Introduction In conventional diffusion tensor imaging (DTI), a Gaussian propagator function of the diffusing spins is postulated. In biological tissue however, substantial deviations from this Gaussian diffusion are observed [1], containing additional information on the tissue microstructure. For the quantification of these deviations, the kurtosis of the propagator function has been proposed [...

For both the academic and the financial communities it is a familiar stylized fact that stock market returns have negative skewness and excess kurtosis. This stylized fact has been supported by a vast collection of empirical studies. Given that the conventional measures of skewness and kurtosis are computed as an average and that averages are not robust, we ask, “How useful are the measures of ...

This paper presents a real time implementation of a blind beamformer for subband speech enhancement. The beamformer adaptively maximizes the statistical kurtosis measure of the beamformer’s output signal. Speech carries high kurtosis and noise often exhibit lower kurtosis. Hence, maximization of the output signal’s kurtosis enhances speech, in general. The implementation is carried out on a nov...

This paper derives conditions for the existence of fourth moments of multivariate GARCH processes in the general vector specification and gives explicit results for the fourth moments and autocovariances of the squares and cross-products. Results are provided for the kurtosis and co-kurtosis between components. Applications of the results include the definition of impulse response functions for...

Diffusional Kurtosis Imaging (DKI) is able to capture nonGaussian diffusion and has become a popular complement to the more traditional Diffusion Tensor Imaging (DTI). In this paper, we demonstrate how strongly the presence of fiber crossings and the exact crossing angle affect measures from diffusional kurtosis, limiting their interpretability as indicators of tissue microstructure. We allevia...

New, functional, concepts of skewness and kurtosis are introduced for large classes of continuous univariate distributions. They are the first skewness and kurtosis measures to be defined directly in terms of the probability density function and its derivative, and are directly interpretable in terms of them. Unimodality of the density is a basic prerequisite. The mode defines the centre of suc...

BACKGROUND AND PURPOSE Ischemic tissue damage is heterogeneous, resulting in complex patterns in the widely used diffusion-weighted MRI. Our study examined the spatiotemporal characteristics of diffusion kurtosis imaging in an animal model of transient middle cerebral artery occlusion. METHODS Adult male Wistar rats (N=18) were subjected to 90 minutes middle cerebral artery occlusion. Multipa...

Kurtosis of a time signal has been a popular tool for detecting nongaussianity. Recently, kurtosis as a function frequency defined in spectral domain has been successfully used in the fault detection of induction motors, machine bearings. A link between the nongaussianity and nonstationaity has been established through Wold-Cramer’s decomposition of a nonstationary signal, and the properties of...

Dairy cream is shown to be a simple, inexpensive, isotropic phantom useful for testing diffusional kurtosis imaging data acquisition and postprocessing. The MR-visible protons of cream exhibit slow and fast diffusion components, attributed to the fat and water protons, respectively, which give rise to a diffusion coefficient of 1.1 μm(2)/ms and a diffusional kurtosis of 1.2. These parameter val...