Mathematics Colloquia and Seminars

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on-invasive wave imaging is a technique to "look into" an object or medium whose internal structure cannot be exposed. It is used to form images of certain physical properties of the object. Examples include using ultrasound to image breasts for cancer detection, ground penetrating radar to search for land mines, and acoustic techniques to look for buried hazardous wastes. In inverse wave imaging, a wave (acoustic or electromagnetic) is launched into an object or medium under evaluation. The scattered field is measured on a surface about it. The goal is to invert mathematically the scattering process and reconstruct the internal structure of the object using the measured scattered field. Operator decomposition is a class of inverse scattering techniques in which the forward scattering operator is decomposed via a singular value decomposition or eigenvalue/eigenvector expansion into an orthogonal set of basis vectors. Using the mathematics of linear algebra, the basis vectors are used to backpropagate the measured scattered field to form an image of the scattering structure. Two specific examples will be given: time-reversal and Hilbert space decomposition, along with examples.