Employee of the Institute of Control Systems of ANAS A. Rahimov presented at the meeting of the Scientific Council his report on the research conducted in France
17.10.2018 / Conferences, assembliesAt the meeting of the Scientific Council of the Institute of Control Systems of ANAS on 17 October 2018, Assoc.Prof. Anar Rahimov, leading researcher of Laboratory of No 3.1, PhD in Applied Mathematics, presented his report on his scientific research activity in France in 2015-2017.
It was noted that he had conducted scientific research works on numerical solution to inverse problems at the Institute of Fresnel under Aix-Marseille University and French National Centre for Scientific Research (CNRS), Ecole Centrale Marseille in Marseille, France for 2 years.
He conducted scientific research works on the "Development of novel numerical solution methods of inverse problems for accurate microwave imaging of human brain" under supervision of head of the HIPE team of Fresnel Institute, Prof. Amelie LITMAN. This problem was raised before Fresnel Institute by The French Alternative Energies and Atomic Energy Commission (CEA, Paris, France).
The scientific research work was devoted to the development of numerical methods and algorithms to determine accurately electromagnetic properties (dielectric permittivity and conductivity) of brain from Magnetic Resonance Imaging (MRI) measurements. Rahimov A.B. has worked on an inverse problem described by the electric Helmholtz equation and by recasting this inverse problem into a constrained optimization algorithm, he investigated a gradient-based inversion algorithm to quantitatively recover the complex permittivity values of human brain tissues based on magnetic field mapping, which can be acquired in MRI setups. He has solved the direct problem using finite element method. He has derived the associated adjoint field equation, obtained the formulas of gradient and employed a Quasi-Newton minimization scheme. He has developed a simulation tool which adequately combines the specificities of microwave imaging (MI) algorithms with the problematic of MRI for the direct and inverse problems. He has stadied the influence of the initial guess, the number of transmitters and measurements, the signal-to-noise ratio (SNR) and a regularisation strategy based on a priori information to the numerical results.
Furthermore, he has also worked on investigation and development of methods of numerical solution to non-local inverse problems for parabolic and hyperbolic type equations during scientific research work period.
Main results of the research work have been published in 2017 in coathorship with French scientists (A. Litman, G. Ferrand) as the paper titled " MRI-based electric properties tomography with a quasi-Newton approach" (http://iopscience.iop.org/article/10.1088/1361-6420/aa7ef2) in the International journal of “Inverse Problems” that is on the list of Science Citation Index by “Thomson Reuters” Agency and has the highest Impact Factor of 1.946 in Inverse problems field. Thus, 22 scientific works have been published by Rahimov A.B. during the scientific research period, 9 of them are journal papers which 5 of them are in the list of Science Citation Index (with Impact Factor) by “Thomson Reuters” Agency (Inverse Problems in Science and Engineering (IF 1.033), Differential Equations (IF 0.431), Automation and Remote Control (IF 0.492), Cybernetics and Systems Analysis) and 13 of them are International conference proceedings.
Rahimov A. has been a reviewer of the international journals which are included the list of Science Citation Index by “Thomson Reuters” Agency, such as “Journal of Inverse and Ill-posed Problems” (De Gruyter, Germany, IF: 0.941), “Applied Mathematics and Computation” (Elsevier, IF: 2.300) and “Journal of Computational and Applied Mathematics” (Elsevier, IF: 1.632), “International Journal of Computational Methods” (IF: 1.053), etc.
Rahimov A. gave a talk at the General Scientific Seminar organized by “Center of Mathematics and Computer Sciences” of Marseille Institute of Mathematics under Aix-Marseille University on 1st of December 2015. (www.i2m.univ-amu.fr/Seminaire-Analyse-Appliquee-AA-112?lang=fr&date_debut=1900-01-01&debut_agenda=72#pagination_agenda)
Rahimov A. was also a winner of competitions to participate in summer schools and participated in "Summer Schools on Inverse Problems" and took mini-courses which consisted of series of lectures by famous scientists on Inverse Problems:
•Summer Pre-School on Inverse Problems at CIRM (Centre International de Rencontres Mathématiques - International Mathematical Conference Center) which was held from 13 April to 17 April, 2015 in Marseille, France (3 mini-courses and 5 keynote talks): https://fconferences.cirm-math.fr/1209.html
•Summer School on Inverse Problems organized at the Department of Mathematics and Statistics of University of Helsinki which was held from 18 May to 22 May, 2015 in Helsinki, Finland (4 mini-courses and 2 keynote talks): www.aip2015.fips.fi/summer_school.php
•Franco-German Summer School on Inverse Problems for Waves organized at Ecole Polytechnique which was held from 24 August to 28 August, 2015 in Paris, France (8 mini-courses): www.math.uni-bremen.de/zetem/ip-school2015
•Summer School on Inverse Problems organized at the University of Munster which was held from 22 September to 25 September, 2015 in Munster, Germany (4 mini-courses): https://wwwmath.uni-muenster.de/ipschool2015/
Rahimov A. participated and gave the talks in the International conferences and symposiums:
- Applied Inverse Problems Conference (AIP2015) which was held on May 25-29, 2015 in University of Helsinki (Helsinki, Finland);
- International Workshop “Recent Developments in Inverse Problems” which was held on September 17-18, 2015 in Weierstrass Institute for Applied Analysis and Stochastics (Berlin, Germany);
- First Applied Mathematics Symposium Munster “Variational Methods for Dynamic Inverse Problems and Imaging” which was held on September 28-30, 2015 in the Department of Mathematics and Computer Science of Munster University (Munster, Germany);
- International Conference on New Trends in Theoretical and Numerical Analysis of Waveguides, May 16-19, 2016, Porquerolles, France
- Eighth International Conference “Inverse Problems: Modeling and Simulation” (IPMS2016), May 23-28, 2016, Fethiye, Turkey;
- International Chemnitz Symposium on Inverse Problems which was held on September 22-23, 2016 in Chemnitz, Germany;
- International Workshop on “Numerical methods for Hamilton-Jacobi equations in optimal control and related fields” which was held on November 21-25, 2016 in Johann Radon Institute for Computational and Applied Mathematics (RICAM) of the Austrian Academy of Sciences (Linz, Austria);
- International Workshop on “Inverse problems and related fields” which was held on November 24-25, 2016 in Aix-Marseille University (Marseille, France).