Moon) in Mathematics and Algorithms in Tomography, edited by M. Burger, A. K. Louis, and E. T. Quinto, Oberwolfach Reports, Vol. 11, Issue 3, EMS, 2014.
  19. Microlocal analysis of an ultrasound transform with circular source and receiver trajectories , (with J. Boman, V. Krishnan, and E. T. Quinto) Contemporary Mathematics, vol. 598 (2013), pp 45-58.
  20. A Series formula for inversion of the V-line transform in a disc, (with S. Moon) Computers & Mathematics with Applications, vol. 66, Issue 9, November 2013, pp 1567-1572.
  21. Effect of refraction on dose reconstruction in optical-CT gel dosimetry, (with L. Florescu and C. Wuu) Journal of Physics: Conference Series vol. 444 (2013), 012063.
  22. A class of singular Fourier integral operators in synthetic aperture radar imaging , (with R. Felea, V. Krishnan, C. Nolan, and E. T. Quinto) Journal of Functional Analysis 264 (2013), pp 246-269.
  23. Invasion speed in cellular automaton models for T. cruzi vector migration , (with B. Crawford, and C. Kribs-Zaleta) Bulletin of Mathematical Biology , vol. 75, no. 7 (2013), pp 1051-1081.
  24. Approximate inversion algorithm of the elliptical Radon transform, (with R. Gouia-Zarrad) Proceedings of ISMA 2012, Biomedical Applications (2012), ISBN 978-1-4673-0862-5.
  25. Inversion of the v-line Radon transform in a disc and its applications in imaging, Computers & Mathematics with Applications, vol. 64, issue 3, August 2012, pp 260-265.
  26. Tomographic reconstruction of nodular images from incomplete data, (with M. Xie) AIP Conference Proceedings, vol. 1301, issue 1, December 2010, pp 167-174.
  27. Inversion of the circular Radon transform on an annulus, (with R. Gouia-Zarrad, and M. Lewis) Inverse Problems 26 (2010), 105015.
  28. Reconstruction algorithms for interior and exterior spherical Radon transform-based ultrasound imaging, (with R. Vaidyanathan, M. Lewis, and T. Aktosun) Proceedings of SPIE, vol. 7265, Medical Imaging 2009: Ultrasonic Imaging and Signal Processing, 2009, 72651I 1-8.
  29. Limited view thermoacoustic tomography, (with Y. Xu, L. Wang, and P. Kuchment) Chapter 9 in Photoacoustic imaging and spectroscopy, edited by L. H. Wang, CRC Press, 2009.
  30. Thermoacoustic tomography: numerical results, (with S. K. Patch) Proceedings of SPIE, vol. 6437, Progress in Biomedical Optics and Imaging, 8 (2007), no. 14, pp 6437 -47, preprint at arXiv:math.NA/0510638.
  31. A range description for the planar circular Radon transform, (with P. Kuchment) SIAM Journal on Mathematical Analysis vol. 38, no. 2 (2006), pp 681-692.
  32. On the injectivity of the circular Radon transform, (with P. Kuchment) Inverse Problems 21 (2005), pp 473-485.
  33. Reconstructions in limited view thermoacoustic tomography, (with Y. Xu, L. Wang, and P. Kuchment) Medical Physics 31(4) April 2004, pp 724-733.
  34. Continuation of functions representable by exponentials of infinite multiplicity with alternating exponents, (with A. Burobin) Matematicheskie Zametki, Russian Academy of Sciences, 73 (2003), no. 2, pp 163-172. (in Russian)
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