Use Of Kurtosis Research Articles

Impacts of model resolution on multiple prediction

Despite theoretical advancements in multiple identification and elimination, the application and success of these advancements are questionable in some cases and are limited to marine environments, especially deepwater. In land seismic, however, a clear understanding of the internal multiple generators is not readily available; thus, efforts to attenuate them often are quite ineffective. We have analyzed, in the case of many thin layers, how the primaries and multiples are affected by fine-scale variations in the velocity model. Cross-coherence is used to measure the similarity of the original primaries/multiples and the ones generated from upscaled velocity models. The combined use of kurtosis and the cross-coherence method enables us to precisely quantify the impact of fine layering on multiples. Test results demonstrate that surface-related multiples and internal multiples are much more sensitive than the primaries to thickness variations of the velocity model. As the thickness of each upscaled layer varies from 1 to 21 m, multiples change rapidly, whereas primaries are almost the same. The high sensitivity of internal multiples on fine layering suggests that the detailed model information should be considered in model parameterization in the internal multiple removal, especially for model-driven methods.

Skewness and kurtosis analysis for non-Gaussian distributions

In this paper we address a number of pitfalls regarding the use of kurtosis as a measure of deviations from the Gaussian. We treat kurtosis in both its standard definition and that which arises in q-statistics, namely q-kurtosis. We have recently shown that the relation proposed by Cristelli et al. (2012) between skewness and kurtosis can only be verified for relatively small data sets, independently of the type of statistics chosen; however it fails for sufficiently large data sets, if the fourth moment of the distribution is finite. For infinite fourth moments, kurtosis is not defined as the size of the data set tends to infinity. For distributions with finite fourth moments, the size, N, of the data set for which the standard kurtosis saturates to a fixed value, depends on the deviation of the original distribution from the Gaussian. Nevertheless, using kurtosis as a criterion for deciding which distribution deviates further from the Gaussian can be misleading for small data sets, even for finite fourth moment distributions. Going over to q-statistics, we find that although the value of q-kurtosis is finite in the range of 0<q<3, this quantity is not useful for comparing different non-Gaussian distributed data sets, unless the appropriate q value, which truly characterizes the data set of interest, is chosen. Finally, we propose a method to determine the correct q value and thereby to compute the q-kurtosis of q-Gaussian distributed data sets.

Evaluation of diffusion weighted imaging in the context of multi-parametric MRI of the prostate in the assessment of suspected low volume prostatic carcinoma

Data from a multi-parametric MRI study of patients with possible early-stage prostate cancer was assessed with a view to creating a more efficient clinical protocol. Based on a correlation analysis suggesting that diffusion-weighted imaging (DWI) scores are more strongly correlated with overall PIRADS scores than other modalities such as dynamic contrast enhanced imaging or spectroscopy, we investigate the combination of T2-weighted imaging (T2w) and DWI as a potential diagnostic tool for prostate cancer detection, staging and guided biopsies. Quantification of the noise floor in the DWI images and careful fitting of the data suggests that the mono-exponential model provides a very good fit to the data and there is no evidence of non-Gaussian diffusion for b-values up to 1000s/mm2. This precludes the use of kurtosis or other non-Gaussian measures as a biomarker for prostate cancer in our case. However, the ADC scores for healthy and probably malignant regions are significantly lower for the latter in all 20 but one patient. The results suggest that a simplified mp-MRI protocol combining T2w and DWI may be a good compromise for a cost and time efficient, early-stage prostate cancer diagnostic programme, combining robust MR biomarkers for prostate cancer that can be reliably quantified and appear well-suited for general clinical practice.

Use of kurtosis for locating deep blood vessels in raw speckle imaging using a homogeneity representation.

Visualization of deep blood vessels in speckle images is an important task as it is used to analyze the dynamics of the blood flow and the health status of biological tissue. Laser speckle imaging is a wide-field optical technique to measure relative blood flow speed based on the local speckle contrast analysis. However, it has been reported that this technique is limited to certain deep blood vessels (about ? = 300 ?? ? m ) because of the high scattering of the sample; beyond this depth, the quality of the vessel’s image decreases. The use of a representation based on homogeneity values, computed from the co-occurrence matrix, is proposed as it provides an improved vessel definition and its corresponding diameter. Moreover, a methodology is proposed for automatic blood vessel location based on the kurtosis analysis. Results were obtained from the different skin phantoms, showing that it is possible to identify the vessel region for different morphologies, even up to 900 ?? ? m in depth.

The use of kurtosis de-noising for EEG analysis of patients suffering from Alzheimer's disease.

