In this paper, a family of kurtosis orderings for multivariate distributions is proposed and studied. Each ordering characterizes in an a¢ ne invariant sense the movement of probability mass from the "shoulders" of a distribution to either the center or the tails or both. All even moments of the Mahalanobis distance of a random vector from its mean (if exists) preserve a subfamily of the orderi...

This discussion presents a new perspective of subspace independent component analysis (ICA). The notion of a function of cumulants (kurtosis) is generalized to vector kurtosis. This vector kurtosis is utilized in the subspace ICA algorithm to estimate subspace independent components. One of the main advantages of the presented approach is its computational simplicity. The experiments have shown...

We presents a new necessary and sufficient condition for the blind separation of sources having non-zero kurtosis, from their linear mixtures. It is shown here that a new blind separation criterion based on both odd ( ) and even ( ) functions, presents desirable solutions, provided that all source signals have negative kurtosis (sub-Gaussian) or have positive kurtosis (super-Gaussian). Based on...

BACKGROUND AND PURPOSE The spinal cord is a site of predilection for MS lesions. While diffusion tensor imaging is useful for the study of anisotropic systems such as WM tracts, it is of more limited utility in tissues with more isotropic microstructures (on the length scales studied with diffusion MR imaging) such as gray matter. In contrast, diffusional kurtosis imaging, which measures both G...

Purpose To examine the usefulness of rich diffusion protocols with high b-values and varying diffusion time for probing microstructure in bone metastases. Analysis techniques including biophysical and mathematical models were compared with the clinical apparent diffusion coefficient (ADC). Methods Four patients were scanned using 13 b-values up to 3,000 s/mm2 and diffusion times ranging 18-52...

Sphericity of erythrocytes can be estimated from analysis of FSC signal distribution in flow cytometry. Previously, Pearson's coefficient of dissymmetry (PCD) and spherical index (SphI) were applied to determine erythrocyte sphericity from the FSC histogram. The aim of the present study is to illustrate the application of kurtosis as an indicator of erythrocyte sphericity in flow cytometry in a...

In various studies on blind separation of sources, one assumes that sources have the same sign of kurtosis. In fact, this assumption seems very strong and in this paper we studied relation between signal distribution and the sign of the kurtosis. A theoretical result has been found in a simple case. However, for more complex distributions, the kurtosis sign cannot be predicted and may change wi...

A computational framework is presented for relating the kurtosis tensor for water diffusion in brain to tissue models of brain microstructure. The tissue models are assumed to be comprised of non-exchanging compartments that may be associated with various microstructural spaces separated by cell membranes. Within each compartment the water diffusion is regarded as Gaussian, although the diffusi...

Diffusion kurtosis imaging (DKI) is an extension of diffusion tensor imaging (DTI), exhibiting improved sensitivity and specificity in detecting developmental and pathological changes in neural tissues. However, little attention was paid to the performances of DKI and DTI in detecting white matter abnormality in schizophrenia. In this study, DKI and DTI were performed in 94 schizophrenia patien...

The generalized lambda distribution (GLD) is a flexible four parameter distribution with many practical applications. L-moments of the GLD can be expressed in closed form and are good alternatives for the central moments. The L-moments of the GLD up to an arbitrary order are presented, and a study of L-skewness and L-kurtosis that can be achieved by the GLD is provided. The boundaries of L-skew...