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GCOE Seminars
Seminar information archive ～04/23｜Next seminar｜Future seminars 04/24～
2011/12/27
14:30-15:30 Room #370 (Graduate School of Math. Sci. Bldg.)
Manabu Machida (University of Michigan)
Wave Transport in Random Media and Inverse Problems (ENGLISH)
Manabu Machida (University of Michigan)
Wave Transport in Random Media and Inverse Problems (ENGLISH)
[ Abstract ]
Wave transport in random media is described by the radiative transport equation, which is a linear Boltzmann equation. Such transport phenomena are characterized by two optical parameters in the equation: the absorption and scattering coefficients. In this talk, inverse problems of determining optical parameters will be considered and the Lipschitz stability will be proved using a Carleman estimate. One application of this inverse problem is optical tomography, which detects tumors in a human body using (unlike X-ray CT scan) near-infrared light. I will also present tomographic images of lemon and lotus root slices which are obtained by numerically solving the radiative transport equation with the method of rotated reference frames.
Wave transport in random media is described by the radiative transport equation, which is a linear Boltzmann equation. Such transport phenomena are characterized by two optical parameters in the equation: the absorption and scattering coefficients. In this talk, inverse problems of determining optical parameters will be considered and the Lipschitz stability will be proved using a Carleman estimate. One application of this inverse problem is optical tomography, which detects tumors in a human body using (unlike X-ray CT scan) near-infrared light. I will also present tomographic images of lemon and lotus root slices which are obtained by numerically solving the radiative transport equation with the method of rotated reference frames.
