In this project we aim to develop new inversion methods of weighted (generaliezed) Radon transforms which are
of particular importance in various applications in the domain of inverse problems (e.g., in tomographies, geophysics).
In particular, we work on methods which could be numerically more stable against the noise in tomographical data
compared to existing methods. For our recent progress in this direction one can look at
At the same time, I'm interested in pure mathematical studies of weighted (generalized) ray/Radon transforms.
Not a long time ago, with professor R. Novikov we had obtained a series of unexpected counterexamples to injectivity of the latter
under minor assumptions. More precisely about these counterexamples one can look at
Numerical inversion of (weighted) ray / Radon transforms in 3D
Here I will put some pictures related to numerical realizations of our algorithms.
The version of my code and the related project can be found on
GitHub (the project is still under development).