An EM‐like reconstruction method for diffuse optical tomography

Abstract

AbstractDiffuse optical tomography (DOT) is an optical imaging modality which provides the spatial distributions of optical parameters inside an object. The forward model of DOT is described by the diffusion approximation of radiative transfer equation, while the DOT is to reconstruct the optical parameters from boundary measurements. In this paper, an EM‐like iterative reconstruction method specifically for the steady state DOT problem is developed. Previous iterative reconstruction methods are mostly based on the assumption that the measurement noise is Gaussian, and are of least‐squares type. In this paper, with the assumption that the boundary measurements have independent and identical Poisson distributions, the inverse problem of DOT is solved by maximizing a log‐likelihood functional with inequality constraints, and then an EM‐like reconstruction algorithm is developed according to the Kuhn–Tucker condition. The proposed algorithm is a variant of the well‐known EM algorithm. The performance of the proposed algorithm is tested with three‐dimensional numerical simulation. Copyright © 2010 John Wiley & Sons, Ltd.