Polyakova, Anna P.; Svetov, Ivan E. A numerical solution of the dynamic vector tomography problem using the truncated singular value decomposition method. (English) Zbl 07803167 J. Inverse Ill-Posed Probl. 32, No. 1, 145-160 (2024). MSC: 65R10 65R32 PDFBibTeX XMLCite \textit{A. P. Polyakova} and \textit{I. E. Svetov}, J. Inverse Ill-Posed Probl. 32, No. 1, 145--160 (2024; Zbl 07803167) Full Text: DOI
Svetov, Ivan E.; Polyakova, Anna P. Inversion of generalized Radon transforms acting on 3D vector and symmetric tensor fields. (English) Zbl 07780885 Inverse Probl. 40, No. 1, Article ID 015009, 37 p. (2024). MSC: 44A12 65R10 PDFBibTeX XMLCite \textit{I. E. Svetov} and \textit{A. P. Polyakova}, Inverse Probl. 40, No. 1, Article ID 015009, 37 p. (2024; Zbl 07780885) Full Text: DOI
Polyakova, Anna P.; Svetov, Ivan E. Singular value decomposition for longitudinal, transverse and mixed ray transforms of 2D tensor fields. (English) Zbl 07770232 Inverse Probl. 39, No. 10, Article ID 105006, 21 p. (2023). MSC: 44A12 33C45 42C05 PDFBibTeX XMLCite \textit{A. P. Polyakova} and \textit{I. E. Svetov}, Inverse Probl. 39, No. 10, Article ID 105006, 21 p. (2023; Zbl 07770232) Full Text: DOI
Svetov, I. E. The method of approximate inverse for the Radon transform operator acting on functions and for the normal Radon transform operators acting on vector and symmetric 2-tensor fields in \(\mathbb R^3\). (Russian. English summary) Zbl 1461.44002 Sib. Èlektron. Mat. Izv. 17, 1073-1087 (2020). MSC: 44A12 44A30 PDFBibTeX XMLCite \textit{I. E. Svetov}, Sib. Èlektron. Mat. Izv. 17, 1073--1087 (2020; Zbl 1461.44002) Full Text: DOI
Svetov, Ivan E.; Maltseva, Svetlana V.; Louis, Alfred K. The method of approximate inverse in slice-by-slice vector tomography problems. (English) Zbl 07250785 Sergeyev, Yaroslav D. (ed.) et al., Numerical computations: theory and algorithms. Third international conference, NUMTA 2019, Crotone, Italy, June 15–21, 2019. Revised selected papers. Part II. Cham: Springer. Lect. Notes Comput. Sci. 11974, 487-494 (2020). MSC: 65-XX PDFBibTeX XMLCite \textit{I. E. Svetov} et al., Lect. Notes Comput. Sci. 11974, 487--494 (2020; Zbl 07250785) Full Text: DOI
Polyakova, Anna P.; Svetov, Ivan E.; Hahn, Bernadette N. The singular value decomposition of the operators of the dynamic ray transforms acting on 2D vector fields. (English) Zbl 07250780 Sergeyev, Yaroslav D. (ed.) et al., Numerical computations: theory and algorithms. Third international conference, NUMTA 2019, Crotone, Italy, June 15–21, 2019. Revised selected papers. Part II. Cham: Springer. Lect. Notes Comput. Sci. 11974, 446-453 (2020). MSC: 65-XX PDFBibTeX XMLCite \textit{A. P. Polyakova} et al., Lect. Notes Comput. Sci. 11974, 446--453 (2020; Zbl 07250780) Full Text: DOI
Svetov, I. E.; Polyakova, A. P.; Mal’tseva, S. V. The method of approximate inverse for ray transform operators on two-dimensional symmetric \(m\)-tensor fields. (Russian, English) Zbl 1438.44003 Sib. Zh. Ind. Mat. 22, No. 1, 104-115 (2019); translation in J. Appl. Ind. Math. 13, No. 1, 157-167 (2019). MSC: 44A12 53C65 PDFBibTeX XMLCite \textit{I. E. Svetov} et al., Sib. Zh. Ind. Mat. 22, No. 1, 104--115 (2019; Zbl 1438.44003); translation in J. Appl. Ind. Math. 13, No. 1, 157--167 (2019) Full Text: DOI
Derevtsov, E. Yu.; Mal’tseva, S. V.; Svetov, I. E. Determination of discontinuities of a function in a domain with refraction from its attenuated ray transform. (Russian, English) Zbl 1438.65317 Sib. Zh. Ind. Mat. 21, No. 4, 51-74 (2018); translation in J. Appl. Ind. Math. 12, No. 4, 619-641 (2018). MSC: 65R10 44A12 65R32 92C55 PDFBibTeX XMLCite \textit{E. Yu. Derevtsov} et al., Sib. Zh. Ind. Mat. 21, No. 4, 51--74 (2018; Zbl 1438.65317); translation in J. Appl. Ind. Math. 12, No. 4, 619--641 (2018) Full Text: DOI
Derevtsov, Evgeny Yu.; Maltseva, Svetlana V.; Svetov, Ivan E.; Sultanov, Murat A. On a problem of reconstruction of discontinuities of a function by its attenuated ray transform along geodesics. (English) Zbl 1486.74017 Kal’menov, Tynysbek (ed.) et al., International conference ‘Functional analysis in interdisciplinary applications’, FAIA2017, Astana, Kazakhstan, October 2–5, 2017. Proceedings. Melville, NY: American Institute of Physics (AIP). AIP Conf. Proc. 1880, 060004, 9 p. (2017). MSC: 74E05 PDFBibTeX XMLCite \textit{E. Yu. Derevtsov} et al., AIP Conf. Proc. 1880, 060004, 9 p. (2017; Zbl 1486.74017) Full Text: DOI
Svetov, I. E.; Derevtsov, E. Yu.; Volkov, Yu. S.; Schuster, Thomas A numerical solver based on \(B\)-splines for 2D vector field tomography in a refracting medium. (English) Zbl 1499.65047 Math. Comput. Simul. 97, 207-223 (2014). MSC: 65D07 PDFBibTeX XMLCite \textit{I. E. Svetov} et al., Math. Comput. Simul. 97, 207--223 (2014; Zbl 1499.65047) Full Text: DOI
Derevtsov, E. Yu.; Mal’tseva, S. V.; Svetov, I. E. Approximate reconstruction from ray integrals of a function on a domain with low refraction. (Russian, English) Zbl 1340.65310 Sib. Zh. Ind. Mat. 17, No. 4, 48-59 (2014); translation in J. Appl. Ind. Math. 9, No. 1, 36-46 (2015). MSC: 65R10 65R32 44A12 PDFBibTeX XMLCite \textit{E. Yu. Derevtsov} et al., Sib. Zh. Ind. Mat. 17, No. 4, 48--59 (2014; Zbl 1340.65310); translation in J. Appl. Ind. Math. 9, No. 1, 36--46 (2015) Full Text: DOI