Speaker：Jianzhong Su，University of Texas at Arlington，USA 

Title: Globally Convergent methods for inverse problems in Diffuse Optical Tomography and its applications

Time：2016-7-29, 11:00-11:50am

Venue: Room 316 of Environment Building, Renmin University

Abstract:  In this talk, we give an overview of both theory and experimental applications of a numerical Globally Convergent Method (GCM) for an inverse problem in Diffuse Optical Tomography. The method is for an inverse problem for an elliptic partial differential equation with an unknown potential, an important mathematical problem at the core of Near-Infrared laser imaging technology. The GCM reconstruction method fundamentally differs from other current methods based on the Newton`s method or optimization scheme. GCM does not require a relative precise first guess and hence it is capable in dealing with complex media and realistic geometry for biomedical applications. Several sets of boundary data measurements are generated by placing the light source at several designated locations. Mathematically, a global convergence theorem assures the success of the numerical reconstruction method. Then we use this method in experiments of an optical phantom emulating rat brain suffering a stroke. We present the experimental setup of optical measurements and report accurate images and their physical parameters of hidden interior objects inside an optical phantom, which are reconstructed based on light intensity data collected on the object’s surface. Finally we test the method in animal experiments. The examples illustrate how the mathematical theory of GCM be used in tomographic reconstruction of experimental data.