A Subspace Pursuit-based Iterative Greedy Hierarchical solution to the neuromagnetic inverse problem

Abstract

Magnetoencephalography (MEG) is an important non-invasive method for studying activity within the human brain. Source localization methods can be used to estimate spatiotemporal activity from MEG measurements with high temporal resolution, but the spatial resolution of these estimates is poor due to the ill-posed nature of the MEG inverse problem. Recent developments in source localization methodology have emphasized temporal as well as spatial constraints to improve source localization accuracy, but these methods can be computationally intense. Solutions emphasizing spatial sparsity hold tremendous promise, since the underlying neurophysiological processes generating MEG signals are often sparse in nature, whether in the form of focal sources, or distributed sources representing large-scale functional networks. Recent developments in the theory of compressed sensing (CS) provide a rigorous framework to estimate signals with sparse structure. In particular, a class of CS algorithms referred to as greedy pursuit algorithms can provide both high recovery accuracy and low computational complexity. Greedy pursuit algorithms are difficult to apply directly to the MEG inverse problem because of the high-dimensional structure of the MEG source space and the high spatial correlation in MEG measurements. In this paper, we develop a novel greedy pursuit algorithm for sparse MEG source localization that overcomes these fundamental problems. This algorithm, which we refer to as the Subspace Pursuit-based Iterative Greedy Hierarchical (SPIGH) inverse solution, exhibits very low computational complexity while achieving very high localization accuracy. We evaluate the performance of the proposed algorithm using comprehensive simulations, as well as the analysis of human MEG data during spontaneous brain activity and somatosensory stimuli. These studies reveal substantial performance gains provided by the SPIGH algorithm in terms of computational complexity, localization accuracy, and robustness.

A geometric correction scheme for spatial leakage effects in MEG/EEG seed‐based functional connectivity mapping

“…The most basic approaches based on regularization priors [Uutela et al, ] typically yield temporally discontinuous source estimates, making them not suitable for FC analysis. More advanced methods have been developed to generate spatially sparse and temporally continuous reconstructions, e.g., temporal projections of ‐norm estimates [Huang et al, ], empirical Bayesian inference [Friston et al, ; Wipf and Nagarajan, ; Wipf et al, ], mixed‐norm regularization [Gramfort et al, ; Ou et al, ] or subspace pursuit algorithms [Babadi et al, ]. By design, these approaches should limit spatial leakage effects and may thus be promising, although they have not yet been evaluated for MEG/EEG FC analyses.…”

Real-Time MEG Source Localization Using Regional Clustering

“…Babadi et al [1] recently proposed a clustering technique which uses the most significant eigenmodes of pre-computed Voronoi regions. In comparison to that, we used an anatomical brain atlas instead of Voronoi regions which allows to keep an anatomical, often related to a functional, representation of the cortex and provides an easily interpretable result for our real-time monitor.…”

Spatially Sparse, Temporally Smooth MEG Via Vector <formula formulatype="inline"><tex Notation="TeX">$\ell_{0}$</tex> </formula>

“…The latter two methods have been found to need significant modification for application to snapshot MEG [3].…”