s-SMOOTH: Sparsity and Smoothness Enhanced EEG Brain Tomography

Ying Li; Jing Qin; Yue-Loong Hsin; Stanley Osher; Wentai Liu

doi:10.3389/fnins.2016.00543

s-SMOOTH: Sparsity and Smoothness Enhanced EEG Brain Tomography

Front Neurosci. 2016 Nov 28:10:543. doi: 10.3389/fnins.2016.00543. eCollection 2016.

Authors

Ying Li¹, Jing Qin², Yue-Loong Hsin³, Stanley Osher⁴, Wentai Liu⁵

Affiliations

¹ Biomimetic Research Lab, Department of Bioengineering, University of California, Los Angeles Los Angeles, CA, USA.
² Department of Mathematical Sciences, Montana State University Bozeman, MT, USA.
³ Department of Neurology, Chung Shan Medical University Taichung, Taiwan.
⁴ Department of Mathematics, University of California, Los Angeles Los Angeles, CA, USA.
⁵ Biomimetic Research Lab, Department of Bioengineering, University of California, Los AngelesLos Angeles, CA, USA; California NanoSystems Institute, University of California, Los AngelesLos Angeles, CA, USA.

Abstract

EEG source imaging enables us to reconstruct current density in the brain from the electrical measurements with excellent temporal resolution (~ ms). The corresponding EEG inverse problem is an ill-posed one that has infinitely many solutions. This is due to the fact that the number of EEG sensors is usually much smaller than that of the potential dipole locations, as well as noise contamination in the recorded signals. To obtain a unique solution, regularizations can be incorporated to impose additional constraints on the solution. An appropriate choice of regularization is critically important for the reconstruction accuracy of a brain image. In this paper, we propose a novel Sparsity and SMOOthness enhanced brain TomograpHy (s-SMOOTH) method to improve the reconstruction accuracy by integrating two recently proposed regularization techniques: Total Generalized Variation (TGV) regularization and ℓ_1-2 regularization. TGV is able to preserve the source edge and recover the spatial distribution of the source intensity with high accuracy. Compared to the relevant total variation (TV) regularization, TGV enhances the smoothness of the image and reduces staircasing artifacts. The traditional TGV defined on a 2D image has been widely used in the image processing field. In order to handle 3D EEG source images, we propose a voxel-based Total Generalized Variation (vTGV) regularization that extends the definition of second-order TGV from 2D planar images to 3D irregular surfaces such as cortex surface. In addition, the ℓ_1-2 regularization is utilized to promote sparsity on the current density itself. We demonstrate that ℓ_1-2 regularization is able to enhance sparsity and accelerate computations than ℓ₁ regularization. The proposed model is solved by an efficient and robust algorithm based on the difference of convex functions algorithm (DCA) and the alternating direction method of multipliers (ADMM). Numerical experiments using synthetic data demonstrate the advantages of the proposed method over other state-of-the-art methods in terms of total reconstruction accuracy, localization accuracy and focalization degree. The application to the source localization of event-related potential data further demonstrates the performance of the proposed method in real-world scenarios.

Keywords: EEG source imaging; alternating direction method of multipliers (ADMM); difference of convex functions algorithm (DCA); inverse problem; total generalized variation (TGV); ℓ1−2 regularization.