Collaborative Research: Image Reconstruction Algorithms for Optical Tomography with Large Data Sets Using the Radiative Transport Equation

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Markel, Vadim A. Univ. of Pennsylvania / Kim, Arnold D. Univ. Of California-Merced0615857 / 0616228Image Reconstruction Algorithms for Optical Tomography with Large Data Sets Using the Radiative Transport EquationIt is well known that modern medical imaging has revolutionized the practiceof clinical medicine. What is perhaps less well known is the critical rolethat advanced mathematical tools have played in the development of imagingtechnologies. In this proposal, we plan to explore fundamental mathematicalproblems at the core of optical tomography. Optical tomography (OT) is anemerging biomedical imaging modality which employs near-infraredlight as probe of tissue structure and function. At the heart of OT is anill-posed nonlinear inverse problem. We propose to develop new mathematicaltools to attack this problem by building on recent progress made by theco-investigators in the areas of inverse scattering theory and radiativetransport theory. The investigators have recently demonstrated the abilityto reconstruct immages using reconstruction algorithms that are valid withinthe diffusion approximation to the radiative transport equation (RTE). Wenow plan to extend this development to physical situations in which the thefull power of the RTE is required. Two key developments pioneered by thecon-investigators makes the research we propose feasible and timely. Thefirst of these is the construction of analytical methods forthe inverse scattering problem in radiative transport. The second enablingdevelopment is the recent discovery of plane-wave decompositions for the RTEGreen's function. The proposed research integrates the development of newmathematical methods with algorithm development and experimental validation.We have assembled an interdisciplinary and highly collaborative team ofinvestigators with complementary skills who are uniquelyqualified to carry out this research. The team consists of a computationalphysicist (Vadim Markel), an applied mathematician (Arnold Kim), and atheoretical optical physicist and physician (John Schotland). The intellectual merit of the proposed research is the development ofefficient imaage reconstruction algorithms which are based on novel andoriginal mathematical theories. One graduate student at the University ofPennsylvania will be trained in computational and analytical methods ofimage reconstruction. A postdoctoral fellow at the Universityof California, Merced will be trained in the area of forward problems intransport theory. The broad impact will include improving the quality of reconstructed imagesin optical tomography. We expect that when the proposed developments arefully realized, they can significantly improve the clinical utility ofoptical tomography. Furthermore, although the proposed work is focused onoptical tomography, some of the results may also lead to a greaterunderstanding of the propagation of multiply scattered waves in randomsystems such as the atmosphere and interstellar media.