Ph.D Thesis

Ph.D StudentDolgin Madlena
SubjectInverse Scattering Models for Reconstruction of Layered
Biological Tissues
DepartmentDepartment of Electrical and Computer Engineering
Supervisor ASSOCIATE PROF. Pinchas Einziger
Full Thesis textFull thesis text - English Version


          The proposed research is focused on some fundamental mathematical and physical characteristics of Electrical Impedance Tomography (EIT), a subject of great scientific and public interest.  The basic EIT's assumption is that different biological tissues can be distinguished by their conductivities. This knowledge allows one to acquire medical insight on the biological structure by reconstruction of its electrical characteristics. In EIT the, generally complex, conductivity profile of the tissues under reconstruction, is estimated by processing voltage and current data measured on the surrounding boundary.

          In applying EIT techniques two crucially important issues have to be clarified and specified: (i) an explicit relation connecting the inverse procedure and the forward problem; (ii) a locality principle, linking between the electrical impedance spatial distribution and the corresponding quasistatic data, measured on the surrounding boundary. The first issue is resolved herein by utilizing a recently proposed image series expansion scheme for layered media, resulting in a novel reconstruction method. Furthermore, in the WKB limit leading to a one to one mapping between each image term and a corresponding layer the second issue is also resolved.

          Our research focuses on reconstruction of layered biological tissues as a case study for real-life three dimensional EIT problems. It should be emphasized that this research aims to validate the feasibility and to gain physical and mathematical insight to the reconstruction process via closed form direct solution for simplified EIT measurement setup. The physical setup of the EIT possesses highly noisy measurements far from the source, thus, in the presented study the Legendre transform was introduced, which uses finite extent window in the space domain. Even though, the image series expansion possesses non linear dependence on the media parameters, we presented a novel two step linear algorithm for their estimation utilizing Legendre transform and Prony method.

           We validate the stability of the proposed estimation algorithm for reconstruction of WKB continuous media. To this end, we solved forward problem for layered piece wise-continuous media allowing abrupt changes in the conductivity values. The algorithm provides accurate reconstruction results for moderate depths. However, for high depth the oscillations were observed. To improve the reconstruction stability for the inner part of the media, we proposed a new kind of grid, namely non homogenous discretization in the depth dimension. This grid clearly improves the accuracy of the estimated conductivity values trading off the resolution in this part of the media.