Supervisor: Dr. Taysir Dyhoum
The mathematics base of this project is relying on a novel combination of the method of fundamental solution (MFS) and Markov chain Monte Carlo (MCMC) estimation techniques will be used to find a stable and highly reliable solution. The MCMC will be used for the simultaneous estimation of the model parameters, and the purpose of assessment, and the uncertainty quantification of the image reconstructions. The project aims to improve the clarity of EIT images and assess the uncertainty of the reconstructions obtained. This is necessary because applying the current EIT techniques in biomedicine does not give all the data necessary to decide treatment or solve a problem, be it finding abnormalities in tissue. However, using numerical methods, computer simulations, and mathematical models, it is possible to determine what the missing information might be, retrieve the properties (conductivity distributions which are used to create images) and other features of the objects (tumors) under scrutinies such as their sizes, locations, and shape. A new mathematical modelling approach and statistical tools can provide a solution to the EIT problem. In short, the numerical algorithm is a complete and unambiguous set of procedures for the solution of a problem currently facing medical practitioners. The proposed numerical approach can provide a stable and reliable result in real (three-dimensional) cases. My research will help with the assessment of what is currently unreliable information and remove the uncertainties in EIT. Completing this project successfully will result in some published work and a 3D tomography imaging package that will benefit the whole community, as it would be a remarkable step towards producing a safer medical imaging device for the treatment and diagnosis of various types of cancer.