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Bölüm: Işık Üniversitesi, Fen Bilimleri Enstitüsü, Matematik Doktora Programı × Konu: Inverse source problem ×

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    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 Programı
    In 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.