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A three-stage method for reconstructing multiple coefficients in coupled photoacoustic and diffuse optical imaging

Yinxi Pan, Kui Ren, Shanyin Tong

TL;DR

This work addresses the problem of recovering the diffusion coefficient $\gamma$, the absorption coefficient $\sigma$, and the Gruneisen coefficient $\Gamma$ from coupled diffuse optical tomography (DOT) and quantitative photoacoustic tomography (QPAT) data collected at a single optical wavelength. It introduces a three-stage PDE-constrained reconstruction: Stage I recovers $\gamma$ on the boundary, Stage II jointly recovers $\gamma$ and $\sigma$ by minimizing a combined DOT and PAT misfit with regularization, and Stage III estimates $\Gamma$ from averaged internal data. Theoretical results establish uniqueness of the coupled problem under suitable boundary conditions, and numerical experiments with synthetic data demonstrate improved accuracy and stability over a direct single-stage approach, including cases with smooth and discontinuous coefficients. The method provides a practical data-fusion framework for simultaneous quantitative imaging of optical properties and thermoelastic efficiency, with potential impact on high-resolution, multi-parameter tissue characterization.

Abstract

This paper studies inverse problems in quantitative photoacoustic tomography with additional optical current data supplemented from diffuse optical tomography. We propose a three-stage image reconstruction method for the simultaneous recovery of the absorption, diffusion, and Grüneisen coefficients. We demonstrate, through numerical simulations, that: (i) when the Grüneisen coefficient is known, the addition of the optical measurements allows a more accurate reconstruction of the scattering and absorption coefficients; and (ii) when the Grüneisen coefficient is not known, the addition of optical current measurements allows us to reconstruct uniquely the Grüneisen, the scattering and absorption coefficients. Numerical simulations based on synthetic data are presented to demonstrate the effectiveness of the proposed idea.

A three-stage method for reconstructing multiple coefficients in coupled photoacoustic and diffuse optical imaging

TL;DR

This work addresses the problem of recovering the diffusion coefficient , the absorption coefficient , and the Gruneisen coefficient from coupled diffuse optical tomography (DOT) and quantitative photoacoustic tomography (QPAT) data collected at a single optical wavelength. It introduces a three-stage PDE-constrained reconstruction: Stage I recovers on the boundary, Stage II jointly recovers and by minimizing a combined DOT and PAT misfit with regularization, and Stage III estimates from averaged internal data. Theoretical results establish uniqueness of the coupled problem under suitable boundary conditions, and numerical experiments with synthetic data demonstrate improved accuracy and stability over a direct single-stage approach, including cases with smooth and discontinuous coefficients. The method provides a practical data-fusion framework for simultaneous quantitative imaging of optical properties and thermoelastic efficiency, with potential impact on high-resolution, multi-parameter tissue characterization.

Abstract

This paper studies inverse problems in quantitative photoacoustic tomography with additional optical current data supplemented from diffuse optical tomography. We propose a three-stage image reconstruction method for the simultaneous recovery of the absorption, diffusion, and Grüneisen coefficients. We demonstrate, through numerical simulations, that: (i) when the Grüneisen coefficient is known, the addition of the optical measurements allows a more accurate reconstruction of the scattering and absorption coefficients; and (ii) when the Grüneisen coefficient is not known, the addition of optical current measurements allows us to reconstruct uniquely the Grüneisen, the scattering and absorption coefficients. Numerical simulations based on synthetic data are presented to demonstrate the effectiveness of the proposed idea.
Paper Structure (19 sections, 1 theorem, 45 equations, 8 figures, 1 algorithm)

This paper contains 19 sections, 1 theorem, 45 equations, 8 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. The mathematical models
  3. The diffusion model in DOT.
  4. The diffusion model in PAT.
  5. The compatibility condition for the coupling.
  6. Theoretical considerations on the coupling
  7. Uniqueness for Coupled Inverse Problem.
  8. Three-stage reconstruction of
  9. Stage I: reconstructing $\gamma_{|\partial\Omega}$.
  10. Stage II: reconstructing $(\gamma, \sigma)$.
  11. Stage III: reconstructing $\Gamma$.
  12. Numerical experiments
  13. Experiment I.
  14. Experiment II.
  15. Experiment III.
  16. ...and 4 more sections

Key Result

Lemma 4.1

Assume sufficient regularity, $\Phi$ is Fréchet differentiable with respect to $\gamma$ and $\sigma$. The derivatives are given as, assuming that $\gamma$ is given on the boundary, as where the three parts of the contributions are respectively given as follows. (i) The PAT part: where we have analytic reconstruction of $\gamma_{|\partial\Omega}$ from proposed stage I and so $\delta\gamma_{|\part

Figures (8)

  • Figure 1: Comparison of the reconstructions using QPAT+DOT coupling data (second column) with those using only QPAT data (third column), when $\Gamma$ is known.
  • Figure 2: True and reconstructed absorption (top row), diffusion (middle row), and Grüneisen (bottom row) coefficients in Experiment II. Shown from left to right are the true coefficients (first column), reconstructions with Dirichlet and Robin boundary conditions (middle two columns), and the relative error of the reconstructions (right two columns).
  • Figure 3: Reconstruction of the product $\mu:=\Gamma\sigma$ in Experiment II with Dirichlet (top) and Robin (bottom) boundary conditions. Shown are the true $\Gamma\sigma$ (first column), the reconstructions (second column), and relative errors (third column) in the reconstructions.
  • Figure 4: True coefficients (left column), reconstructions from noise-free data (middle column), and the relative error (right column) in Experiment III.
  • Figure 5: True coefficients (left), reconstructions from noisy data (middle column), and the relative error (right column) in Experiment III.
  • ...and 3 more figures

Theorems & Definitions (4)

  • Remark 2.1: Nature of the coupling strategy
  • Remark 2.2: On boundary conditions
  • Lemma 4.1
  • Remark 4.2