Stable and Convergent Computational Algorithms for Current Density Imaging

University Of South Carolina At Columbia, Columbia SC

Investigators

Abstract

Coupling together two distinct physical fields in medical and geophysical imaging is capable of enhancing both the space and contrast resolution of imaging modalities. This project concerns one of such a modality - Current Density Imaging (CDI) that couples the magnetic and radio-frequency electromagnetic fields used in Magnetic Resonance Imaging (MRI) with the electric field used in Electrical Impedance Tomography (EIT). Such a coupling is resulted in images of the electrical conductivity with significantly higher quality and accuracy than those obtained by the routine medical imaging modalities. The general aim of this project is to develop the computationally efficient and robust algorithms for CDI. The proposed research is in the field of coupled physics (hybrid) inverse problems whose distinctive feature is utilizing the interior data available in new imaging modalities in order to reconstruct material parameters of an object to be investigated. Speaking about the possible applications of such inverse problems, it should be particularly emphasized medical diagnostics and marine controlled source electromagnetic sounding due to their importance for early detection of cancer, minimizing the rate of false diagnoses, more efficient treatment of diseases, etc., and for geophysical exploration of hydrocarbon deposits on a shelf. The innovation of this project is that it is concerned with the development of computational tools for CDI by utilizing an initial boundary value problem for the weighted mean curvature flow equation. In order to achieve the general aim, the principal investigator will: (1) analyze the level set formulation of motion by the weighted mean curvature associated with the Dirichlet problem for the weighted 1-Laplacian, which is considered as a mathematical model of CDI, (2) develop the stable and convergent computational algorithms, and (3) conduct the numerical convergence study in order to demonstrate in numerical experiments the effectiveness of computational algorithms and quality of reconstruction. The approach developed in this project is expected to advance understanding of the geometrical features of CDI. One undergraduate student will be involved in the project and trained in numerical methods for the inverse problems. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.