2D Empirical Transforms. Wavelets, Ridgelets, and Curvelets Revisited

Gilles, Jérôme; Tran, Giang; Osher, Stanley

doi:10.1137/130923774

Cited by 148 publications

(97 citation statements)

References 21 publications

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“…Subsequently, the instantaneous amplitude ( ) ( = 1,…, ) is obtained using Eq. (14). The feature matrix is therefore constructed from the instantaneous amplitude ( ) , and the fault feature vector ( ( ) = , , … , ) by applying the SVD.…”

Section: Singular Value Decomposition On the Hewtmentioning

confidence: 99%

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Gear fault feature extraction and classification of singular value decomposition based on Hilbert empirical wavelet transform

Rahmoune¹,

Merainani²,

Benazzouz³

et al. 2018

J. vibroeng.

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Abstract. Vibration signal of gearbox systems carries the important dynamic information for fault diagnosis. However, vibration signals always show non stationary behavior and overwhelmed by a large amount of noise make this task challenging in many cases. Thus, a new fault diagnosis method combining the Hilbert empirical wavelet transform (HEWT), the singular value decomposition (SVD) and Elman neural network is proposed in this paper. Vibration signals of normal gear, gear with tooth root crack, gear with chipped tooth in width, gear with chipped tooth in length, gear with missing tooth and gear with general surface wear are collected in different speed and load conditions. HEWT, a new self-adaptive time-frequency analysis, was applied to the vibration signals to obtain the instantaneous amplitude matrices. Singular value vectors, as the fault feature vectors were then acquired by applying the SVD. Last, the Elman neural network was used for automatic gearbox fault identification and classification. Through experimental results, it was concluded that the proposed method can accurately extract and classify the gear fault features under variable conditions. Moreover, the performance of the proposed HEWT-SVD method has an advantage over that of Hilbert-Huang transform (HHT)-SVD, local mean decomposition (LMD)-SVD or wavelet packet transform (WPT)-PCA for feature extraction.

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Section: Singular Value Decomposition On the Hewtmentioning

confidence: 99%

“…It may not only supply richer information but also supply more promise frequency localization information. However, the WPT is not self-adaptive, it has prescribed dyadic subdivision in time and frequency which may leads to severe damage in identifying transient vibration features that lie in transient areas of dyadic packets [13,14].…”

Section: Introductionmentioning

confidence: 99%

Gear fault feature extraction and classification of singular value decomposition based on Hilbert empirical wavelet transform

Rahmoune¹,

Merainani²,

Benazzouz³

et al. 2018

J. vibroeng.

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“…Adaptivity and tuned sparsity concerns have been addressed through synchrosqueezed wavelet transforms [9,14,72,74], where unimportant wavelet coefficients are removed by thresholding based on energy content. In pursuit of the same goal, the 2D empirical wavelet transform (EWT) [29,30] decomposes an image by creating a more adaptive wavelet basis.…”

Section: Recent and Related Workmentioning

confidence: 99%

“…These results should be compared against the exhaustive 2D empirical wavelet transform results in [30].…”

Section: Synthetic Overlapping Texture Decompositionmentioning

confidence: 99%

Two-Dimensional Compact Variational Mode Decomposition

et al. 2017

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Decomposing multidimensional signals, such as images, into spatially compact, potentially overlapping modes of essentially wavelike nature makes these components accessible for further downstream analysis. This decomposition enables space-frequency analysis, demodulation, estimation of local orientation, edge and corner detection, texture analysis, denoising, inpainting, or curvature estimation. Our model decomposes the input signal into modes with narrow Fourier bandwidth; to cope with sharp region boundaries, incompatible with narrow bandwidth, we introduce binary support functions that act as masks on the narrow-band mode for image recomposition. L 1 and TV terms promote sparsity and spatial compactness. Constraining the support functions to partitions of the signal domain, we effectively get an image segmentation model based on spectral homogeneity. By coupling several submodes together with a single support function, we are able to decompose an image into several crystal grains. Our efficient algorithm is based on variable splitting and alternate direction optimization; we employ Merriman-Bence-Osher-like threshold dynamics to handle efficiently the motion by mean curvature of the support function boundaries under the sparsity promoting terms. The versatility and effectiveness of our proposed model is demonstrated on a broad variety of example images from different modalities. These demonstrations include the decomposition of images into overlapping modes with smooth or sharp boundaries, segmentation of images of crystal grains, and inpainting of damaged image regions through artifact detection.

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“…As illustrated in the paper, Gilles designed an appropriate wavelet filter bank adapted to the processed signal. The EWT has shown its advantage in image processing and other applications have been explored [12].…”

Section: Empirical Wavelet Transformmentioning

confidence: 99%

Instantaneous pitch estimation based on empirical wavelet transform

Xue

Zhu

2014

2014 19th International Conference on Digital Signal Processing

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In this paper, a novel approach is proposed specially for capturing the instantaneous pitch that may reveals some innate character of the speech. Firstly, the original signal is decomposed into several modes with empirical wavelet transform, and then the mode containing the pitch is picked out, finally the instantaneous pitch is calculated via Hilbert transform. Intensive evaluation and direct comparisons with existing method are conducted with the standard Chinese and English speech database, all showing the effectiveness of the proposed method in acquiring the instantaneous pitch.

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2D Empirical Transforms. Wavelets, Ridgelets, and Curvelets Revisited

Cited by 148 publications

References 21 publications

Gear fault feature extraction and classification of singular value decomposition based on Hilbert empirical wavelet transform

Gear fault feature extraction and classification of singular value decomposition based on Hilbert empirical wavelet transform

Two-Dimensional Compact Variational Mode Decomposition

Instantaneous pitch estimation based on empirical wavelet transform

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