Adaptive non-local algorithms for inverse problems with applications in medical imaging

The main purpose of this proposal is development of new adaptive non-local numericalmethods for solving the multidimensional coefficient inverse problems (MCIP´s) and  inverse source problems (IPS’s) in the framework of hyperbolic and parabolic PDE’s studiedin the project.

Development of Carleman estimates to prove global uniqueness of reconstructedparameters in MCIP’s and sources in ISP’s is one of the main challenges of the project.New non-local methods for hyperbolic MCIP’s (for wave and Maxwell’s equations) will allow us con-struct non-local algorithms to detect skin and breast tumours in real time, as well as use microwavesin the real-time monitoring of tumour heating in the process of hyperthermia.

Additionally, devel-oped methods for diffuse interface models for ISP’s will be used in real-time monitoring of physicalparameters in blood which will allow detection of tumours on early stages.