Empirical Wavelet Transform

Gilles, Jérôme

doi:10.1109/tsp.2013.2265222

Cited by 1,741 publications

(889 citation statements)

References 16 publications

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“…This idea is similar in spirit to the definition of the degree of nonlinearity introduced by Huang et al in [20]. They used the deviation of the instantaneous frequency to quantify the degree of nonlinearity, 9) where IF stands for the instantaneous frequency, IF z stands for the constant mean frequency over one wave cycle and · denotes the average over one wave cycle. Actually, the deviation of the instantaneous frequency is closely related to the Fourier coefficients of the shape function.…”

Section: Example 52 (Duffing Equation)mentioning

confidence: 99%

Extracting a shape function for a signal with intra-wave frequency modulation

Hou

Shi

2016

Phil. Trans. R. Soc. A.

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Section: Example 52 (Duffing Equation)mentioning

confidence: 99%

Extracting a shape function for a signal with intra-wave frequency modulation

Hou

Shi

2016

Phil. Trans. R. Soc. A.

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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%

“…We now proceed to solve the constrained, sparsity promoting n-D VMD functional (27) through its augmented Lagrangian (29). Consider the following saddle point problem:…”

Section: N-d-tv-vmd Minimizationmentioning

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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“…Where an IMF is defined as an amplitude modulated-frequency modulated function (AM-FM): [10] proposed the method based on the theoretical framework of wavelet analysis. According to the Fourier spectral characteristics，the signal adaptively selects a group of wavelet filter banks to extract the signal of different AM-FM components.…”

Section: Empirical Wavelet Transformmentioning

confidence: 99%

“…In view of the shortcomings of EMD, Gilles [10] combined with EMD adaptive and wavelet analysis of the theoretical framework, proposed a new adaptive signal processing method, the empirical wavelet transform (EWT). In this paper, the EWT is introduced into the EEG feature extraction of motor imagery.…”

Section: Introductionmentioning

confidence: 99%

EEG Recognition of Motor Imagery Based on EWT in Driving Assistance

Shan¹,

Wang²,

He³

et al. 2017

Advances in Computer Science Research

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Abstract. Electroencephalogram (EEG) feature extraction is one of the key techniques for BrainComputer Interface (BCI) in driving assistance. In this paper, empirical wavelet transform (EWT) is introduced for EEG feature extraction, and then a new EEG recognition method based on EWT is proposed. In the proposed method, the EEG features of the left arm flexion and extension motor imagery mode were first extracted via EWT and compared with those extracted by the empirical mode decomposition (EMD), and then the extracted features were classified by support vector machine (SVM). The results show that the EWT method significantly outperforms the EMD method, which can effectively decompose the intrinsic modes of EEG, and it presents several merits of fewer modes, no false mode and low computation cost. Therefore, the EWT method can effectively extract the local transient features of EEG and realize the effective classification through SVM, thus providing the chance of driving assistance through the arm flexion and extension imagination.

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Empirical Wavelet Transform

Cited by 1,741 publications

References 16 publications

Extracting a shape function for a signal with intra-wave frequency modulation

Extracting a shape function for a signal with intra-wave frequency modulation

Two-Dimensional Compact Variational Mode Decomposition

EEG Recognition of Motor Imagery Based on EWT in Driving Assistance

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