Inverse transport problems in quantitative PAT for molecular imaging

Abstract

Fluorescence photoacoustic tomography (fPAT) is a molecular imaging modality that combines photoacoustic tomography (PAT) with fluorescence imaging to obtain high-resolution imaging of fluorescence distributions inside heterogeneous media. The objective of this work is to study inverse problems in the quantitative step of fPAT where we intend to reconstruct physical coefficients in a coupled system of radiative transport equations using internal data recovered from ultrasound measurements. We derive uniqueness and stability results on the inverse problems and develop some efficient algorithms for image reconstructions. Numerical simulations based on synthetic data are presented to validate the theoretical analysis. The results we present here complement these in [57] on the same problem but in the diffusive regime.

Characterizing Impacts of Model Uncertainties in Quantitative Photoacoustics

“…In Figure 9 we show the true absorption coefficient σ a,xf , the mean of the reconstruction of it and two realizations of the reconstructions formed from the reconstructed PCE coefficients. We observe again that the averaged reconstruction is very accurate, comparable to the numerical simulations in [72,71]. The uncertainty in the reconstructions depends on the uncertainty in the ultrasound speed as in the PAT case in Experiment I: piecewise smooth random ultrasound speed could produce larger uncertainty in the reconstructions than smooth random ultrasound speed; see the top and bottom rows of Figure 10 for a comparison.…”

“…However, the calculations are slightly more lengthy since we have to deal with system of diffusion equations as in (53) instead of a single diffusion equation as in (1). For more details on the mathematical modeling, as well as uniqueness results on image reconstructions, in fPAT, we refer to [71,72]. We make the following regularity assumptions on the background coefficients:…”

Comparative study of one-step and two-step quantitative fluorescence photoacoustic tomography

“…Significant quantum efficiencies (ϕ 0.2, 0.4, 0.6) were chosen for comparison of the FPAT and QPAT frameworks. Such ranges of values are also used in [10][11][12]32].…”

“…They have proved the uniqueness and stability properties of this inversion problem and shown the reconstructions using AOED as data. The group further developed the theory for radiative transport equation (RTE) based FPAT and validated it using numerical simulations [11]. Recently, Wang and Zhou (2018) proposed an approach that combines a squeeze iterative method (SIM) with a nonlinear optimization technique to enhance the quantitative accuracy and convergence of RTE-based FPAT reconstructions [12].…”

“…The partial optical inverse problem of reconstructing an unknown fluorophore absorption coefficient under diffusion approximation assuming a known pressure source has been discussed in [10]. The corresponding RTE-based FPAT problem has been solved in [11,12]. The inverse problem of FPAT can be formulated in two ways:…”