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D Wang - One of the best experts on this subject based on the ideXlab platform.
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some further thoughts about spectral Kurtosis spectral l2 l1 norm spectral smoothness index and spectral gini index for characterizing repetitive transients
Mechanical Systems and Signal Processing, 2018Co-Authors: D WangAbstract:Abstract Thanks to the great efforts made by Antoni (Mech. Syst. Signal Pr. 20 (2006) 282–307), spectral Kurtosis has been recognized as a milestone to characterize repetitive transients, especially bearing fault signals caused by bearing defects. The basic idea of spectral Kurtosis is to use Kurtosis to quantify an analytic bearing fault signal constructed from band-pass filtering and Hilbert transform. In our previous study (Mech. Syst. Signal Pr. 104 (2018) 290–293), we mathematically showed that spectral Kurtosis can be decomposed into squared envelope and squared L2/L1 norm. Based on this finding, we defined spectral L2/L1 norm and then extended spectral L2/L1 norm to spectral Lp/Lq norm. Moreover, when p = 1 and q = 0, we mathematically showed that spectral L1/L0 norm is the reciprocal of spectral smoothness index. Here, being similar with the functionality of Kurtosis, smoothness index introduced by Bozchalooi and Liang (J. Sound Vib., 308 (2007) 246–267) has been recognized as another attractive and important statistical parameter to characterize repetitive transients. Hence, the mathematical connection between spectral Kurtosis and the reciprocal of spectral smoothness index was well established. Further, we derived an analytical expression of spectral Lp/Lq norm when complex Gaussian noises were considered as an input to spectral Lp/Lq norm. Consequently, spectral Lp/Lq norm was able to be normalized by the analytical expression. In this paper, we give some further thoughts about spectral Kurtosis, spectral L2/L1 norm, the reciprocal of spectral smoothness index and spectral Gini index for characterizing repetitive transients. Firstly, we formulate extraction of repetitive transients as maximization of spectral Lp/Lq norm. Most existing fault detection algorithms derived from spectral Kurtosis can be naturally extended to maximize spectral Lp/Lq norm. Secondly, we formally define spectral Gini index and then mathematically clarify its relationship with spectral L2/L1 norm. Moreover, we calculate spectral Gini index for complex Gaussian noises so as to normalize and redefine spectral Gini index. Thirdly, the relationship between spectral Kurtosis, spectral L2/L1 norm, spectral Lp/Lq norm, the reciprocal of spectral smoothness index and spectral Gini index for characterizing repetitive transients is revealed. Finally, we mathematically show that each of spectral Kurtosis, spectral L2/L1 norm, the reciprocal of spectral smoothness index and spectral Gini index is a monotonically increasing function of the maximum of squared envelope, which indicates that spectral Kurtosis, spectral L2/L1 norm, the reciprocal of spectral smoothness index and spectral Gini index are affected by outliers. Based on this finding, experimental comparisons are conducted to show that the reciprocal of spectral smoothness index and spectral Gini index are less sensitive to outliers and they are more preferable to be used in most existing algorithms instead of maximization of spectral Kurtosis for extraction of repetitive transients, especially bearing fault signals.
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spectral l2 l1 norm a new perspective for spectral Kurtosis for characterizing non stationary signals
Mechanical Systems and Signal Processing, 2018Co-Authors: D WangAbstract:Thanks to the great efforts made by Antoni (2006), spectral Kurtosis has been recognized as a milestone for characterizing non-stationary signals, especially bearing fault signals. The main idea of spectral Kurtosis is to use the fourth standardized moment, namely Kurtosis, as a function of spectral frequency so as to indicate how repetitive transients caused by a bearing defect vary with frequency. Moreover, spectral Kurtosis is defined based on an analytic bearing fault signal constructed from either a complex filter or Hilbert transform. On the other hand, another attractive work was reported by Borghesani et al. (2014) to mathematically reveal the relationship between the Kurtosis of an analytical bearing fault signal and the square of the squared envelope spectrum of the analytical bearing fault signal for explaining spectral correlation for quantification of bearing fault signals. More interestingly, it was discovered that the sum of peaks at cyclic frequencies in the square of the squared envelope spectrum corresponds to the raw 4th order moment. Inspired by the aforementioned works, in this paper, we mathematically show that: (1) spectral Kurtosis can be decomposed into squared envelope and squared L2 / L1 norm so that spectral Kurtosis can be explained as spectral squared L2 / L1 norm; (2) spectral L2 / L1 norm is formally defined for characterizing bearing fault signals and its two geometrical explanations are made; (3) spectral L2 / L1 norm is proportional to the square root of the sum of peaks at cyclic frequencies in the square of the squared envelope spectrum; (4) some extensions of spectral L2 / L1 norm for characterizing bearing fault signals are pointed out.
Ed X. Wu - One of the best experts on this subject based on the ideXlab platform.
