Sparsity-driven spatio-temporal EEG source estimation (Seyreklik tabanlı uzam-zamansal EEG kaynak kestirimi)

We consider the problem of sparse source estimation using multiple time samples. We propose the use of a spatio-temporal constraint which is a combination of spatial ℓ1-norm for sparsity and temporal ℓ2-norm for nonspiky pattern in time. We demonstrate the effectiveness of this spatio-temporal method through experiments based on both simulated and human EEG data

Non-parametric statistical thresholding for sparse magnetoencephalography source reconstructions.

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

A two-way regularization method for MEG source reconstruction

The MEG inverse problem refers to the reconstruction of the neural activity of the brain from magnetoencephalography (MEG) measurements. We propose a two-way regularization (TWR) method to solve the MEG inverse problem under the assumptions that only a small number of locations in space are responsible for the measured signals (focality), and each source time course is smooth in time (smoothness). The focality and smoothness of the reconstructed signals are ensured respectively by imposing a sparsity-inducing penalty and a roughness penalty in the data fitting criterion. A two-stage algorithm is developed for fast computation, where a raw estimate of the source time course is obtained in the first stage and then refined in the second stage by the two-way regularization. The proposed method is shown to be effective on both synthetic and real-world examples.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS531 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Functional brain imaging with M/EEG using structured sparsity in time-frequency dictionaries

International audienceMagnetoencephalography (MEG) and electroencephalography (EEG) allow functional brain imaging with high temporal resolution. While time-frequency analysis is often used in the field, it is not commonly employed in the context of the ill-posed inverse problem that maps the MEG and EEG measurements to the source space in the brain. In this work, we detail how convex structured sparsity can be exploited to achieve a principled and more accurate functional imaging approach. Importantly, time-frequency dictionaries can capture the non-stationary nature of brain signals and state-of-the-art convex optimization procedures based on proximal operators allow the derivation of a fast estimation algorithm. We compare the accuracy of our new method to recently proposed inverse solvers with help of simulations and analysis of real MEG data.On s'intéresse au problème inverse mal posé rencontré dans la localisation de sources d'activité cérébrale par M/EEG (magneto/électro-encéphalographie). Bien qu'on ait à disposition un modèle physique réaliste de la diffusion (ou du mélange) des sources, le caractère très sous-déterminé le rend très difficile à inverser. La nécessité de trouver des a priori forts et pertinents physiquement sur les sources est une des parties difficiles de ce problème. Bien que les ondelettes et les gaborettes soient largement utilisées en traitement du signal pour l'analyse temps-fréquence et le débruitage, elles n'ont été que relativement peu employées afin d'améliorer le problème inverse M/EEG. On présente comment les décompositions temps-fréquence et les a priori de parcimonie structurée peuvent être utilisés afin d'obtenir un a priori convexe et physiologiquement motivé. L'a priori introduit ici favorise des estimations avec peu de sources cérébrales actives, tout en ayant un décours temporel lisse. La méthode présentée est alors capable de reconstruire des signaux corticaux non-stationnaires. Les résultats obtenus sont comparés avec ceux obtenus par l'état de l'art sur des signaux MEG simulés, mais aussi sur des données réelles

Brain source imaging: from sparse to tensor models

International audienceA number of application areas such as biomedical engineering require solving an underdetermined linear inverse problem. In such a case, it is necessary to make assumptions on the sources to restore identifiability. This problem is encountered in brain source imaging when identifying the source signals from noisy electroencephalographic or magnetoencephalographic measurements. This inverse problem has been widely studied during the last decades, giving rise to an impressive number of methods using different priors. Nevertheless, a thorough study of the latter, including especially sparse and tensor-based approaches, is still missing. In this paper, we propose i) a taxonomy of the algorithms based on methodological considerations, ii) a discussion of identifiability and convergence properties, advantages, drawbacks, and application domains of various techniques, and iii) an illustration of the performance of selected methods on identical data sets. Directions for future research in the area of biomedical imaging are eventually provided