{
  "id": "1309.4657",
  "version": "v1",
  "published": "2013-09-18T14:25:34.000Z",
  "updated": "2013-09-18T14:25:34.000Z",
  "title": "Time reversal for photoacoustic tomography based on the wave equation of Nachman, Smith and Waag",
  "authors": [
    "Richard Kowar"
  ],
  "journal": "Phys. Rev. E 89, 023203 (2014)",
  "doi": "10.1103/PhysRevE.89.023203",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "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 Waag\\cite{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 $\\I(\\tau_1,\\kappa_1)\\to\\varphi$ for $\\kappa_1\\to 0$. 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 $\\sigma\\approx 0.036\\cdot mm$ is feasible (in the noise-free case).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-18T14:25:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35L05",
      "47A52",
      "45A05",
      "65J20",
      "43.60.+d",
      "43.80.Qf",
      "43.60.Tj",
      "43.35.Ud"
    ],
    "keywords": [
      "wave equation",
      "photoacoustic tomography",
      "time reversal image satisfies",
      "time reversal method",
      "wave number approximation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2014,
      "month": "Feb",
      "volume": 89,
      "number": 2,
      "pages": "023203"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014PhRvE..89b3203K"
    }
  }
}