Nikolay Koshev

Nikolay is an expert in the field of inverse and ill-posed problems of mathematical physics, graduated from M.V. Lomonosov MSU (Department of Physics) in 2008. He defended his Ph.D. thesis in 2012 at MSU. The research has been devoted to inverse problems in electronic microscopy and provided at the MSU and Chalmers University (Sweden, Gothenburg). Before joining Skoltech at the end of 2018, Nikolay worked in many areas of science and industry, including inverse problems of voltammetry (electrochemistry), fast inversion of sinograms (X-ray tomography, 2015-2017, Brazil, Campinas), globally convergent methods for Cauchy problems (2016-2018, USA, Charlotte), globally convergent methods for coefficient inverse problems (2017-2018, USA, Charlotte). Currently, the main research area of Nikolay is magneto- and electroencephalography (MEG and EEG).

  • Inverse and ill-posed problems of mathematical physics
  • Differential equations
  • Integral equations
  • Mathematical modelling
  • Magneto- and electroencephalography (MEG/EEG)
  • Microscopy
  • Tomography
  • Signal and Image processing



  • Koshev, Nikolay, et al. “FEM-based Scalp-to-Cortex EEG data mapping via the solution of the Cauchy problem.” Journal of Inverse and Ill-posed Problems 28.4 (2020): 517-532.
  • Razorenova, A., Yavich, N., Malovichko, M., Fedorov, M., Koshev, N., & Dylov, D. V. (2020). Deep Learning for Non-Invasive Cortical Potential Imaging. In Machine Learning in Clinical Neuroimaging and Radiogenomics in Neuro-oncology (pp. 45-55). Springer, Cham.
  • Malovichko, M., Koshev, N., Yavich, N., Razorenova, A., & Fedorov, M. (2020). Electroencephalographic source reconstruction by the finite-element approximation of the elliptic Cauchy problem. IEEE Transactions on Biomedical Engineering.
  • Borzunov, A. A., Karaulov, V. Y., Koshev, N. A., Lukyanenko, D. V., Rau, E. I., Yagola, A. G., & Zaitsev, S. V. (2019). 3D Surface Topography Imaging in SEM With Improved Backscattered Electron Detector: Arrangement and Reconstruction Algorithm. Ultramicroscopy207, 112830.
  • Michael V.Klibanov, Nikolay A. Koshev, Dinh-Liem Nguyen, Loc H. Nguyen, Aaron Brettin,
    Vasily N. Astratov. A numerical method to solve a phaseless coefficient inverse problem from a
    single measurement of experimental data. SIAM J. Imaging Sci., Vol.11(4), 2339-2367, 2018.
  • E. Miqueles, N. Koshev, E.S. Helou. A Backprojection Slice Theorem for Tomographic Re-
    construction. IEEE Transactions on Image Processing, V PP, Issue 99, 14 pp, 2017.
  • Anatoly B. Bakushinskii, Michael V. Klibanov and Nikolaj A. Koshev. Carleman weight
    functions for a globally convergent numerical method for ill-posed Cauchy problems for some
    quasilinear PDEs. Nonlinear Analysis Series B: Real World Applications, Vol. 34, 201-224,
  • Michael V. Klibanov, Nikolay Koshev, Anatoly G. Yagola, Jingzhi Li. Numerical solution of
    an ill-posed Cauchy problem for a quasilinear parabolic equation using a Carleman weight
    function. Journal of Inverse and ill-posed Problems, 2016.
  • N.A. Koshev, A.N. Koshev, V.V. Kuzina. Voltammetry: mathematical modelling and Inverse
    Problem, Chemometrics and Intelligent Laboratory Systems, Vol.157, 78-84, 2016.
  • N. Koshev. On the solution of forward and inverse problems of voltammetry, Inverse Problems
    and Applications, Springer Proceedings in Mathematics & Statistics, 120, 153-164, 2015.
  • A. Koshev, I.Gvozdeva, N. Koshev, Mathematical Model and Software for Calculation the
    Parameters of Control of Automated Process Extraction of Metals in Reactor with Flowing
    Three-Dimensional Electrode, Applied Mathematical Sciences, Vol. 8, no. 124, 6171 – 6179,
  • N. Koshev and L. Beilina, A posteriori error estimates for Fredholm integral equations of the
    first kind, Applied Inverse Problems, Springer Proceedings in Mathematics & Statistics, V. 48,
    75-93, 2013.
  • N. Koshev and L. Beilina, An adaptive finite element method for Fredholm integral equations
    of th:we first kind and its verification on experimental data, Central European Journal of
    Mathematics, V. 11, 1489-1509, 2013.
  • Yagola A.G., Koshev N.A. Restoration of smeared and defocused color images, Numerical
    Methods and Programming, V.9, 207-212, 2008 (in Russian).
  • Koshev N.A., Orlikovsky N.A., Rau E.I., Yagola A.G. Solution of the inverse problem of
    restoring the signals from an electronic microscope in the backscattered electron mode on the
    class of bounded variation functions, Numerical Methods and Programming, V.11, 362-367,
    2011 (in Russian).
  • N.A. Koshev, F.A. Luk’anov, E.I. Rau, R.A. Sennov, and A.G. Yagola. Increasing Spatial
    Resolution in the Backscattered Electron Mode of Scanning Electron Microscopy, Bulletin ofthe Russian Academy of Sciences. Physics, V. 75, 1181-1184, Allerton Press, 2011.
  • S.I. Zaycev, N.A. Koshev, F.A. Lukyanov, E.I. Rau, E.B. Yakimov. Straight measurement
    of diameter and current density arrangement in crossover of the electron probe, Abstracts for
    XXIII Rissian Conference in Electronic Microscopy, Chernogolovka, 2010.
  • N. A. Koshev, N. A. Orlikovskii, E. I. Rau, and A. G. Yagola. Reconstructing the Energy
    Spectra of Backscattered Electrons with Allowance for the Spectrometer’s Spread Function,
    Bulletin of the Russian Academy of Sciences. Physics, V. 76, 959-964, Allerton Press, Inc.,
  • A.V. Gostev, N. A. Koshev, N.A. Orlikovsky, E.I. Rau. Hardware function of the toroidal spec-
    trometer and its influence on detected electrons spectra. XXIV Russian electronic microscopy
    conference, Chernogolovka, Russia, p. 177, 2012 (In Russian).
Anna Butorina
Research Scientist

Course “Scientific Computing”