In the recently established research with Associate Professor K. Niinimäki (Faculty of Medicine, Paris-Sud University) we study the Ultrasort Time Echo (UTE) radial MRI problem with applications in monitoring of a bone replacement cement in treatments of traumatological damages and degenerative diseases. Currently we develop an adaptive finite element method for MR imaging and improvement of quality of MR images. New numerical methods are efficiently implemented using C++/PETSc libraries on the base of the software package WavES and existing numerical methods developed by CNRS Professor G. Guillot, laboratory IR4M CNRS UMR8081 at Paris-Syd University. We have following main goals in the ongoing research: 1) Development of an adaptive finite element method for high resolution reconstruction of smoothed, defocused or smeared image with applications in MR imaging; 2) Development of PCA analysis for data compression of MR image obtained after an adaptive finite element reconstruction.

Currently the work is focused on the development of an adaptive finite element method with application in MRI, numerical implementation and verification of it in order to reconstruct an unknown spatially distributed proton density function. MR data measurements are performed in vitro on a 4.7 Tesla magnet in the laboratory IR4M CNRS UMR8081 at Paris-Syd University, France.

First results on this research are published in the paper

L. Beilina, G. Guillot, K. Niinimäki, On finite element method for magnetic resonance imaging,

Currently the work is focused on the development of an adaptive finite element method with application in MRI, numerical implementation and verification of it in order to reconstruct an unknown spatially distributed proton density function. MR data measurements are performed in vitro on a 4.7 Tesla magnet in the laboratory IR4M CNRS UMR8081 at Paris-Syd University, France.

First results on this research are published in the paper

L. Beilina, G. Guillot, K. Niinimäki, On finite element method for magnetic resonance imaging,

*Springer Proceedings in Mathematics and Statistics,*Volume 243, pp. 119-132, 2018.Within this project, there are two ongoing student projects:

- Bachelor thesis project: "Machine learning algorithms for classification problems"
- Master thesis project: "Deep learning-based methods for a coefficient inverse problem for time-harmonic acoustic waves", by student Themis Mouliakos