The use of electroencephalograms (EEGs) to diagnose and analyses Alzheimer's disease (AD) has received much attention in recent years. The sample entropy (SE) has been widely applied to the diagnosis of AD. In our study, nine EEGs from 21 scalp electrodes in 3 AD patients and 9 EEGs from 3 age-matched controls are recorded. The calculations show that the kurtoses of the AD patients' EEG are positive and much higher than that of the controls. This finding encourages us to introduce a kurtosis-based de-noising method. The 21-electrode EEG is first decomposed using independent component analysis (ICA), and second sort them using their kurtoses in ascending order. Finally, the subspace of EEG signal using back projection of only the last five components is reconstructed. SE will be calculated after the above de-noising preprocess. The classifications show that this method can significantly improve the accuracy of SE-based diagnosis. The kurtosis analysis of EEG may contribute to increasing the understanding of brain dysfunction in AD in a statistical way.

Breast Cancer: Diffusion Kurtosis MR Imaging-Diagnostic Accuracy and Correlation with Clinical-Pathologic Factors.

To assess diagnostic accuracy with diffusion kurtosis imaging (DKI) in patients with breast lesions and to evaluate the potential association between DKI-derived parameters and breast cancer clinical-pathologic factors. Institutional review board approval and written informed consent were obtained. Data from 97 patients (mean age ± standard deviation, 45.7 years ± 13.1; range, 19-70 years) with 98 lesions (57 malignant and 41 benign) who were treated between January 2014 and April 2014 were retrospectively analyzed. DKI (with b values of 0-2800 sec/mm(2)) and conventional diffusion-weighted imaging data were acquired. Kurtosis and diffusion coefficients from DKI and apparent diffusion coefficients from diffusion-weighted imaging were measured by two radiologists. Student t test, Wilcoxon signed-rank test, Jonckheere-Terpstra test, receiver operating characteristic curves, and Spearman correlation were used for statistical analysis. Kurtosis coefficients were significantly higher in the malignant lesions than in the benign lesions (1.05 ± 0.22 vs 0.65 ± 0.11, respectively; P < .0001). Diffusivity and apparent diffusion coefficients in the malignant lesions were significantly lower than those in the benign lesions (1.13 ± 0.27 vs 1.97 ± 0.33 and 1.02 ± 0.18 vs 1.48 ± 0.33, respectively; P < .0001). Significantly higher specificity for differentiation of malignant from benign lesions was shown with the use of kurtosis and diffusivity coefficients than with the use of apparent diffusion coefficients (83% [34 of 41] and 83% [34 of 41] vs 76% [31 of 41], respectively; P < .0001) with equal sensitivity (95% [54 of 57]). In patients with invasive breast cancer, kurtosis was positively correlated with tumor histologic grade (r = 0.75) and expression of the Ki-67 protein (r = 0.55). Diffusivity was negatively correlated with tumor histologic grades (r = -0.44) and Ki-67 expression (r = -0.46). DKI showed higher specificity than did conventional diffusion-weighted imaging for assessment of benign and malignant breast lesions. Patients with grade 3 breast cancer or tumors with high expression of Ki-67 were associated with higher kurtosis and lower diffusivity coefficients; however, this association must be confirmed in prospective studies.

L‐moments skewness and kurtosis as measures of regional convergence and cohesion

The paper deals with the statistical modeling of convergence and cohesion over time with the use of kurtosis, skewness and L‐moments. Changes in the shape of the distribution related to the spatial allocation of socio‐economic phenomena are considered as an evidence of global shift, divergence or convergence. Cross‐sectional time‐series statistical modeling of variables of interest is to overpass the minors of econometric theoretical models of convergence and cohesion determinants. L‐moments perform much more stable and interpretable than classical measures. Empirical evidence of panel data proves that one pure pattern (global shift, polarization or cohesion) rarely exists and joint analysis is required.

Analysis of Kurtosis-Based LOS/NLOS Identification Using Indoor MIMO Channel Measurement

The location of a mobile station (MS) can be estimated from distance measures between an MS and several base stations (BSs). However, distance measure accuracy is degraded due to the complicated indoor environment, particularly non line-of-sight (NLOS) propagation. To improve the accuracy of wireless localization, knowledge of whether the BS-MS path is line-of-sight (LOS) or NLOS may be of significant importance. Several papers have proposed the use of kurtosis for NLOS identification in ultrawideband systems. In this paper, we investigate the kurtosis of different channel impulse response (CIR) forms and explore the potential of kurtosis for LOS/NLOS identification with two sets of bandwidth and number of frequency tap configurations in terms of simulations. A statistical analysis of kurtosis is also conducted with an extensive set of multiple-input-multiple-output (MIMO) channel measurement data collected at Aalto University, Finland. Both simulation and measurement results indicate that using decibels of CIR amplitude in kurtosis calculation provides consistent information about the LOS/NLOS condition regardless of system parameters. The results also show that average kurtosis over MIMO channels, when available, gives a better indication of LOS/NLOS conditions.

