This project is supported by the Swedish Institute,  Visby Program.
The goal of this project is to develop a radically new and effective mathematical idea: applications of adaptivity technique in medical optical tomographic imaging of human organs (e.g., brains and female breasts), in imaging using electromagnetic waves as well as in signal reconstruction in scanning electron tomography. Developed numerical methods will be tested on experimental data. First such tests are recently published by PI and co-authors [13]To do this, a new  scientific teams between Chalmers University of Technology and GU (L. Beilina, M. Asadzadeh), Sweden, and Moscow State University (prof.A.Yagola, Dr.G.Kuramshina), Penza
State University (N.Koshev), the Institute of  System Analysis of the Russian Academy of Sciences, Moscow  (prof. A. Bakushinskiy) and Sobolev Institute of Mathematics, Novosibirsk (I.Gainova) will be created.

The mathematical apparatus will be based on two recently developed new ideas  for numerical solutions of Multidimensional Coefficient Inverse Problems (MCIPs): (1) a globally convergent numerical
method for MCIPs [2] and (2) a synthesis of the globally convergence method with the Finite Element Adaptive Method (adaptivity) for MCIPs [1,3,4] . Recently in [13] a globally convergent algorithm [2] was verified on experimental data in the picosecond scale regime. Blind tests of [13] have demonstrated an accurate imaging of refractive indexes of dielectric abnormalities. 

Since conventional numerical methods for MCIPs  converge locally, whereas our methods will converge globally, there is a good chance that this project will lead to quite more reliable and accurate images than ones obtained so far.