Graph- and finite element-based total variation models for the inverse problem in diffuse optical tomography.

Wenqi Lu,Lionel Herve,David Orive-Miguel,Iain B Styles,Jinming Duan

doi:10.1364/boe.10.002684

Abstract

Total variation (TV) is a powerful regularization method that has been widely applied in different imaging applications, but is difficult to apply to diffuse optical tomography (DOT) image reconstruction (inverse problem) due to unstructured discretization of complex geometries, non-linearity of the data fitting and regularization terms, and non-differentiability of the regularization term. We develop several approaches to overcome these difficulties by: i) defining discrete differential operators for TV regularization using both finite element and graph representations; ii) developing an optimization algorithm based on the alternating direction method of multipliers (ADMM) for the non-differentiable and non-linear minimization problem; iii) investigating isotropic and anisotropic variants of TV regularization, and comparing their finite element (FEM)- and graph-based implementations. These approaches are evaluated on experiments on simulated data and real data acquired from a tissue phantom. Our results show that both FEM and graph-based TV regularization is able to accurately reconstruct both sparse and non-sparse distributions without the over-smoothing effect of Tikhonov regularization and the over-sparsifying effect of L1 regularization. The graph representation was found to out-perform the FEM method for low-resolution meshes, and the FEM method was found to be more accurate for high-resolution meshes.

Highlights

Diffuse optical tomography (DOT) is an important non-invasive imaging technique whose major applications include diagnosing breast cancer [1,2,3], imaging small animals for the study of disease and analyzing brain function in functional neuroimaging [4,5,6,7]
The results show that A-FETV keeps reconstructing the target with boundaries that align with the coordinate axes which is same to the assumption of the anisotropic Total variation (TV) regularization
We introduce finite element and graph representations to discretize the TV regularization term in DOT reconstruction

Summary

Introduction

Diffuse optical tomography (DOT) is an important non-invasive imaging technique whose major applications include diagnosing breast cancer [1,2,3], imaging small animals for the study of disease and analyzing brain function in functional neuroimaging [4,5,6,7]. In DOT, near-infrared light (spectral range of 650-900 nm) is injected into the object through optical fibers placed on the surface of the object. Image reconstruction algorithms are used to recover the internal distribution of the underlying optical properties of the object from the boundary measurements. Due to the limited availability of boundary measurements and diffusive nature of near-infrared light propagation, image reconstruction in DOT is an underdetermined, ill-posed and nonlinear inverse problem. Regularization is often used to constrain the inverse problem to yield physiologically and anatomically plausible solutions, resulting in the following minimization problem with respect to the optical properties μ μ∗ = arg min μ

Methods

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Discussion

Conclusion