Anisotropic diffusion regularization methods for diffuse optical tomography using edge prior information

Abstract

Diffuse optical tomography (DOT) is a non-invasive functional imaging modality that aims to image the optical properties of biological organs. The forward problem of the light propagation of DOT can be modelled as a diffusion process and is expressed as a differential diffusion equation with boundary conditions. The solution of the DOT inverse problem can be formulated as a minimization of some functional that measures the discrepancy between the measured data and the data produced by representation of the modelled object. The minimization of this term alone would force the solution to be consistent with the data and the solver used for this purpose. But since in practice data are always accompanied with noise and with some jump discontinuities, these will unavoidably yield unsatisfactory solutions, so some regularization to restore the solution is required. In this paper we introduce an anisotropic regularization term using a priori structural information about the object. This term aims to reduce the noise associated with the data and to preserve the edges in the solution by a combined strategy using the a priori edge information and the diffusion flux analysis of the local structures at each iteration. To accelerate the iterative solver we use a particular method called the lagged diffusivity Newton–Krylov method. The whole proposed strategy, which makes use of a priori diffusion information has been developed and evaluated on simulated data.