Frequency domain optical tomography based on the equation of radiative transfer

Optical tomography consists of reconstructing the spatial distribution of absorption and scattering properties of a medium from surface measurements of transmitted light intensities. Mathematically, this problem amounts to parameter identification for the equation of radiative transfer (ERT) with diffusion-type boundary measurements. Because they are posed in the phase-space, radiative transfer equations are quite challenging to solve computationally. Most past works have considered the steady-state ERT or the diffusion approximation of the ERT. In both cases, substantial cross-talk has been observed in the reconstruction of the absorption and scattering properties of inclusions. In this paper, we present an optical tomographic reconstruction algorithm based on the frequency-domain ERT. The inverse problem is formulated as a regularized least-squares minimization problem, in which the mismatch between forward model predictions and measurements is minimized. The ERT is discretized by using a discrete ordinates method for the directional variables and a finite volume method for the spatial variables. A limited-memory quasi-Newton algorithm is used to minimize the least-squares functional. Numerical simulations with synthetic data show that the cross-talk between the two optical parameters is significantly reduced in reconstructions based on frequency-domain data as compared to those based on steady-state data.