Abstract
Uncovering brain activity from magnetoencephalography (MEG) data requires solving an ill-posed inverse problem, greatly confounded by noise, interference, and correlated sources. Sparse reconstruction algorithms, such as Champagne, show great promise in that they provide focal brain activations robust to these confounds. In this paper, we address the technical considerations of statistically thresholding brain images obtained from sparse reconstruction algorithms. The source power distribution of sparse algorithms makes this class of algorithms ill-suited to “conventional” techniques. We propose two non-parametric resampling methods hypothesized to be compatible with sparse algorithms. The first adapts the maximal statistic procedure to sparse reconstruction results and the second departs from the maximal statistic, putting forth a less stringent procedure that protects against spurious peaks. Simulated MEG data and three real data sets are utilized to demonstrate the efficacy of the proposed methods. Two sparse algorithms, Champagne and generalized minimum-current estimation (G-MCE), are compared to two non-sparse algorithms, a variant of minimum-norm estimation, sLORETA, and an adaptive beamformer. The results, in general, demonstrate that the already sparse images obtained from Champagne and G-MCE are further thresholded by both proposed statistical thresholding procedures. While non-sparse algorithms are thresholded by the maximal statistic procedure, they are not made sparse. The work presented here is one of the first attempts to address the problem of statistically thresholding sparse reconstructions, and aims to improve upon this already advantageous and powerful class of algorithm.
Highlights
Magnetoencephalography (MEG) and electroencephalography (EEG) are powerful non-invasive neuroimaging technologies that can resolve brain activity on the order of a millisecond
Can non-parametric resampling-based statistical thresholding methods be applied to the inverse solution obtained from sparse algorithms? Second, can non-parametric statistical thresholding reject spurious peaks in the already sparse image? And third, can brain images obtained from non-sparse algorithms resemble the sparse maps through stringent thresholding? First we introduce a source localization procedure with unaveraged sensor data and two proposed nonparametric statistical thresholding techniques hypothesized to be compatible with sparse algorithms
We focus on the performance of statistical thresholding of sparse images with Champagne and compare the results to another sparse method, a variant of minimum-current estimate (MCE) referred to as generalized MCE (G-MCE; Wipf et al, 2009), and to two non-sparse methods, minimum-variance adaptive beamforming (MVAB; Sekihara and Nagarajan, 2008) and sLORETA (SL; Pascual-Marqui, 2002), a variant of minimum-norm estimate (MNE) similar to dSPM (Dale et al, 2000)
Summary
Magnetoencephalography (MEG) and electroencephalography (EEG) are powerful non-invasive neuroimaging technologies that can resolve brain activity on the order of a millisecond. Unlike brain imaging methods that directly measure correlates of brain activity, such as functional magnetic resonance imaging (fMRI) and positron emission tomography (PET), the neural activity at every location in the brain or “voxel” must be estimated from the surface magnetic or electric fields recorded with M/EEG. This estimation process is referred to as “source localization” and solving this ill-posed inverse problem is one of the greatest challenges to using M/EEG to elucidate neural activations. In the voxel-level statistics step a test statistic is calculated for each voxel along with a corresponding p-value, the probability that the statistic value would exceed that which was observed under the null hypothesis
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