Optical tomography with the discontinuous Galerkin formulation of the radiative transfer equation in frequency domain

Optical tomography is an inverse method of probing semi-transparent media with the help of light sources. The reconstruction of the optical properties usually employs finite volumes or continuous finite elements formulations of light transport as a forward model for the predictions. In a previous study, we have introduced a generalization of the inversion approach with finite elements formulations by using an integral form of the objective function. The novelty is that the surfaces of the detectors are taken into account in the reconstruction and compatibility is obtained for all finite element formulations. This present paper illustrates this new approach by developing a Discontinuous Galerkin formulation as a forward model for an optical tomography application in the frequency domain framework. Numerical tests are performed to gauge the accuracy of the method in recovering optical properties distribution with a gradient-based algorithm where the adjoint method is used to fastly compute the objective function gradient. It is seen that the reconstruction is accurate and can be affected by noise on the measurements as expected. Filtering of the gradient at each iteration of the reconstruction is used to cope with the ill-posed nature of the inverse problem and to improves the quality and accuracy of the reconstruction.

► A novel approach for optical tomography with finite elements formulations of discontinuous Galerkin type. ► An integral form of objective function is used to get compatibility with discontinuous finite elements framework. ► Gradient-based algorithm with the adjoint method is used for the reconstruction. ► An improvement is obtained by filtering the objective function gradient at each iteration.