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Diffusion Kurtosis imaging with tract-based spatial statistics reveals white matter alterations in preschool children
2012 Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2012Co-Authors: Xianjun Li, Ed X. Wu, Kevin C. Chan, Abby Ding, Jian YangAbstract:Diffusion Kurtosis imaging (DKI), an extension of diffusion tensor imaging (DTI), provides a practical method to describe non-Gaussian water diffusion in neural tissues. The sensitivity of DKI to detect the subtle changes in several chosen brain structures has been studied. However, intuitive and holistic methods to validate the merits of DKI remain to be explored. In this paper, tract-based spatial statistics (TBSS) was used to demonstrate white matter alterations in both DKI and DTI parameters in preschool children (1-6 years; n=10). Correlation analysis was also performed in multiple regions of interest (ROIs). Fractional anisotropy, mean Kurtosis, axial Kurtosis and radial Kurtosis increased with age, while mean diffusivity and radial diffusivity decreased significantly with age. Fractional anisotropy of Kurtosis and axial diffusivity were found to be less sensitive to the changes with age. These preliminary findings indicated that TBSS could be used to detect subtle changes of DKI parameters on the white matter tract. Kurtosis parameters, except fractional anisotropy of Kurtosis, demonstrated higher sensitivity than DTI parameters. TBSS may be a convenient method to yield higher sensitivity of DKI.
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towards better mr characterization of neural tissues using directional diffusion Kurtosis analysis
NeuroImage, 2008Co-Authors: Matthew M. Cheung, Liqun Qi, Ed X. WuAbstract:Abstract MR diffusion Kurtosis imaging (DKI) was proposed recently to study the deviation of water diffusion from Gaussian distribution. Mean Kurtosis, the directionally averaged Kurtosis, has been shown to be useful in assessing pathophysiological changes, thus yielding another dimension of information to characterize water diffusion in biological tissues. In this study, orthogonal transformation of the 4th order diffusion Kurtosis tensor was introduced to compute the diffusion kurtoses along the three eigenvector directions of the 2nd order diffusion tensor. Such axial (K//) and radial (K┴) kurtoses measured the kurtoses along the directions parallel and perpendicular, respectively, to the principal diffusion direction. DKI experiments were performed in normal adult (N = 7) and formalin-fixed rat brains (N = 5). DKI estimates were documented for various white matter (WM) and gray matter (GM) tissues, and compared with the conventional diffusion tensor estimates. The results showed that Kurtosis estimates revealed different information for tissue characterization. For example, K// and K┴ under formalin fixation condition exhibited large and moderate increases in WM while they showed little change in GM despite the overall dramatic decrease of axial and radial diffusivities in both WM and GM. These findings indicate that directional Kurtosis analysis can provide additional microstructural information in characterizing neural tissues.
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Advanced MR diffusion characterization of neural tissue using directional diffusion Kurtosis analysis
2008 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2008Co-Authors: Matthew M. Cheung, Liqun Qi, Ed X. WuAbstract:MR Diffusion Kurtosis imaging (DKI) was proposed recently to study the deviation of water diffusion from Gaussian distribution. Mean Kurtosis (MK), directionally averaged Kurtosis, has been shown to be useful in assessing pathophysilogical changes. However, MK is not sensitive to Kurtosis change occurring along a specific direction. Therefore, orthogonal transformation of the 4th order Kurtosis tensor was introduced in the current study to compute kurtoses along the 3 eigenvector directions of the 2nd order diffusion tensor. Such axial (K∥) and radial (K⊥) kurtoses measured the kurtoses along the directions parallel and perpendicular, respectively, to the principal diffusion direction. DKI experiments were performed in normal adult and formalin-fixed rat brain, and developmental brains. The results showed that directional Kurtosis analysis revealed different information for tissue characterization.
Zhi Ding - One of the best experts on this subject based on the ideXlab platform.
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Stationary points of a Kurtosis maximization algorithm for blind signal separation and antenna beamforming
IEEE Transactions on Signal Processing, 2000Co-Authors: Zhi DingAbstract:Blind source separation has been the subject of extensive research. In particular, blind antenna beamforming is an effective signal separation technique for communication systems to combat co-channel interference. Among many potential candidate approaches, the simple constant modulus algorithm (CMA) has been widely studied and used in practice. The CMA is designed to capture and separate signals with negative Kurtosis. However, when some signals have positive kurtoses, the CMA is unable to capture and separate these sources. We show that the Kurtosis maximum algorithm (KMA) can capture signals with both the positive and negative kurtoses. Its global convergence proof is presented for noiseless systems with multiple signals sources and for systems with a single source and zero-Kurtosis (such as Gaussian) additive noise
Yang Ji - One of the best experts on this subject based on the ideXlab platform.
