Three-dimensional reconstruction of shape and piecewise constant region values for optical tomography using spherical harmonic parametrization and a boundary element method

Abstract

We consider the recovery of smooth 3D region boundaries with piecewise constant coefficients in optical tomography. The method is based on a parametrization of the closed boundaries of the regions by spherical harmonic coefficients, and a Newton type optimization process. A boundary integral formulation is used for the forward modelling. The calculation of the Jacobian is based on an adjoint scheme for calculating the corresponding shape derivatives. We show reconstructions for 3D situations. In addition we show the extension of the method for cases where the constant optical coefficients are also unknown. An advantage of the proposed method is the implicit regularization effect arising from the reduced dimensionality of the inverse problem.