Gauss-Newton reconstruction method for optical tomography using the finite element solution of the radiative transfer equation

The radiative transfer equation can be utilized in optical tomography in situations in which the more commonly applied diffusion approximation is not valid. In this paper, an image reconstruction method based on a frequency domain radiative transfer equation is developed. The approach is based on a total variation output regularized least squares method which is solved with a Gauss-Newton algorithm. The radiative transfer equation is numerically solved with a finite element method in which both the spatial and angular discretizations are implemented in piecewise linear bases. Furthermore, the streamline diffusion modification is utilized to improve the numerical stability. The approach is tested with simulations. Reconstructions from different cases including domains with low-scattering regions are shown. The results show that the radiative transfer equation can be utilized in optical tomography and it can produce good quality images even in the presence of low-scattering regions.