کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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470525 | 698512 | 2013 | 12 صفحه PDF | دانلود رایگان |
We study the problem of recovering the initial data of the two dimensional wave equation from values of its solution on the boundary ∂Ω∂Ω of a smooth convex bounded domain Ω⊂R2Ω⊂R2. As a main result we establish back-projection type inversion formulas that recover any initial data with support in ΩΩ modulo an explicitly computed smoothing integral operator KΩKΩ. For circular and elliptical domains the operator KΩKΩ is shown to vanish identically and hence we establish exact inversion formulas of the back-projection type in these cases. Similar results are obtained for recovering a function from its mean values over circles with centers on ∂Ω∂Ω. Both reconstruction problems are, amongst others, essential for the hybrid imaging modalities photoacoustic and thermoacoustic tomography.
Journal: Computers & Mathematics with Applications - Volume 65, Issue 7, April 2013, Pages 1025–1036