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.

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.