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.

Implementation of the extended Kalman filter for determining the optical and geometrical properties of turbid layered media by time-resolved single distance measurements

“…The Extended Kalman Filter (EKF) [15,22] is a non-linear, non-optimal generalization of the Kalman Filter which is suitable for problems where the forward model is non-linear. In our specific application we will name x to the vector containing the optical properties µ a and µ s (for the corresponding layer), the geometrical parameter l and t 0 (an optional time shift to account for an imperfect correction of the delay due to different fiber arrangements in IRF and phantom measurements), and y to the measured DTOF.…”

Simultaneous retrieval of optical and geometrical parameters of multilayered turbid media via state-estimation algorithms

“…6, where the MAP of every iteration is shown in real (unscaled) parameters. Using Eqns (25), (26) and (27) with the corresponding 0.99 credibility interval limits, the Kalman Filter evolves marginally. In Fig.…”

“…It is a non-linear extension to the linear Kalman Filter [30], which has been used, for example, in estimation of physiological parameters [31]. In [26], the EKF was employed to perform optical tomography on phantoms with good results. Considering a state-evolution model written in the form:…”

“…The main goal of this work is thus to propose and validate an algorithm based on the Extended Kalman Filter (EKF) [24,25], which is a Bayesian method for Observation-Evolution problems that has been adapted for use in Optical Tomography as a parameter estimation tool [26]. It can incorporate information about the measurement noise, as well as prior knowledge about the variables of interest.…”

Optical tomography of turbid media containing diffusive and non-diffusive inclusions: An error modeling approach

“…There are many approaches to F, such as analytic results 13,32,33 when the medium is homogeneous and the geometry is simple or numerical results (finite differences, 6 finite elements, 16,43 and MC solutions 18 ) otherwise. In this work, we employed the TOASTþþ 43 toolbox to construct the operator F. To perform the reconstructions, we used the methodology proposed in Baez et al 7 which employed the extended Kalman filter (EKF) as an iterative alternative for the non-linear problem of tomography.…”