Conductivity Imaging using Deep Neural Networks

Speaker 

Dr. Bangti Jin received his PhD degree in applied mathematics from the Chinese University of Hong Kong, Hong Kong, in 2008. Currently he is a professor of mathematics at Department of Mathematics, The Chinese University of Hong Kong. Previously he was a lecturer, reader and professor of inverse problems at Department of Computer Science, University College London (2014-2022), an assistant professor of Mathematics at University of California, Riverside (2013-2014), a visiting assistant professor at Texas A&M University (2010-2013), an Alexandre von Humboldt postdoctoral researcher at the University of Bremen (2009-2010). His research interests include computational inverse problems and numerical analysis of differential equations.

Abstract

Conductivity imaging is one fundamental task in medical imaging and provides a valuable tool for medical diagnosis. It is commonly formulated as recovering the conductivity coefficient in second-order elliptic PDEs from various observational data. We discuss several classes of numerical methods for the problem. Commonly, a regularized formulation consists of a data fidelity and a regularizer is employed, and then it is discretized using finite difference method, finite element methods or deep neural networks. One key issue is to establish a priori error estimates for the recovered conductivity distribution. In this talk, we discuss our recent findings on using deep neural networks for this class of problems, by effectively utilizing relevant stability estimates.