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Yayın An inverse source problem connected thermoacoustic imaging in multi-layer planar medium(Işık Üniversitesi, 2018-06-04) Yücel, Hazel; Uzun, Banu; Işık Üniversitesi, Fen Bilimleri Enstitüsü, Matematik Doktora ProgramıIn this thesis, we mentioned imaging technics used today, and microwave induced thermoacoustic procedure and imaging. We made literature survey about solution of the thermoacoustic equation for homogeneous and inhomogeneous medium. We modelled the inhomogenity of medium as a multi-layer planar structure and de?ned initial condition, continuity conditions on the layer boundaries and radiation conditions at in?nity, then we derived analytical forward and inverse solution of the thermoacoustic wave equation for inhomogeneous medium with the source distribution existing in all layers. Our solution of inverse source problem is based on the methods of the Green’s functions for layered planar media. For qualitative testing and comparison of the point-spread functions associated with the conventional solution for homogeneous medium and our derived layered solutions, we performed numerical simulations. In numerical simulations ?rst we generated the measured data by using the derived forward solution for multi-layer planar medium and then we used conventional inverse solution and our derived inverse solution to image source distribution. Our simulation results showed that the conventional inverse solution based on homogeneous medium assumption, as expected, produced incorrect locations of point sources, whereas our inverse solution involving the multi-layer planar medium produced point sources at the correct source locations. Also, we showed that the performance of layered inverse solution is sensitive to the validity of the layer parameters and medium parameters used as prior information in the measured data. Our inverse solutions based on multi-layer planar media are applicable for cross-sectional 2 dimensional imaging of the organs such as breast, skin, and abdominal structure.Yayın An inverse source problem connected with thermoacoustic imaging in multi-layer planar medium(Springer, 2019-02-20) Yücel, Hazel; Ünalmış Uzun, BanuWe derived analytical forward and inverse solution of thermoacoustic wave equation for nonhomogeneous medium. We modelled the nonhomogeneous medium as a multi-layer planar medium and defined initial conditions, continuity conditions on the layer boundaries and radiation conditions at infinity assuming the source distribution existing in all layers. These solutions of thermoacoustic wave equation are based on the method of Green’s functions for layered planar media. For qualitative testing and comparison of the point-spread functions associated with the homogeneous and layered solutions, we performed numerical simulations. Our simulation results showed that the conventional inverse solution based on homogeneous medium assumption, as expected, produced incorrect locations of point sources, whereas our inverse solution involving the multi-layer planar medium produced point sources at the correct source locations. Also, we examined whether the performance of our layered inverse solution is sensitive to medium parameters used as priority information in the measured data. Our inverse solutions based on multi-layer planar media are applicable for cross-sectional two-dimensional imaging of abdominal structure and the organs such as breast and skin.
