3D Shape Reconstruction in Optical Tomography Using Spherical Harmonics and BEM

Abstract

We consider the recovery of smooth 3D region boundaries with piecewise constant coefficients in Optical Tomography (OT). The method is based on a parametrisation of the closed boundaries of the regions by spherical harmonic coefficients, and a Newton type optimisation process. 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 are shown which demonstrate the performance of the new method in a realistic situation.