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| Most of the known theoretical and algorithmic results pertaining to the inverse problem of the thermo- and photo- acoustic tomography are obtained under the assumption that the acoustic waves propagate in free space. However, neglecting the reflections of the waves from the detectors is not always possible. When optically scanned solid plates surrounding the object are used to measure the acoustic signal, one nas to account for the multiple reflections of the acoustic waves from these plates. In this case the forward problem is accurately modeled by the wave equation with the Neumann boundary conditions on the walls of the resonant cavity formed by the detecting surfaces. The energy of waves in such a cavity does not decay in time (if we neglect the absorption) which renders inapplicable the classical analytic results. In the talk I will discuss the possibility ofan approximate time reversal in the problems of photo/thermo- acoustic tomography within a reverberant cavity. I will also present a fast reconstruction algorithm for the practically important particular case of a rectangular cavity in 3D. |
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