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An Inverse Source Problem Connected with Thermoacoustic Imaging in Multi-layer Planar Medium

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Abstract

We 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.

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Acknowledgements

This work was supported by TUBITAK of Turkey through ARDEB-1003 Program under Grant 213E038. We are immensely grateful to Prof. Dr. Mustafa Karaman who provided insight and expertise that assisted the research.

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  1. Mathematics Department, Işık University, 34980, Şile, Istanbul, Turkey

    Banu Uzun & Hazel Yücel

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  1. Banu Uzun
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Correspondence to Banu Uzun.

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Uzun, B., Yücel, H. An Inverse Source Problem Connected with Thermoacoustic Imaging in Multi-layer Planar Medium. J Math Imaging Vis 61, 874–884 (2019). https://doi.org/10.1007/s10851-019-00875-2

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