“Optical Tomography: Models, Analysis, Numerics, and Inverse Problems”
Optical tomography aims at reconstructing cross-sectional images of an object by measurements of intensities of light penetrating through the object. The underlying physical process is, like in several other emerging medical imaging applications, the propagation of electromagnetic radiation through biological tissue.
In this talk, we shortly review the most commonly used mathematical models for light propagation in highly scattering media and we summarize basic results about solvability of the governing equations. We then present numerical methods for their solution and sketch their basic analysis. Based on solvability and numerical approximability, we finally turn to the inverse problem of image reconstruction, and discuss uniqueness issues and the stable solution by regularization methods.