Almost all known image reconstruction algorithms for photoacoustic and
thermoacoustic tomography assume that the acoustic waves leave the region of
interest after a finite time. This assumption is reasonable if the reflections
from the detectors and surrounding surfaces can be neglected or filtered out
(for example, by time-gating). However, when the object is surrounded by
acoustically hard detector arrays, and/or by additional acoustic mirrors, the
acoustic waves will undergo multiple reflections. (In the absence of absorption
they would bounce around in such a reverberant cavity forever). This disallows
the use of the existing free-space reconstruction techniques. This paper
proposes a fast iterative reconstruction algorithm for measurements made at the
walls of a rectangular reverberant cavity. We prove the convergence of the
iterations under a certain sufficient condition, and demonstrate the
effectiveness and efficiency of the algorithm in numerical simulations.Comment: 21 pages, 6 figure
