American Institute of Mathematical Sciences

August  2014, 8(3): 811-829. doi: 10.3934/ipi.2014.8.811

Approximate marginalization of unknown scattering in quantitative photoacoustic tomography

 1 Department of Applied Physics, University of Eastern Finland, P.O.Box 1627, 70211 Kuopio, Finland, Finland 2 University of Eastern Finland, Department of Applied Physics, P.O.Box 1627, 70211 Kuopio 3 Department of Mathematics, University of Auckland, Private Bag 92019, Auckland Mail Centre, Auckland 1142 4 Department of Medical Physics and Bioengineering, University College London, Gower Street, London WC1E 6BT, United Kingdom 5 Department of Computer Science, University College London, Gower Street, London WC1E 6BT, United Kingdom

Received  May 2013 Revised  June 2014 Published  August 2014

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.
Citation: Aki Pulkkinen, Ville Kolehmainen, Jari P. Kaipio, Benjamin T. Cox, Simon R. Arridge, Tanja Tarvainen. Approximate marginalization of unknown scattering in quantitative photoacoustic tomography. Inverse Problems & Imaging, 2014, 8 (3) : 811-829. doi: 10.3934/ipi.2014.8.811
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References:
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