On Time Reversal in Photoacoustic Tomography for Tissue Similar to Water

Abstract

This paper is concerned with time reversal in photoacoustic tomography of dissipative media that are similar to water. Under an appropriate condition, it is shown that the time reversal method in [A. Wahab, Modeling and Imaging of Attenuation in Biological Media, Ph.D. dissertation, Ecole Polytechnique Palaiseau, Paris, 2011; H. Ammari et al., in Mathematical and Statistical Methods for Imaging, AMS, Providence, RI, 2011, pp. 151--163] based on the noncausal thermoviscous wave equation can be used if the noncausal data are replaced by a time shifted set of causal data. We investigate a similar imaging functional for time reversal and an operator equation with the time reversal image as the right-hand side. If required, an enhanced image can be obtained by solving this operator equation. Although time reversal (for noise-free data) does not lead to the exact initial pressure function, the theoretical and numerical results of this paper show that regularized time reversal in dissipative media similar to water is a valuable method. We note that the presented time reversal method can be considered as an alternative to the causal approach in [K. Kalimeris and O. Scherzer, Math. Methods Appl. Sci., 36 (2013), pp. 2254--2264] and a similar operator equation may hold for their approach.