Photoacoustic imaging in attenuating acoustic media based on strongly causal models

Abstract

In this paper, we derive time reversal imaging functionals for two strongly causal acoustic attenuation models, which have been proposed recently. The time reversal techniques are based on recently proposed ideas of Ammari et al. for the thermo-viscous wave equation. Here and there, an asymptotic analysis provides reconstruction functionals from first order corrections for the attenuating effect. In addition, we present a novel approach for higher order corrections. Copyright

Mathematical and Statistical Methods for Multistatic Imaging

“…One refers, for instance, to [76] and the references therein. Many interesting mathematical works have dealt with different aspects of time-reversal phenomena: see, for instance, [44,45] for time-reversal in the time-domain, [65,66,73,128] for time-reversal in the frequency domain, [53,79] for time-reversal in random media, and [4,6,104] for time-reversal in attenuating media. The results provided in this chapter on time-reversal techniques are from [4].…”

On Time Reversal in Photoacoustic Tomography for Tissue Similar to Water

“…However, in the long run, it seems indispensable to base some of the high quality imaging methods on causal integro-differential equations (cf. [11]). We consider the work presented in this paper as a trade off between the approaches [2] and [11].…”

“…[11]). We consider the work presented in this paper as a trade off between the approaches [2] and [11]. This paper is organized as follows: In Section 2 the properties of dissipative waves propagating forward and backward in time are investigated.…”

“…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 [11] and a similar operator equation may hold for their approach. …”

“…In this paper we focus on a time reversal method in dissipative media [2,3,5,9,11,14,16,20,22,23] and show that under an appropriate condition…”