Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media

The paper starts with a comparative discussion of features and limitations of the three types of recent approaches to reconstruction in thermoacoustic/photoacoustic tomography: backprojection formulae, eigenfunction expansions and time reversal. The latter method happens to be the least restrictive. It is then considered in more detail, e. g. its relation to trapping properties of the medium. The time reversal method is exact only in the case of a constant sound speed in odd dimension, due to validity of the Huygens' principle. The next best case is of non-trapping speed in odd dimensions. The authors provide 2D examples and discuss the features of numerical reconstructions for constant and variable ( both non-trapping and trapping) speeds, showing that this technique works surprisingly well even under the most unfavorable circumstances ( variable, and even trapping sound speed in 2D). In particular, a `limited view' effect due to trapping is observed and explained. Finally, an initial consideration of the problem of sound speed recovery is also provided.