Imaging brain source extent from EEG/MEG by means of an iteratively reweighted edge sparsity minimization (IRES) strategy

Abstract

Estimating extended brain sources using EEG/MEG source imaging techniques is challenging. EEG and MEG have excellent temporal resolution at millisecond scale but their spatial resolution is limited due to the volume conduction effect. We have exploited sparse signal processing techniques in this study to impose sparsity on the underlying source and its transformation in other domains (mathematical domains, like spatial gradient). Using an iterative reweighting strategy to penalize locations that are less likely to contain any source, it is shown that the proposed iteratively reweighted edge sparsity minimization (IRES) strategy can provide reasonable information regarding the location and extent of the underlying sources. This approach is unique in the sense that it estimates extended sources without the need of subjectively thresholding the solution. The performance of IRES was evaluated in a series of computer simulations. Different parameters such as source location and signal-to-noise ratio were varied and the estimated results were compared to the targets using metrics such as localization error (LE), area under curve (AUC) and overlap between the estimated and simulated sources. It is shown that IRES provides extended solutions which not only localize the source but also provide estimation for the source extent. The performance of IRES was further tested in epileptic patients undergoing intracranial EEG (iEEG) recording for pre-surgical evaluation. IRES was applied to scalp EEGs during interictal spikes, and results were compared with iEEG and surgical resection outcome in the patients. The pilot clinical study results are promising and demonstrate a good concordance between noninvasive IRES source estimation with iEEG and surgical resection outcomes in the same patients. The proposed algorithm, i.e. IRES, estimates extended source solutions from scalp electromagnetic signals which provide relatively accurate information about the location and extent of the underlying source.

s-SMOOTH: Sparsity and Smoothness Enhanced EEG Brain Tomography

“…If further decreasing the voxel number to be 2000, the computation time is reduced to 1.2 s, or 0.9 s with pre-computed matrices. Compared to relevant work (Haufe et al, 2008; Chang et al, 2010; Sohrabpour et al, 2016), the proposed algorithm has reduced the computational cost significantly.…”

“…On the other hand, if choosing α 1 , α 2 and β to be 0, it becomes the L1 method. In addition, some relevant methods that combine two regularization terms (Haufe et al, 2008; Chang et al, 2010; Sohrabpour et al, 2016) usually describe the data fidelity by using an inequality constraint. Instead, we integrate this term into our objective function.…”

“…This enables us to apply efficient optimization methods such as ADMM to derive a fast and robust algorithm. Compared to the optimization algorithms used in these methods (Haufe et al, 2008; Chang et al, 2010; Sohrabpour et al, 2016), the proposed algorithm in this paper is more efficient and robust, and it is also able to tackle large-scale problems. Further, with this type of problem formation, it is possible to adopt some computing techniques (Peng et al, 2015) to further accelerate the algorithm, which will be the future work.…”

“…Although the focalization is greatly improved, these methods fail to estimate the extent of the sources since the reconstructed source is over-focused. To address this issue, efforts have been devoted to exploring sparsity on transform domains of the current density, such as the spatial Laplacian domain (Haufe et al, 2008; Vega-Hernández et al, 2008; Chang et al, 2010), wavelet-basis domain (Chang et al, 2010; Liao et al, 2012; Zhu et al, 2014), Gaussian-basis domain (Haufe et al, 2011), or variation domain (Adde et al, 2005; Ding, 2009; Gramfort, 2009; Luessi et al, 2011; Becker et al, 2014; Sohrabpour et al, 2016). Furthermore, in order to obtain a local smooth and global sparse result, some approaches impose sparsity on both the transform domain and the original source domain.…”

“…However, the Laplacian operator, i.e., the sum of all unmixed second partial derivatives, tends to assign high weight to the central voxel and relatively low weights to its neighbors, which results in the over-smoothing effect of the reconstructed image (refer to Section 4). Sparse Total Variation (TV) methods, also known as TV-ℓ 1 (Becker et al, 2014; Sohrabpour et al, 2016), impose the sparsity constraint on both the spatial gradient and the current density itself. They assume that the current density distribution is piecewise constant, and are able to preserve well the extent of the sources.…”