Journal ArticleDOI
Wavelet Transform With Tunable Q-Factor
TLDR
A discrete-time wavelet transform for which the Q-factor is easily specified and the transform can be tuned according to the oscillatory behavior of the signal to which it is applied, based on a real-valued scaling factor.Abstract:
This paper describes a discrete-time wavelet transform for which the Q-factor is easily specified. Hence, the transform can be tuned according to the oscillatory behavior of the signal to which it is applied. The transform is based on a real-valued scaling factor (dilation-factor) and is implemented using a perfect reconstruction over-sampled filter bank with real-valued sampling factors. Two forms of the transform are presented. The first form is defined for discrete-time signals defined on all of Z. The second form is defined for discrete-time signals of finite-length and can be implemented efficiently with FFTs. The transform is parameterized by its Q-factor and its oversampling rate (redundancy), with modest oversampling rates (e.g., three to four times overcomplete) being sufficient for the analysis/synthesis functions to be well localized.read more
Citations
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Journal ArticleDOI
Sparsity-optimized separation of body waves and ground-roll by constructing dictionaries using tunable Q-factor wavelet transforms with different Q-factors
Journal ArticleDOI
Machine learning approach for epileptic seizure detection using the tunable-Q wavelet transform based time–frequency features
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Wavelet-Based Sparse Representation for Helicopter Main Rotor Blade Radar Backscatter Signal Separation
TL;DR: In the proposed algorithm, a sparse signal representation is applied with the use of tunable Q wavelet transform to construct the dictionary, and basis pursuit denoising is used for the signal reconstruction of the component of interest.
Journal ArticleDOI
EEG analysis of Parkinson's disease using time-frequency analysis and deep learning
TL;DR: Wang et al. as discussed by the authors proposed two EEG analysis methods for diagnosis and monitoring of Parkinson's disease by combining time-frequency analysis with deep learning, tunable Q-factor wavelet transform with deep residual shrinkage network (TQWT-DRSN) and the wavelet packet transform with DRSN.
References
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Book
Ten lectures on wavelets
TL;DR: This paper presents a meta-analyses of the wavelet transforms of Coxeter’s inequality and its applications to multiresolutional analysis and orthonormal bases.
Journal ArticleDOI
Ten Lectures on Wavelets
TL;DR: In this article, the regularity of compactly supported wavelets and symmetry of wavelet bases are discussed. But the authors focus on the orthonormal bases of wavelets, rather than the continuous wavelet transform.
Journal ArticleDOI
Atomic Decomposition by Basis Pursuit
TL;DR: Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions.
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Fast Image Recovery Using Variable Splitting and Constrained Optimization
TL;DR: A new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective includes an l2 data-fidelity term and a nonsmooth regularizer is proposed.
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Calculation of a constant Q spectral transform
TL;DR: In this article, a constant Q transform with a constant ratio of center frequency to resolution has been proposed to obtain a constant pattern in the frequency domain for sounds with harmonic frequency components.