Multiwave tomography in a closed domain: averaged sharp time reversal

Abstract

We study the mathematical model of multiwave tomography including thermo and photoacoustic tomography with a variable speed for a fixed time interval $[0,T]$. We assume that the waves reflect from the boundary of the domain. We propose an averaged sharp time reversal algorithm. In case of measurements on the whole boundary, we give an explicit solution in terms of a Neumann series expansion. When the measurements are taken on a part of the boundary, we show that the same algorithm produces a parametrix.

21 pages, 5 figures

References in corpus (4)

• Thermoacoustic tomography with variable sound speed
• Thermoacoustic tomography arising in brain imaging
• Photoacoustic Tomography in a Rectangular Reflecting Cavity
• Carleman estimates for the Zaremba Boundary Condition and Stabilization of Waves

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• A weight-adjusted discontinuous Galerkin method for wave propagation in coupled elastic-acoustic media
• Photoacoustic imaging taking into account thermodynamic attenuation
• Compressed sensing photoacoustic tomography reduces to compressed sensing for undersampled Fourier measurements