Reliable gradient search directions for kurtosis-based deflationary ICA: Application to physiological signal processing.

Efficient gradient search directions for the optimisation of the kurtosis-based deflationary RobustICA algorithm in the case of real-valued data are proposed in this paper. The proposed scheme employs, in the gradient-like algorithm typically used to optimise the considered kurtosis-based objective function, search directions computed from a more reliable approximation of the negentropy than the kurtosis. The proposed scheme inherits the exact line search of the conventional RobustICA for which a good convergence property through a given direction is guaranteed. The efficiency of the proposed scheme is evaluated in terms of estimation quality, the execution time and the iterations count as a function of the number of used sensors and for different signal to noise ratios in the contexts of non-invasive epileptic ElectroEncephaloGraphic (EEG) and Magnetic Resonance Spectroscopic (MRS) analysis. The obtained results show that the proposed approach offer the best estimation performance/iterations count and execution time trade-off, especially in the case of high number of sensors.

SISSY: An efficient and automatic algorithm for the analysis of EEG sources based on structured sparsity.

Over the past decades, a multitude of different brain source imaging algorithms have been developed to identify the neural generators underlying the surface electroencephalography measurements. While most of these techniques focus on determining the source positions, only a small number of recently developed algorithms provides an indication of the spatial extent of the distributed sources. In a recent comparison of brain source imaging approaches, the VB-SCCD algorithm has been shown to be one of the most promising algorithms among these methods. However, this technique suffers from several problems: it leads to amplitude-biased source estimates, it has difficulties in separating close sources, and it has a high computational complexity due to its implementation using second order cone programming. To overcome these problems, we propose to include an additional regularization term that imposes sparsity in the original source domain and to solve the resulting optimization problem using the alternating direction method of multipliers. Furthermore, we show that the algorithm yields more robust solutions by taking into account the temporal structure of the data. We also propose a new method to automatically threshold the estimated source distribution, which permits to delineate the active brain regions. The new algorithm, called Source Imaging based on Structured Sparsity (SISSY), is analyzed by means of realistic computer simulations and is validated on the clinical data of four patients.

Complex patterns of spatially extended generators of epileptic activity: Comparison of source localization methods cMEM and 4-ExSo-MUSIC on high resolution EEG and MEG data.

Electric Source Imaging (ESI) and Magnetic Source Imaging (MSI) of EEG and MEG signals are widely used to determine the origin of interictal epileptic discharges during the pre-surgical evaluation of patients with epilepsy. Epileptic discharges are detectable on EEG/MEG scalp recordings only when associated with a spatially extended cortical generator of several square centimeters, therefore it is essential to assess the ability of source localization methods to recover such spatial extent. In this study we evaluated two source localization methods that have been developed for localizing spatially extended sources using EEG/MEG data: coherent Maximum Entropy on the Mean (cMEM) and 4th order Extended Source Multiple Signal Classification (4-ExSo-MUSIC). In order to propose a fair comparison of the performances of the two methods in MEG versus EEG, this study considered realistic simulations of simultaneous EEG/MEG acquisitions taking into account an equivalent number of channels in EEG (257 electrodes) and MEG (275 sensors), involving a biophysical computational neural mass model of neuronal discharges and realistically shaped head models. cMEM and 4-ExSo-MUSIC were evaluated for their sensitivity to localize complex patterns of epileptic discharges which includes (a) different locations and spatial extents of multiple synchronous sources, and (b) propagation patterns exhibited by epileptic discharges. Performance of the source localization methods was assessed using a detection accuracy index (Area Under receiver operating characteristic Curve, AUC) and a Spatial Dispersion (SD) metric. Finally, we also presented two examples illustrating the performance of cMEM and 4-ExSo-MUSIC on clinical data recorded using high resolution EEG and MEG. When simulating single sources at different locations, both 4-ExSo-MUSIC and cMEM exhibited excellent performance (median AUC significantly larger than 0.8 for EEG and MEG), whereas, only for EEG, 4-ExSo-MUSIC showed significantly larger AUC values than cMEM. On the other hand, cMEM showed significantly lower SD values than 4-ExSo-MUSIC for both EEG and MEG. When assessing the impact of the source spatial extent, both methods provided consistent and reliable detection accuracy for a wide range of source spatial extents (source sizes ranging from 3 to 20cm2 for MEG and 3 to 30cm2 for EEG). For both EEG and MEG, 4-ExSo-MUSIC localized single source of large signal-to-noise ratio better than cMEM. In the presence of two synchronous sources, cMEM was able to distinguish well the two sources (their location and spatial extent), while 4-ExSo-MUSIC only retrieved one of them. cMEM was able to detect the spatio-temporal propagation patterns of two synchronous activities while 4-ExSo-MUSIC favored the strongest source activity. Overall, in the context of localizing sources of epileptic discharges from EEG and MEG data, 4-ExSo-MUSIC and cMEM were found accurately sensitive to the location and spatial extent of the sources, with some complementarities. Therefore, they are both eligible for application on clinical data.

