An improved extended Kalman filter for diffuse optical tomography

Abstract

In diffuse optical tomography (DOT) the main objective is to estimate the absorption coefficent and the reduced scattering coefficient of a certain media given a set of boundary measurements. Biological tissues contains many objects such as arteries, skin and fat whose optical properties are rather different than those of the media. When these values are near to those of the background, linear techniques are usually used to estimate them. However, certain objects, such as tumors, may have properties which cannot be well estimated with linear models. In this article we present a non-linear approach for the frequency-domain problem based on an improvement of the extended Kalman filter (EKF) which is used in estimation-observation problems, and modified to the DOT parameter estimation problem. The EKF allows to incorporate prior information of the measurement noise as well as certain characteristics of the objective media. We show that the proposed methodology is equivalent to existing methods but can be applied to other schemes such as model reduction as suggested in previous works. Some computer simulations as well as experimental results are shown to validate our proposal.