The dual-tree complex wavelet transform

By Ivan W. Selesnick, Richard Baraniuk, N. Kingsbury. 2005

2,598 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Media Technology, Signal Processing

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Citations in the corpus

End-to-end Optimized Image Compression (2016, background): “…representations – e.g., the steerable pyramid (Simoncelli, Freeman, et al., 1992), curvelets (Cand ` es and Donoho, 2002), and dual-tree complex wavelets (Selesnick, Baraniuk, and Kingsbury, 2005) – the ﬁlters in this ﬁrst stage are localized and oriented and the representation is overcomplete .”
ALL Snow Removed: Single Image Desnowing Algorithm Using Hierarchical Dual-tree Complex Wavelet Representation and Contradict Channel Loss (2021, methodology): “Therefore, in this paper, we propose a novel snow removal architecture which can handle the complicated snow scenes by embedding the hierarchical dual-tree complex wavelet transform [9] to the network.”
Tomographic inversion using L1-norm regularization of wavelet coefficients (2006, methodology): “This particular method of thresholding is borrowed from image denoising where it is found to make a big difference in avoiding artefacts (van Spaendonck et al. 2003; Selesnick et al. 2005; Guleryuz 2006).”
Wave atoms and sparsity of oscillatory patterns (2007, methodology): “Note that considering Hilbert-transformed bases, and performing the combination (12) in 2D, are both well-known tricks in wavelet theory: for instance, they are part of the definition of the 2D dual-tree complex wavelet transform (CWT, see [29] for a review), as well as the definition of brushlets [”
The continuous wavelet transform : a primer (2011, positive): “The many useful features of analytic wavelets are covered in more depth by Selesnick, Baraniuk and Kinsbury [42]; see also Olhede and Walden [34] and Lilly and Olhede [31].”
Groundwater level prediction in arid areas using wavelet analysis and Gaussian process regression (2021, background): “Accordingly, any finite energy analog signal x(t) can be separated in terms of wavelets and scale functions by Equation (11) (Selesnick et al., 2005): x(t) = ∞∑ n=−∞ c(n)∅(t − n) + ∞∑ j=0 ∞∑ n=−∞ d(j, n)2 ( j 2 ) ψ(2jt − n) (11) where ψ(t) is the mother wavelet function, j is the scale factor, and…”
Intermittent process analysis with scattering moments (2013, methodology): “All numerical computations in the paper are performed with the compactly supported complex wavelets of Selesnick [34], whose real and imaginary parts have 4 vanishing moments and are nearly Hilbert transform pairs.”
Dictionaries for Sparse Representation Modeling (2010, background): “The complex wavelet transform [65], [66] is an oriented and near-translation-invariant high-dimensional extension of the wavelet transform, achieved through the utilization of two mother wavelets satisfying a specific relationship between them.”
Wavelets for fault diagnosis of rotary machines: A review with applications (2014, background): “growth in the theory and practice of wavelets [1–10], and many publications have been seen, describing advance-”
Higher-Order Properties of Analytic Wavelets (2008, background): “ the analysis of oscillatory signals. These results for continuous analytic wavelets could also contribute to an improved understanding of the behavior of discrete analytic wavelets, such as those of [5]. One member of the generalized Morse wavelet family was found to have zero asymmetry in the time”
Wavelet-based EEG processing for computer-aided seizure detection and epilepsy diagnosis. (2015, positive): “Employing nonlinear dynamics and chaos theory researchers have extracted various nonlinear features such as entropies [24], energy [25], correlation dimension [47], fractal dimension [47,27], Lyapunov exponent [47], Higher Order Spectra (HOS) [28,25] from both detailed and approximate coefficients o”
Remote Sensing Image Classification: No Features, No Clustering (2015, methodology): “Log-Gabor and log-DTCWT have similar performances next to BoW, followed by frFT that performs better than all the remaining methods.”