We propose a novel l(1)l(2)-norm inverse solver for estimating the sources of EEG/MEG signals. Based on the standard l(1)-norm inverse solvers, this sparse distributed inverse solver integrates the l(1)-norm spatial model with a temporal model of the source signals in order to avoid unstable activation patterns and "spiky" reconstructed signals often produced by the currently used sparse solvers. The joint spatio-temporal model leads to a cost function with an l(1)l(2)-norm regularizer whose minimization can be reduced to a convex second-order cone programming (SOCP) problem and efficiently solved using the interior-point method. The efficient computation of the SOCP problem allows us to implement permutation tests for estimating statistical significance of the inverse solution. Validation with simulated and human MEG data shows that the proposed solver yields source time course estimates qualitatively similar to those obtained through dipole fitting, but without the need to specify the number of dipole sources in advance. Furthermore, the l(1)l(2)-norm solver achieves fewer false positives and a better representation of the source locations than the conventional l(2) minimum-norm estimates.

Abstract. We propose a novel 1 2-norm inverse solver for estimating the sources of EEG/MEG signals. Based on the standard 1-norm inverse solver, the proposed sparse distributed inverse solver integrates the 1-norm spatial model with a temporal model of the source signals in order to avoid unstable activation patterns and "spiky" reconstructed signals often produced by the original solvers. The joint spatio-temporal model leads to a cost function with an 1 2-norm regularizer whose minimization can be reduced to a convex second-order cone programming problem and efficiently solved using the interior-point method. Validation with simulated and real MEG data shows that the proposed solver yields source time course estimates qualitatively similar to those obtained through dipole fitting, but without the need to specify the number of dipole sources in advance. Furthermore, the 1 2-norm solver achieves fewer false positives and a better representation of the source locations than the conventional 2 minimum-norm estimates.

The theories of signal sampling, filter banks, wavelets, and "overcomplete wavelets" are well established for the Euclidean spaces and are widely used in the processing and analysis of images. While recent advances have extended some filtering methods to spherical images, many key challenges remain. In this paper, we develop theoretical conditions for the invertibility of filter banks under continuous spherical convolution. Furthermore, we present an analogue of the Papoulis generalized sampling theorem on the 2-Sphere. We use the theoretical results to establish a general framework for the design of invertible filter banks on the sphere and demonstrate the approach with examples of self-invertible spherical wavelets and steerable pyramids. We conclude by examining the use of a self-invertible spherical steerable pyramid in a denoising experiment and discussing the computational complexity of the filtering framework.

By combining diffuse optical imaging (DOI) and magnetoencephalography (MEG) we investigate neurovascular coupling non-invasively in human subjects using median-nerve stimulation. Previous fMRI studies have shown a habituation effect in the hemodynamic blood oxygen level-dependent (BOLD) response for stimulation periods longer than 2 s. With DOI and MEG we can test whether this effect in hemodynamic response can be accounted for by a habituation effect in the neural response. Our experimental results show that the habituation effect in the hemodynamic response is stronger than that in the earliest cortical neural response (N20). Using a linear convolution model to predict hemodynamic responses we found that including late neural components (≥30 ms) improves the prediction of the hemoglobin response. This finding suggests that in addition to the initial evoked-response deflections related to the talamic afferent input, later cortical activity is needed to predict the hemodynamic response.

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