In this paper we consider the recovery of ellipsoidal 3D shapes with piecewise constant coefficients in Diffuse Optical Tomography (DOT). We use an adjoint scheme for calculating gradients for the shape parameters defining the unknown ellipsoids, and a Newton-type optimisation process for the minimization of a least squares data misfit functional. A boundary integral formulation is used for the forward modelling. An advantage of the proposed method is the implicit regularisation effect arising from the reduced dimensionality of the inverse problem. Results of a numerical experiment in 3D are shown which demonstrate the performance of the method.
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Zacharopoulos A, Arridge S, Dorn O, Kolehmainen V and Sikora J 2006 Three dimensional reconstruction of shape and piecewise constant region values for Optical Tomography using spherical harmonic parameterisation and a Boundary Element Method Inverse Problems 22 2175-2196
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Zacharopoulos, A., Dorn, O., Arridge, S.R., Kolehmainen, V., Sikora, J. (2008). Reconstruction of Simple Geometric Objects in 3D Optical Tomography Using an Adjoint Technique and a Boundary Element Method. In: Bonilla, L.L., Moscoso, M., Platero, G., Vega, J.M. (eds) Progress in Industrial Mathematics at ECMI 2006. Mathematics in Industry, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71992-2_100
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DOI: https://doi.org/10.1007/978-3-540-71992-2_100
Publisher Name: Springer, Berlin, Heidelberg
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