Abstract
Many reconstruction problems in optical tomography, such as the imaging of haematoma in the brain, or breast tumour screening, require the detection and localisation of well-defined objects on a homogeneous or weakly varying background. A conventional parameter identification approach is to represent the image in a finite dimensional set of basis functions and to find the coefficients of this set using an optimisation strategy. Shape-based reconstruction techniques on the other hand, seek to find the boundaries of objects and possibly a representation of the interior either as constant or slowly varying functions. In this paper we compare both explicit and implicit shape reconstruction methods for the simultaneous recovery of absorption and diffusion inclusions in a three-dimensional scattering medium. Images reconstructed from simulated frequency-domain boundary measurements are compared to a voxel-based conjugate gradient method. The results demonstrate the feasibility of the shape based methods.