Flow Cytometric Assessment of Erythrocyte Shape through Analysis of FSC Histograms: Use of Kurtosis and Implications for Longitudinal Evaluation

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 broad range of FSC distributions. Moreover, the possibility of longitudinal evaluation of erythrocyte sphericity is studied. Change of erythrocyte sphericity of 10 healthy subjects was induced by variation of buffer osmolarity to validate applicability of sphericity measures. Agreement between the sphericity indicators was then studied in samples from 20 healthy donors taken at three time points, which were processed through density gradient centrifugation and incubated with FITC-labelled antibodies to induce a broad variation of erythrocyte form (1086 samples). SphI, PCD and kurtosis of FSC distribution were calculated. Correlation of the respective measures, standard error of measurement (SEM) and r ratio (intra- to interindividual variance) were determined to illustrate agreement between the sphericity indicators. In the first study part, all sphericity indicators illustrated change of erythrocyte shape as induced by osmolarity variation. In the second part, correlation between kurtosis and SphI was −0.97 and correlation between kurtosis and PCD was 0.58 (p<0.05). In isotype control samples, correlation between kurtosis and SphI was −0.98 and correlation between kurtosis and PCD was 0.48 (p<0.05). In these samples, mean kurtosis was −0.80 (SEM 0.03), mean SphI was 2.19 (SEM 0.04) and mean PCD was −0.31 (SEM 0.02). r ratios of all measures of sphericity were <0.6. Our results show that kurtosis is closely correlated with SphI in a broad range of erythrocyte FSC distributions. Moreover, all measures of sphericity feature r ratios <0.6, highlighting that erythrocyte sphericity appears as a feasible parameter for individual longitudinal data monitoring.

Amplitude of Probability Density Function (APDF) of Vibration Response as a Robust Tool for Gearbox Diagnosis

Abstract: A ‘Go’ or ‘No Go’ assessment is a safety requirement for quick and robust estimation of the condition of gearboxes used in helicopters and other critical machines. A range of vibration‐based condition indicators (CIs) has been developed to meet this requirement. CIs are compared automatically with pre‐set threshold values representing a healthy system, so that the health of the gearbox can be assessed and diagnosis made where necessary. The use of kurtosis of the residual signal of the measured vibration data, computed as part of the ‘FM4’ method, is widespread, because it is accepted as a good and reliable indicator. However, it has been observed in some cases that FM4 may not show a continually increasing trend with the propagation of a fault. This behaviour may lead to improper assessment of the severity of the fault. Hence, a new CI, based on the deviation in the normal probability density function (PDF) of the measured vibration data, is suggested which demonstrates an increasing trend that is more robustly and monotonically correlated with the fault propagation.

Non-Gaussianity in single-particle tracking: Use of kurtosis to learn the characteristics of a cage-type potential

Nonlinear interaction of membrane proteins with cytoskeleton and membrane leads to non-Gaussian structure of their displacement probability distribution. We propose a statistical analysis technique for learning the characteristics of the nonlinear potential from the time dependence of the cumulants of the displacement distribution. The efficiency of the approach is demonstrated on the analysis of the kurtosis of the displacement distribution of the particle traveling on a membrane in a cage-type potential. Results of numerical simulations are supported by analytical predictions. We show that the approach allows robust identification of some characteristics of the potential for the much lower temporal resolution compared with the mean-square displacement analysis and we demonstrate robustness to experimental errors in determining the particle positions.

Non-Gaussianity in Single Particle Tracking: Use of Kurtosis to Learn the Characteristics of a Cage-Type Potential

Nonlinear interaction of membrane proteins with cytoskeleton and membrane leads to non-Gaussian structure of their displacement probability distribution. We propose a statistical analysis technique for learning the characteristics of the nonlinear potential from the time dependence of the cumulants of the displacement distribution. The efficiency of the approach is demonstrated on the analysis of the kurtosis of the displacement distribution of the particle traveling on a membrane in a cage-type potential. Results of numerical simulations are supported by analytical predictions. We show that the approach allows robust identification of some characteristics of the potential for the much lower temporal resolution compared with the mean-square displacement analysis and we demonstrate robustness to experimental errors in determining the particle positions.

