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- W2016113542 abstract "The goal of emph{photoacoustic tomography} (PAT) is to estimate an emph{initial pressure function} $varphi$ from pressure data measured at a boundary surrounding the object of interest. This paper is concerned with a time reversal method for PAT that is based on the dissipative wave equation of Nachman, Smith and Waagcite{NaSmWa90}. This equation has the advantage that it is more accurate than the emph{thermo-viscous} wave equation. For simplicity, we focus on the case of one emph{relaxation process}. We derive an exact formula for the emph{time reversal image} $I$, which depends on the emph{relaxation time} $tau_1$ and the emph{compressibility} $kappa_1$ of the dissipative medium, and show $I(tau_1,kappa_1)tovarphi$ for $kappa_1to 0$. This implies that $I=varphi$ holds in the dissipation-free case and that $I$ is similar to $varphi$ for sufficiently small compressibility $kappa_1$. Moreover, we show for tissue similar to water that the emph{small wave number approximation} $I_0$ of the time reversal image satisfies $I_0 = eta_0 *_x varphi$ with $hat eta_0(|k|)approx const.$ for $|k|<< frac{1}{c_0,tau_1}$. For such tissue, our theoretical analysis and numerical simulations show that the time reversal image $I$ is very similar to the initial pressure function $varphi$ and that a resolution of $sigmaapprox 0.036cdot mm$ is feasible (in the noise-free case)." @default.
- W2016113542 created "2016-06-24" @default.
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- W2016113542 date "2014-02-13" @default.
- W2016113542 modified "2023-09-30" @default.
- W2016113542 title "Time reversal for photoacoustic tomography based on the wave equation of Nachman, Smith, and Waag" @default.
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- W2016113542 doi "https://doi.org/10.1103/physreve.89.023203" @default.
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