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

An inversion method based on random sampling for real-time MEG neuroimaging

The MagnetoEncephaloGraphy (MEG) is a non-invasive neuroimaging technique with a high temporal resolution which can be successfully used in real-time applications, such as brain-computer interface training or neurofeedback rehabilitation. The localization of the active area of the brain from MEG data results in a highly ill-posed and ill-conditioned inverse problem that requires fast and efficient inversion methods to be solved. In this paper we use an inversion method based on random spatial sampling to solve the MEG inverse problem. The method is fast, efficient and has a low computational load. The numerical tests show that the method can produce accurate map of the electric activity inside the brain even in case of deep neural sources

Neuroelectric source localization by random spatial sampling

The magnetoencephalography (MEG) aims at reconstructing the unknown neuroelectric activity in the brain from the measurements of the neuromagnetic field in the outer space. The localization of neuroelectric sources from MEG data results in an ill-posed and ill-conditioned inverse problem that requires regularization techniques to be solved. In this paper we propose a new inversion method based on random spatial sampling that is suitable to localize focal neuroelectric sources. The method is fast, efficient and requires little memory storage. Moreover, the numerical tests show that the random sampling method has a high spatial resolution even in the case of deep source localization from noisy magnetic data

Inverse Modeling for MEG/EEG data

We provide an overview of the state-of-the-art for mathematical methods that are used to reconstruct brain activity from neurophysiological data. After a brief introduction on the mathematics of the forward problem, we discuss standard and recently proposed regularization methods, as well as Monte Carlo techniques for Bayesian inference. We classify the inverse methods based on the underlying source model, and discuss advantages and disadvantages. Finally we describe an application to the pre-surgical evaluation of epileptic patients.Comment: 15 pages, 1 figur

Sparse wavelet-based solutions for the M/EEG inverse problem

This paper is concerned with variational and Bayesian approaches to neuro-electromagnetic inverse problems (EEG and MEG). The strong indeterminacy of these problems is tackled by introducing sparsity inducing regularization/priors in a transformed domain, namely a spatial wavelet domain. Sparsity in the wavelet domain allows to reach ''data compression'' in the cortical sources domain. Spatial wavelets defined on the mesh graph of the triangulated cortical surface are used, in combination with sparse regression techniques, namely LASSO regression or sparse Bayesian learning, to provide localized and compressed estimates for brain activity from sensor data. Numerical results on simulated and real MEG data are provided, which outline the performances of the proposed approach in terms of localization

Time-Frequency Mixed-Norm Estimates: Sparse M/EEG imaging with non-stationary source activations

International audienceMagnetoencephalography (MEG) and electroencephalography (EEG) allow functional brain imaging with high temporal resolution. While solving the inverse problem independently at every time point can give an image of the active brain at every millisecond, such a procedure does not capitalize on the temporal dynamics of the signal. Linear inverse methods (Minimum-norm, dSPM, sLORETA, beamformers) typically assume that the signal is stationary: regularization parameter and data covariance are independent of time and the time varying signal-to-noise ratio (SNR). Other recently proposed non-linear inverse solvers promoting focal activations estimate the sources in both space and time while also assuming stationary sources during a time interval. However such an hypothesis only holds for short time intervals. To overcome this limitation, we propose time-frequency mixed-norm estimates (TF-MxNE), which use time-frequency analysis to regularize the ill-posed inverse problem. This method makes use of structured sparse priors defined in the time-frequency domain, offering more accurate estimates by capturing the non-stationary and transient nature of brain signals. State-of-the-art convex optimization procedures based on proximal operators are employed, allowing the derivation of a fast estimation algorithm. The accuracy of the TF-MxNE is compared to recently proposed inverse solvers with help of simulations and by analyzing publicly available MEG datasets