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in vivo microscopic diffusional Kurtosis imaging with symmetrized double diffusion encoding epi
Magnetic Resonance in Medicine, 2019Co-Authors: Dongshuang Lu, Yang Ji, Iris Yuwen Zhou, Jeffrey Paulsen, Patrick Machado, Yiqiao SongAbstract:PURPOSE: Diffusional Kurtosis imaging (DKI) measures the deviation of the displacement probability from a normal distribution, complementing the data commonly acquired by diffusion MRI. It is important to elucidate the sources of Kurtosis contrast, particularly in biological tissues where microscopic Kurtosis (intrinsic Kurtosis) and diffusional heterogeneity may co-exist. METHODS: We have developed a technique for microscopic Kurtosis MRI, dubbed microscopic diffusional Kurtosis imaging (µDKI), using a symmetrized double diffusion encoding (s-DDE) EPI sequence. We compared this newly developed µDKI to conventional DKI methods in both a triple compartment phantom and in vivo. RESULTS: Our results showed that whereas conventional DKI and µDKI provided similar measurements in a compartment of monosphere beads, Kurtosis measured by µDKI was significantly less than that measured by conventional DKI in a compartment of mixed Gaussian pools. For in vivo brain imaging, µDKI showed small yet significantly lower Kurtosis measurement in regions of the cortex, CSF, and internal capsule compared to the conventional DKI approach. CONCLUSIONS: Our study showed that µDKI is less susceptible than conventional DKI to sub-voxel diffusional heterogeneity. Our study also provided important preliminary demonstration of our technique in vivo, warranting future studies to investigate its diagnostic use in examining neurological disorders.
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journal club evaluation of diffusion Kurtosis imaging of stroke lesion with hemodynamic and metabolic mri in a rodent model of acute stroke
American Journal of Roentgenology, 2018Co-Authors: Dongshuang Lu, Yinghua Jiang, Yang Ji, Iris Yuwen Zhou, Emiri T Mandeville, Eng H Lo, Xiaoying WangAbstract:OBJECTIVE. Diffusion Kurtosis imaging (DKI) has emerged as a new acute stroke imaging approach, augmenting routine DWI. Although it has been shown that a diffusion lesion without Kurtosis abnormality is more likely to recover after reperfusion, whereas a Kurtosis lesion shows poor response, little is known about the underlying pathophysiologic profile of the Kurtosis lesion versus the Kurtosis lesion-diffusion lesion mismatch. MATERIALS AND METHODS. We performed multiparametric MRI, including arterial spin labeling, pH-sensitive amide proton transfer, and DKI, in a rodent model of acute stroke caused by embolic middle cerebral artery occlusion. Diffusion and Kurtosis lesions were semiautomatically segmented, and multiparametric MRI indexes were compared among the Kurtosis lesion, diffusion lesion, Kurtosis lesion-diffusion lesion mismatch, and the contralateral normal tissue area. RESULTS. We confirmed a significant difference between diffusion lesion and Kurtosis lesion volumes (mean [± SD] volume, 151 ±...
Xiangzeng Meng - One of the best experts on this subject based on the ideXlab platform.
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ICME - Kurtosis-based super-resolution algorithm
2009 IEEE International Conference on Multimedia and Expo, 2009Co-Authors: Jianping Qiao, Xiangzeng MengAbstract:A Kurtosis-based super-resolution image reconstruction algorithm is proposed in this paper. Firstly, we give the definition of the Kurtosis image and analyze its two properties: (i) the Kurtosis image is Gaussian noise invariant, and (ii) the absolute value of a Kurtosis image becomes smaller as the the image gets smoother. Then we build a constrained absolute local Kurtosis maximization function to estimate the high-resolution image by fusing multiple blurred low-resolution images corrupted by intensive white Gaussian noise. The Lagrange multiplier is used to solve the combinatorial optimization problem. Experimental results demonstrate that the proposed method is better than the conventional algorithms in terms of visual inspection and robustness, using both synthetic and real world examples under severe noise background. It has an improvement of 0.5 to 2.0 dB in PSNR over other approaches.
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Kurtosis-based super-resolution algorithm
2009 IEEE International Conference on Multimedia and Expo, 2009Co-Authors: Jianping Qiao, Xiangzeng MengAbstract:A Kurtosis-based super-resolution image reconstruction algorithm is proposed in this paper. Firstly, we give the definition of the Kurtosis image and analyze its two properties: (i) the Kurtosis image is Gaussian noise invariant, and (ii) the absolute value of a Kurtosis image becomes smaller as the the image gets smoother. Then we build a constrained absolute local Kurtosis maximization function to estimate the high-resolution image by fusing multiple blurred low-resolution images corrupted by intensive white Gaussian noise. The Lagrange multiplier is used to solve the combinatorial optimization problem. Experimental results demonstrate that the proposed method is better than the conventional algorithms in terms of visual inspection and robustness, using both synthetic and real world examples under severe noise background. It has an improvement of 0.5 to 2.0 dB in PSNR over other approaches.
