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The limited-view problem is studied for thermoacoustic tomography, which is also referred to as photoacoustic or optoacoustic tomography depending on the type of radiation for the induction of acoustic waves. We define a ''detection region,'' within which all points have sufficient detection views. It is explained analytically and shown numerically that the boundaries of any objects inside this region can be recovered stably. Otherwise some sharp details become blurred. One can identify in advance the parts of the boundaries that will be affected if the detection view is insufficient. If the detector scans along a circle in a two-dimensional case, acquiring a sufficient view might require covering more than a -, or less than a -arc of the trajectory depending on the position of the object. Similar results hold in a three-dimensional case. In order to support our theoretical conclusions, three types of reconstruction methods are utilized: a filtered backprojection ͑FBP͒ approximate inversion, which is shown to work well for limited-view data, a local-tomography-type reconstruction that emphasizes sharp details ͑e.g., the boundaries of inclusions͒, and an iterative algebraic truncated conjugate gradient algorithm used in conjunction with FBP. Computations are conducted for both numerically simulated and experimental data. The reconstructions confirm our theoretical predictions.

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.