Reconstructions in limited‐view thermoacoustic tomography

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 π‐, or less than a π‐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 (FBP) 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 inclusions), 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.