Southern Federal University has announced a scientific project at the Russian-Armenian University aimed at developing mathematical methods for medical diagnostics and creating advanced tomography technologies. The research team is led by Professor Rafik Aramyan, Head of the Department of Mathematical Cybernetics at the Russian-Armenian University and Director of the Institute of Mathematics of the National Academy of Sciences of the Republic of Armenia. Professor Alexey Karapetyants of Southern Federal University serves as the project’s scientific advisor.

The project, “Probabilistic Methods in Integral Geometry and Group Theory with Applications to Tomography,” has received support under the RAU Development Program, funded by the Ministry of Science and Higher Education of the Russian Federation. The research is scheduled to run from 2026 to 2029.

One of the project’s key areas is the development of the mathematical foundations of thermoacoustic tomography (TAT), which is considered a promising alternative to conventional imaging methods and uses safe physical signals. For approximately 40 years, the international scientific community widely held the view that reconstructing images of internal organs from local detector data was impossible, as information had to be collected across an entire plane or line. Professor Rafik Aramyan challenges this established view in his research.

In his work, Professor Aramyan proposed the so-called “method of consistency,” which made it possible to derive local inversion formulas for the spherical Radon transform. The research also introduced a new concept known as the two-data Radon (Funk) transform. This mathematical framework makes it possible to overcome limitations inherent in earlier methods. In the future, these results could provide the foundation for developing compact and portable tomography systems. The methods also have potential applications in radar imaging and other fields.

An important component of the project is the training of young specialists. Young researchers, postgraduate students, and undergraduates from RAU are involved in the research, gaining experience in advanced scientific developments. Professor Varuzhan Atabekyan coordinates the part of the project related to group theory. The project also contributes to expanding scientific cooperation, including through the participation of Professor Alexey Karapetyants as a scientific advisor. Further details are available on the Southern Federal University website >>

As part of this project, Professor Aramyan’s research was published in the September issue of the prestigious international journal Analysis and Mathematical Physics >>, a Q1-ranked journal published by Springer Nature. In his article, “Weighted Funk Transforms,” the author examines weighted Funk transforms on the unit two-dimensional sphere, with weights represented by finite Fourier series in the angular variable. The paper focuses on the injectivity of these transforms depending on the choice of weight. Weighted Funk transforms are studied for the first time in this work.

The research was carried out with the support of the Science Committee of the Republic of Armenia under research project 21AG-1A045, as well as the RAU Development Program. This publication marks another milestone in Rafik Aramyan’s research on integral transforms and inverse problems.