Analysis of RFI Issue Using the CAROLS L-Band Experiment

In this paper, different methods are proposed for the detection and mitigation of the undesirable effects of radio-frequency interference (RFI) in microwave radiometry. The first of these makes use of kurtosis to detect the presence of non-Gaussian signals, whereas the second imposes a threshold on the standard deviation of brightness temperatures in order to distinguish natural-emission variations from RFI. Finally, the third approach is based on the use of a threshold applied to the third and fourth Stokes parameters. All these methods have been applied and tested, with the cooperative airborne radiometer for ocean and land studies radiometer operating in the L-band, on the data acquired during airborne campaigns made in the spring of 2009 over the southwest of France. The performance of each approach, or of two combined approaches, is analyzed with our database. We thus show that the kurtosis method is well suited to detect pulsed RFI, whereas the method based on the second moment of brightness temperatures seems to be better suited to detect continuous-wave RFI in airborne brightness-temperature measurements.

Semi-blind source extraction of atrial activity by combining statistical and spectral features

Atrial fibrillation is the most common human arrhythmia. During atrial fibrillation episodes, the surface electrocardiogram contains the linear superposition of the atrial and ventricular rhythms in addition to other non-cardiac artifacts. Since these signals can be considered statistically independent, a Blind Source Separation (BSS) approach fits the problem properly. The signal that contains useful clinical information is the atrial one. We present a solution that focuses on the extraction of the atrial activity, enforcing simultaneously the statistical and temporal properties of the atrial signal. In addition, we propose the use of kurtosis as a parameter to measure the quality of the extraction. The algorithm is applied successfully to synthetic and real data. It improves the extraction of the atrial signal in comparison to other BSS methods, recovers only the interesting atrial rhythm using the information contained in all the leads and reduces the computational cost. The results obtained are shown to be highly satisfactory, with an average of 53.9% of spectral concentration, -0.04 of kurtosis value, 2.98 of ventricular residua and 4.77% of significant QRS residua over a database of thirty patients.

Burst mode synchronization of QPSK on AWGN channels using kurtosis

This paper explores the use of kurtosis in synchronizing with a QPSK burst transmission. The start and end of the burst are a priori unknown and are detected without the use of pilot signals. After frame level synchronization, signal level synchronization is performed. The symbol timing, carrier frequency and carrier phase are recovered without the assistance of known symbols or synchronization words in the data stream, i.e. totally blind synchronization. The performance of frame, symbol and carrier synchronization algorithms is evaluated through computer simulations.

The Statistical Meaning of Kurtosis and Its New Application to Identification of Persons Based on Seismic Signals.

This paper presents a new algorithm making use of kurtosis, which is a statistical parameter, to distinguish the seismic signal generated by a person's footsteps from other signals. It is adaptive to any environment and needs no machine study or training. As persons or other targets moving on the ground generate continuous signals in the form of seismic waves, we can separate different targets based on the seismic waves they generate. The parameter of kurtosis is sensitive to impulsive signals, so it's much more sensitive to the signal generated by person footsteps than other signals generated by vehicles, winds, noise, etc. The parameter of kurtosis is usually employed in the financial analysis, but rarely used in other fields. In this paper, we make use of kurtosis to distinguish person from other targets based on its different sensitivity to different signals. Simulation and application results show that this algorithm is very effective in distinguishing person from other targets.

Enhanced automatic artifact detection based on independent component analysis and Renyi’s entropy

Artifacts are disturbances that may occur during signal acquisition and may affect their processing. The aim of this paper is to propose a technique for automatically detecting artifacts from the electroencephalographic (EEG) recordings. In particular, a technique based on both Independent Component Analysis (ICA) to extract artifactual signals and on Renyi's entropy to automatically detect them is presented. This technique is compared to the widely known approach based on ICA and the joint use of kurtosis and Shannon's entropy. The novel processing technique is shown to detect on average 92.6% of the artifactual signals against the average 68.7% of the previous technique on the studied available database. Moreover, Renyi's entropy is shown to be able to detect muscle and very low frequency activity as well as to discriminate them from other kinds of artifacts. In order to achieve an efficient rejection of the artifacts while minimizing the information loss, future efforts will be devoted to the improvement of blind artifact separation from EEG in order to ensure a very efficient isolation of the artifactual activity from any signals deriving from other brain tasks.

On the meaning and use of kurtosis.

For symmetric unimodal distributions, positive kurtosis indicates heavy tails and peakedness relative to the normal distribution, whereas negative kurtosis indicates light tails and flatness. Many textbooks, however, describe or illustrate kurtosis incompletely or incorrectly. In this article, kurtosis is illustrated with well-known distributions, and aspects of its interpretation and misinterpretation are discussed. The role of kurtosis in testing univariate and multivariate normality; as a measure of departures from normality; in issues of robustness, outliers, and bimodality; in generalized tests and estimators, as well as limitations of and alternatives to the kurtosis measure [32, are discussed.

On the meaning and use of kurtosis.

On the meaning and use of kurtosis.

Measuring Intracultural Diversity: A Comment on Smith's Use of Kurtosis

Measuring Intracultural Diversity: A Comment on Smith's Use of Kurtosis