Gaik Ambartsoumian
Research Interests
- Computerized Tomography
- Integral Geometry
- Inverse Problems
- Mathematical Problems of Imaging
Publications
- Microlocal analysis of the generalized V-line transforms, (with V. Krishnan and E. T. Quinto) in preparation.
- Inversion and symmetries of the star transform, (with M. J. Latifi-Jebelli) to appear in The Journal of Geometric Analysis .
- Generalized V-line transforms in 2D vector tomography, (with M. J. Latifi-Jebelli, and R. K. Mishra) Inverse Problems 36 (2020), no. 10, 104002.
- Improved interior tomography reconstruction based on prior knowledge, (with L. Florescu and E. Bridges) American Institute of Physics Conference Proceedings, vol. 2302, 060002 (2020).
- Generalized Radon transforms and applications in tomography, (with E. T. Quinto) Inverse Problems 36 (2019), no. 2, 020301.
- 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.
- 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.
- The V-line transform with some generalizations and cone differentiation, (with M. J. Latifi-Jebelli) Inverse Problems 35 (2019), no. 3, 034003.
- 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.
- 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.
- 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.
- Inversion of a class of circular and elliptical Radon transforms, (with V. Krishnan) Contemporary Mathematics, vol. 653 (2015), 13174.
- 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.
- 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.
- Exact inversion of the conical Radon transform with a fixed opening angle, (with R. Gouia-Zarrad) Inverse Problems 30 (2014), no. 4, 045007.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Tomographic reconstruction of nodular images from incomplete data, (with M. Xie) AIP Conference Proceedings, vol. 1301, issue 1, December 2010, pp 167-174.
- Inversion of the circular Radon transform on an annulus, (with R. Gouia-Zarrad, and M. Lewis) Inverse Problems 26 (2010), 105015.
- 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.
- 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.
- 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.
- 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.
- On the injectivity of the circular Radon transform, (with P. Kuchment) Inverse Problems 21 (2005), pp 473-485.
- Reconstructions in limited view thermoacoustic tomography, (with Y. Xu, L. Wang, and P. Kuchment) Medical Physics 31(4) April 2004, pp 724-733.
- 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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