Recursive least squares algorithm for optical diffusion tomography

Algebraic reconstruction techniques (ART) is a family of practical algorithms which sets algebraic equations for the unknowns in terms of the measured data and solves these equations iteratively. It is typical that the system of linear equations obtained in Diffuse Optical Tomography (DOT) is underdetermined and/or ill-conditioned. ART is one of the most popular image reconstruction techniques used in DOT to solve this kind of system of linear equations. There is, however, no natural way of including a priori information about the image in ART algorithm. Moreover ART requires a large number of iterations to reconstruct the image and hence convergence to the solution is slow. In this paper, for the inverse problem in DOT, we apply a Recursive Least Squares Algorithm (RLS) that converges in only one iteration and enables the use of a priori information such as image smoothness. We present comparison between the images reconstructed by ART and RLS.