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Independent component analysis (ICA) has become an increasingly utilized approach for analyzing brain imaging data. In contrast to the widely used general linear model (GLM) that requires the user to parameterize the data (e.g. the brain's response to stimuli), ICA, by relying upon a general assumption of independence, allows the user to be agnostic… (More)

Multivariate analysis methods such as independent component analysis (ICA) have been applied to the analysis of functional magnetic resonance imaging (fMRI) data to study brain function. Because of the high dimensionality and high noise level of the fMRI data, order selection, i.e., estimation of the number of informative components, is critical to reduce… (More)

We introduce and apply a synthesis/analysis model for analyzing functional Magnetic Resonance Imaging (fMRI) data using independent component analysis (ICA). Our model assumes statistically independent spatial sources in the brain. We also assume that the fMRI scanner acquires overdetermined data such that there are more time points than brain sources. We… (More)

Let and be cocyclic Jacket matrices; we have (39) Let (40) where. On the other hand, we have. That is a Jacket matrix. Assume that and are cocyclic under the following row and column index orders: (41) where and and denote the first row index and first column index of matrix as well as and , the form indicates that the index is next to the index. Then, for… (More)

— The generalized Gaussian distribution (GGD) provides a flexible and suitable tool for data modeling and simulation, however the characterization of the complex-valued GGD, in particular generation of samples from a complex GGD have not been well defined in the literature. In this study, we provide a thorough presentation of the complex-valued GGD by i)… (More)

—A novel (differential) entropy estimator is introduced where the maximum entropy bound is used to approximate the en-tropy given the observations, and is computed using a numerical procedure thus resulting in accurate estimates for the entropy. We show that such an estimator exists for a wide class of measuring functions, and provide a number of design… (More)

We propose a new entropy rate estimator for a second and/or higher-order correlated source by modeling it as the output of a linear filter, which can be mixed-phase, driven by Gaussian or non-Gaussian noise. Based on this estimator, we develop a new spatiotemporal blind source separation (BSS) algorithm, full BSS (FBSS), by minimizing the entropy rate of… (More)

We investigate the approximation ability of a multilayer perceptron (MLP) network when it is extended to the complex domain. The main challenge for processing complex data with neural networks has been the lack of bounded and analytic complex nonlinear activation functions in the complex domain, as stated by Liouville's theorem. To avoid the conflict… (More)