Finite elements parameterization of optical tomography with the radiative transfer equation in frequency domain

Optical tomography is a technique of probing semi-transparent media with the help of light sources. In this method, the spatial distribution of the optical properties inside the probed medium is reconstructed by minimizing a cost function based on the errors between the measurements and the predictions of a numerical model of light transport (also called forward/direct model) within the medium at the detectors locations. Optical tomography with finite elements methods involves generally continuous formulations where the optical properties are constant per mesh elements. This study proposes a numerical analysis in the parameterization of the finite elements space of the optical properties in order to improve the accuracy and the contrast of the reconstruction. Numerical tests with noised data using the same algorithm show that continuous finite elements spaces give better results than discontinuous ones by allowing a better transfer of the information between the whole computational nodes of the inversion. It is seen that the results are more accurate when the number of degrees of freedom of the finite element space of the optical properties (number of unknowns) is lowered. This shows that reducing the number of unknowns decreases the ill-posed nature of the inverse problem, thus it is a promising way of regularizing the inversion.