Low cost and efficient kurtosis-based deflationary ICA method: application to MRS sources separation problem.

Improving the execution time and the numerical complexity of the well-known kurtosis-based maximization method, the RobustICA, is investigated in this paper. A Newton-based scheme is proposed and compared to the conventional RobustICA method. A new implementation using the nonlinear Conjugate Gradient one is investigated also. Regarding the Newton approach, an exact computation of the Hessian of the considered cost function is provided. The proposed approaches and the considered implementations inherit the global plane search of the initial RobustICA method for which a better convergence speed for a given direction is still guaranteed. Numerical results on Magnetic Resonance Spectroscopy (MRS) source separation show the efficiency of the proposed approaches notably the quasi-Newton one using the BFGS method.

Feasibility of blind source separation methods for the denoising of dense-array EEG.

High-density electroencephalographic recordings have recently been proved to bring useful information during the pre-surgical evaluation of patients suffering from drug-resistant epilepsy. However, these recordings can be particularly obscured by noise and artifacts. This paper focuses on the denoising of dense-array EEG data (e.g. 257 channels) contaminated with muscle artifacts. In this context, we compared the efficiency of several Independent Component Analysis (ICA) methods, namely SOBI, SOBIrob, PICA, InfoMax, two different implementations of FastICA, COM2, ERICA, and SIMBEC, as well as that of Canonical Correlation Analysis (CCA). We evaluated the performance using the Normalized Mean Square Error (NMSE) criterion and calculated the numerical complexity. Quantitative results obtained on realistic simulated data show that some of the ICA methods as well as CCA can properly remove muscular artifacts from dense-array EEG.

Localization of spatially distributed brain sources after a tensor-based preprocessing of interictal epileptic EEG data.

This paper addresses the localization of spatially distributed sources from interictal epileptic electroencephalographic data after a tensor-based preprocessing. Justifying the Canonical Polyadic (CP) model of the space-time-frequency and space-time-wave-vector tensors is not an easy task when two or more extended sources have to be localized. On the other hand, the occurrence of several amplitude modulated spikes originating from the same epileptic region can be used to build a space-time-spike tensor from the EEG data. While the CP model of this tensor appears more justified, the exact computation of its loading matrices can be limited by the presence of highly correlated sources or/and a strong background noise. An efficient extended source localization scheme after the tensor-based preprocessing has then to be set up. Different strategies are thus investigated and compared on realistic simulated data: the "disk algorithm" using a precomputed dictionary of circular patches, a standardized Tikhonov regularization and a fused LASSO scheme.

EEG extended source localization: tensor-based vs. conventional methods.

The localization of brain sources based on EEG measurements is a topic that has attracted a lot of attention in the last decades and many different source localization algorithms have been proposed. However, their performance is limited in the case of several simultaneously active brain regions and low signal-to-noise ratios. To overcome these problems, tensor-based preprocessing can be applied, which consists in constructing a space-time-frequency (STF) or space-time-wave-vector (STWV) tensor and decomposing it using the Canonical Polyadic (CP) decomposition. In this paper, we present a new algorithm for the accurate localization of extended sources based on the results of the tensor decomposition. Furthermore, we conduct a detailed study of the tensor-based preprocessing methods, including an analysis of their theoretical foundation, their computational complexity, and their performance for realistic simulated data in comparison to conventional source localization algorithms such as sLORETA, cortical LORETA (cLORETA), and 4-ExSo-MUSIC. Our objective consists, on the one hand, in demonstrating the gain in performance that can be achieved by tensor-based preprocessing, and, on the other hand, in pointing out the limits and drawbacks of this method. Finally, we validate the STF and STWV techniques on real measurements to demonstrate their usefulness for practical applications.