Approximate marginalization of unknown scattering in quantitative photoacoustic tomography
Aki Pulkkinen Ville Kolehmainen Jari P. Kaipio Benjamin T. Cox Simon R. Arridge Tanja Tarvainen
Inverse Problems & Imaging 2014, 8(3): 811-829 doi: 10.3934/ipi.2014.8.811
Quantitative photoacoustic tomography is a hybrid imaging method, combining near-infrared optical and ultrasonic imaging. One of the interests of the method is the reconstruction of the optical absorption coefficient within the target. The measurement depends also on the uninteresting but often unknown optical scattering coefficient. In this work, we apply the approximation error method for handling uncertainty related to the unknown scattering and reconstruct the absorption only. This way the number of unknown parameters can be reduced in the inverse problem in comparison to the case of estimating all the unknown parameters. The approximation error approach is evaluated with data simulated using the diffusion approximation and Monte Carlo method. Estimates are inspected in four two-dimensional cases with biologically relevant parameter values. Estimates obtained with the approximation error approach are compared to estimates where both the absorption and scattering coefficient are reconstructed, as well to estimates where the absorption is reconstructed, but the scattering is assumed (incorrect) fixed value. The approximation error approach is found to give better estimates for absorption in comparison to estimates with the conventional measurement error model using fixed scattering. When the true scattering contains stronger variations, improvement of the approximation error method over fixed scattering assumption is more significant.
keywords: quantitative photoacoustic tomography uncertainty quantification numerical methods. approximation error parameter estimation Inverse problems

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