Markel, Vadim A. Univ. of Pennsylvania / Kim, Arnold D. Univ. Of California-Merced 0615857 / 0616228 Image Reconstruction Algorithms for Optical Tomography with Large Data Sets Using the Radiative Transport Equation It is well known that modern medical imaging has revolutionized the practice of clinical medicine. What is perhaps less well known is the critical role that advanced mathematical tools have played in the development of imaging technologies. In this proposal, we plan to explore fundamental mathematical problems at the core of optical tomography. Optical tomography (OT) is an emerging biomedical imaging modality which employs near-infrared light as probe of tissue structure and function. At the heart of OT is an ill-posed nonlinear inverse problem. We propose to develop new mathematical tools to attack this problem by building on recent progress made by the co-investigators in the areas of inverse scattering theory and radiative transport theory. The investigators have recently demonstrated the ability to reconstruct immages using reconstruction algorithms that are valid within the diffusion approximation to the radiative transport equation (RTE). We now plan to extend this development to physical situations in which the the full power of the RTE is required. Two key developments pioneered by the con-investigators makes the research we propose feasible and timely. The first of these is the construction of analytical methods for the inverse scattering problem in radiative transport. The second enabling development is the recent discovery of plane-wave decompositions for the RTE Green's function. The proposed research integrates the development of new mathematical methods with algorithm development and experimental validation. We have assembled an interdisciplinary and highly collaborative team of investigators with complementary skills who are uniquely qualified to carry out this research. The team consists of a computational physicist (Vadim Markel), an applied mathematician (Arnold Kim), and a theoretical optical physicist and physician (John Schotland).
The intellectual merit of the proposed research is the development of efficient imaage reconstruction algorithms which are based on novel and original mathematical theories. One graduate student at the University of Pennsylvania will be trained in computational and analytical methods of image reconstruction. A postdoctoral fellow at the University of California, Merced will be trained in the area of forward problems in transport theory.
The broad impact will include improving the quality of reconstructed images in optical tomography. We expect that when the proposed developments are fully realized, they can significantly improve the clinical utility of optical tomography. Furthermore, although the proposed work is focused on optical tomography, some of the results may also lead to a greater understanding of the propagation of multiply scattered waves in random systems such as the atmosphere and interstellar media.
