Signal reconstruction for the diffusion transport equation using tensorial spline Galerkin approximation

In this paper, we discuss the deterministic transport problem with Robin boundary conditions in optically diffusion medium. Existence and uniqueness for the such elliptic equation are given. An approximation of the photon density in frequency-domain is proposed by using a Galerkin method based on the tensorial B-splines. We propose the Gauss–Hermite quadrature formulation for the computation of the inverse Fourier transform of the temporal signal. This technique allows us to avoid the use of a method such as finite difference method. Error estimates are studied and some numerical examples are given.