Reconstructing absorption and diffusion shape profiles in optical tomography by a level set technique

A shape reconstruction algorithm for optical tomography is introduced that uses a level-set formulation for the shapes. Evolution laws based on gradient directions for a cost functional are derived for two different level-set functions, one describing the absorption and one the diffusion parameter, as well as for the parameter values inside these shapes. Numerical experiments are presented in 2D that show that the new method is able to simultaneously recover shapes and contrast values of absorbing and scattering objects embedded in a moderately heterogeneous background medium from simulated noisy data.