Projections for handling uncertainties and enabling domain truncation in diffuse optical tomography

TL;DR

This paper introduces a projection-based method to improve diffuse optical tomography by reducing errors from domain truncation and parameter misspecification, enhancing reconstruction accuracy.

Contribution

The novel approach projects the forward model onto orthogonal complements of nuisance Jacobians, effectively mitigating modeling errors in diffuse optical tomography.

Findings

Method reduces impact of domain truncation errors.

Improves robustness against optical parameter misspecification.

Validated on simulated neonatal brain data.

Abstract

This paper presents a projection-based technique to mitigate the impact of modeling errors related to domain truncation, changes in the optode coupling coefficients, and misspecified optical parameters of different tissue types in diffuse optical tomography. The approach considers the primary Jacobian matrix of the forward map in the image reconstruction scheme, linking the primary unknown, i.e., the per-voxel absorption coefficient changes in the region of interest, to the optode measurements, as well as the nuisance Jacobians that do the same for the auxiliary unknown parameters of secondary interest. To mitigate mismodeled coupling coefficients or domain truncation, the method projects the linearized forward model defined by the primary Jacobian onto the orthogonal complement of the range of a nuisance Jacobian, or onto the orthogonal complement of the span of a number of first left singular vectors for the nuisance Jacobian that has been weighted to account for prior information on the measurement setup. In the case of a misspecified baseline optical parameter for some tissue type, the nullspace of the utilized orthogonal projection is defined to be the span of first left singular vectors for a (weighted) difference of two Jacobian matrices evaluated at two different levels for the considered tissue-wise optical parameter. The reconstruction is formed by applying Bayesian inversion with Gaussian prior and noise models to the projected linearized equation. We evaluate the method on simulated brain activity data obtained via Monte Carlo simulations of the radiative transfer equation in a voxelized head anatomy for a neonate with combined gestational and chronological age of 41.7 weeks.