Symbols and Abbreviations

$t = 1,\ldots,T$ Time sequence with observations.

$k = 1,\ldots,K$ Source sequence with sources.

$v = 1,\ldots,V$ Volumetric sequence with voxels.

$\mathbf{\tilde{X}}$ Observed data matrix.

$\mathbf{X}$ Whitened data matrix.

$\mathbf{\tilde{A}}$ Arbitrary mixing matrix.

$\mathbf{A}$ Orthonormal mixing matrix.

$\mathbf{\hat{A}}$ Normalized concatenated mixing matrix.

$\mathbf{W}$ Orthonormal demixing matrix.

$\mathbf{S}$ Independent sources matrix.

$\mathbf{x}_t^T$ Row vector of matrix $\mathbf{X}$ .

$\mathbf{a}_k$ Column vector of matrix $\mathbf{A}$ .

$\mathbf{\bar{a}}_k$ Mean value of vector $\mathbf{a}_k$ .

$\mathbf{w}_k^T$ Row vector of matrix $\mathbf{W}$ .

$\mathbf{s}_k^T$ Row vector of matrix $\mathbf{S}$ .

$a_{ij}$ Scalar element of matrix $\mathbf{A}$ .

$\mathbf{M}$ Arbitrary square matrix.

$\lambda_i$ The th eigenvalue.

$\mathbf{v}_i$ Eigenvector corresponding to $\lambda_i$ .

$\mathbf{D}$ Diagonal matrix of eigenvalues.

$\mathbf{V}$ Orthogonal matrix of eigenvectors.

$g(\cdot)$ Nonlinear function.

$g'(\cdot)$ Derivative of function $g(\cdot)$ .

$E\{\cdot\}$ Statistical expectation function.

$p(\cdot)$ Probability density function.

$f(\cdot)$ Arbitrary function.

$\mathbf{C}$ Correlation matrix.

$c_{ij}$ Scalar element of matrix $\mathbf{C}$ .

$\mathbf{\tilde{C}}$ Thresholded binary correlation matrix.

$\mathbf{R}$ Relations matrix.

$r_{ij}$ Scalar element of matrix $\mathbf{R}$ .

CNS Central Nervous System

EEG ElectroEncephaloGraphy

MEG MagnetoEncephaloGraphy

CT Computed Tomography

PET Positron Emission Tomography

MRI Magnetic Resonance Imaging

fMRI functional Magnetic Resonance Imaging

NIRS Near-InfraRed Spectroscopy

DOI Diffuse Optical Imaging

BOLD Blood Oxygenation Level Dependent

GLM General Linear Model

SPM Statistical Parametric Mapping

BSS Blind Source Separation

SOBI Second-Order Blind Identification

TDSEP Temporal Decorrelation source SEParation

PCA Principal Component Analysis

EVD EigenValue Decomposition

ICA Independent Component Analysis

DSS Denoising Source Separation

$t = 1,\ldots,T$	Time sequence with observations.
$k = 1,\ldots,K$	Source sequence with sources.
$v = 1,\ldots,V$	Volumetric sequence with voxels.
$\mathbf{\tilde{X}}$	Observed data matrix.
$\mathbf{X}$	Whitened data matrix.
$\mathbf{\tilde{A}}$	Arbitrary mixing matrix.
$\mathbf{A}$	Orthonormal mixing matrix.
$\mathbf{\hat{A}}$	Normalized concatenated mixing matrix.
$\mathbf{W}$	Orthonormal demixing matrix.
$\mathbf{S}$	Independent sources matrix.
$\mathbf{x}_t^T$	Row vector of matrix $\mathbf{X}$ .
$\mathbf{a}_k$	Column vector of matrix $\mathbf{A}$ .
$\mathbf{\bar{a}}_k$	Mean value of vector $\mathbf{a}_k$ .
$\mathbf{w}_k^T$	Row vector of matrix $\mathbf{W}$ .
$\mathbf{s}_k^T$	Row vector of matrix $\mathbf{S}$ .
$a_{ij}$	Scalar element of matrix $\mathbf{A}$ .
$\mathbf{M}$	Arbitrary square matrix.
$\lambda_i$	The th eigenvalue.
$\mathbf{v}_i$	Eigenvector corresponding to $\lambda_i$ .
$\mathbf{D}$	Diagonal matrix of eigenvalues.
$\mathbf{V}$	Orthogonal matrix of eigenvectors.
$g(\cdot)$	Nonlinear function.
$g'(\cdot)$	Derivative of function $g(\cdot)$ .
$E\{\cdot\}$	Statistical expectation function.
$p(\cdot)$	Probability density function.
$f(\cdot)$	Arbitrary function.
$\mathbf{C}$	Correlation matrix.
$c_{ij}$	Scalar element of matrix $\mathbf{C}$ .
$\mathbf{\tilde{C}}$	Thresholded binary correlation matrix.
$\mathbf{R}$	Relations matrix.
$r_{ij}$	Scalar element of matrix $\mathbf{R}$ .

CNS	Central Nervous System
EEG	ElectroEncephaloGraphy
MEG	MagnetoEncephaloGraphy
CT	Computed Tomography
PET	Positron Emission Tomography
MRI	Magnetic Resonance Imaging
fMRI	functional Magnetic Resonance Imaging
NIRS	Near-InfraRed Spectroscopy
DOI	Diffuse Optical Imaging
BOLD	Blood Oxygenation Level Dependent
GLM	General Linear Model
SPM	Statistical Parametric Mapping
BSS	Blind Source Separation
SOBI	Second-Order Blind Identification
TDSEP	Temporal Decorrelation source SEParation
PCA	Principal Component Analysis
EVD	EigenValue Decomposition
ICA	Independent Component Analysis
DSS	Denoising Source Separation