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Linear structural equation models (SEMs) have been very successful in identifying the topology of complex graphs, such as those representing social and brain networks. In many cases however, the presence of highly correlated nodes hinders performance of the available SEM estimators that rely on the least-absolute shrinkage and selection operator (LASSO). To this end, an elastic net based SEM is put...
A framework for reliable seperation of a low-rank subspace from grossly corrupted multi-dimensional signals is pivotal in modern signal processing applications. Current methods fall short of this separation either due to the radical simplification or the drastic transformation of data. This has motivated us to propose two new robust low-rank tensor models: Tensor Orthonormal Robust PCA (TORCPA) and...
In this paper, we are going to localize the onset regions and investigate the dynamics of absence epileptic seizures using local field potential recording by depth electrode. We assume that there are some hidden states (under Markovian model) during the seizure and each spike of the seizure is generated when one of the states is activated. Each state is considered as the linear superposition of a...
Hyperparameter estimation is a recurrent problem in the signal and statistics literature. Popular strategies are cross-validation or Bayesian inference, yet it remains an active topic of research in order to offer better or faster algorithms. The models considered here are sparse regression models with convex or non-convex group-Lasso-like penalties. Following the recent work of Pereyra et al. [1]...
Simultaneous recording of electroencephalographic (EEG) signals and functional magnetic resonance images (fMRI) has gained wide interest in brain research, thanks to the highly complementary spatiotemporal nature of both modalities. We propose a novel technique to extract sources of neural activity from the multimodal measurements, which relies on a structured form of coupled matrix-tensor factorization...
Numerous physical phenomena are well modeled by partial differential equations (PDEs); they describe a wide range of phenomena across many application domains, from modeling EEG signals in electroencephalography to, modeling the release and propagation of toxic substances in environmental monitoring. In these applications it is often of interest to find the sources of the resulting phenomena, given...
In this paper we investigate task-related changes in brain functional connectivity (FC) by applying different methods namely event-related desynchronization (ERD), coherence and graph-theoretical analysis to electroencephalographic (EEG) recordings. While ERD provides an estimate of the differences in power spectral densities between task and rest conditions, coherence allows assessing the level of...
In this paper, we extend the classic analytic signal to the Vector-valued Hyperanalytic Signal (VHaS) that is denoted to distinguish from the multivariate hypercomplex data. The 2d-Dimensional (2d-D) VHaS, S(t) : [0,1] → C2d, is defined by a complexification of two d-D Vector-valued Hypercomplex Signals (VHcS), S(t) := G(t)e0 + HC2ded[G](t) ed, where HC2ded and ei represent the Hilbert transform and...
A high quality model of newborn EEG background can aid in the analysis of newborn EEG. This paper proposes an improvement to the current time-varying, power-law spectrum model for newborn EEG background by using a band- limited fractional Brownian process with time-varying Hurst exponent. This model provides a more detailed definition of newborn EEG background than current models. The advantages of...
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