Empirical Wavelet Transforms
The Empirical Wavelet Transform (EWT) aims to decompose a signal or an image on wavelet tight frames which are built adaptively. In 1D, the procedure consists in detecting the supports of some "modes" in the Fourier spectrum and then using these supports to build Littlewood-Paley type wavelets. In 2D, based on the same principle, we propose empirical versions of the tensor wavelet transform, a 2D Littlewood-Paley transform, the Ridgelet transform and the Curvelet transform. The advantage of this empirical approach is to keep together some information that otherwise would be split in the case of dyadic filters. The provided Matlab toolbox performs all these transforms.
You can refer to these papers to learn more about these wavelets: 1D and 2D
Feel free to contact me if you need some help, report a bug, or any other suggestions.
Some examples of EWT coefficients in 1D and 2D:
- 1D EWT on an Electrocardiogram signal:
- 2D Empirical Curvelet Transform - II:
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ECG signal |
EWT components |
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Input image |
Detected Fourier supports |
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Curvelet coefficients |
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The Empirical Wavelet Transform Matlab Toolbox Archive
The current version is- v3.0 (July 21, 2015) bug fixes in the curvelet transform (crash due to odd image sizes + wrong high frequency filters for option 2) + new curvelet transform option 3 (scales per angular sectors)
- v2.0 (April 24, 2014) ftc algorithm removed + bugs fixes + new functions
- v1.2 (June 12, 2013) ftc_seg.c fixed and can now be compiled on Windows
- v1.0 (June 10, 2013)