Toward a Unified Approach to Diffuse Wave Inverse Problems

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Miller, EricNortheastern UThe objective of this work is the creation of a unified approach to characterizing the internal structure of a medium given diffuse wavefield data collected at the boundaries. Diffusive inverse problems are found in anumber of areas including (1) medical imaging for breast cancer detection using diffuse optical tomography (DOT); (2) non-destructive evaluation (NDE) in the steel and semi-conductor industries with photo-thermal methods; and (3) monitoring of environmental cleanup processes via electrical resistancetomography (ERT). Despite the ubiquity of these problems, researchers have typically treated them in application-specific ways due to differences in the physical scale, materials under consideration, and sensing systems. Here, a unified approach to solving this class of inverse problems is constructed by exploiting the underlying similarities in the physics and processing objectives of each of these problems.The investigators focus on three fundamental difficulties. First, they design regularization techniques to overcome the ill-posedness of these inverse problems. Specifically they explore the use of adaptive, geometric, low-order models for the unknown and reconstruct the relatively small number of descriptive parameters in these models. Second, they design inversion methods that, unlike traditional approaches, do not require precise knowledge of the background structure of the medium. Solving these nonlinear inverse problems is extremely computationally intensive, in part because a three-dimensional forward problem must be solved thousands of times. Therefore, a third focus of the research is the development ofcomputationally efficient inversion techniques by exploiting the relationships among the forward problems. The resulting theory and algorithms will be validated using real sensor data from the threeapplication areas described in the first paragraph: DOT, photo-thermal NDE, and ERT.