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The dual-tree complex wavelet transform
TLDR
Several methods for filter design are described for dual-tree CWT that demonstrates with relatively short filters, an effective invertible approximately analytic wavelet transform can indeed be implemented using the dual- tree approach. Expand
Introduction to Wavelets and Wavelet Transforms: A Primer
1. Introduction to Wavelets. 2. A Multiresolution Formulation of Wavelet Systems. 3. Filter Banks and the Discrete Wavelet Transform. 4. Bases, Orthogonal Bases, Biorthogonal Bases, Frames, TightExpand
Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency
TLDR
This work proposes new non-Gaussian bivariate distributions, and corresponding nonlinear threshold functions (shrinkage functions) are derived from the models using Bayesian estimation theory, but the new shrinkage functions do not assume the independence of wavelet coefficients. Expand
Bivariate shrinkage with local variance estimation
TLDR
This letter presents a locally adaptive denoising algorithm using the bivariate shrinkage function and is illustrated using both the orthogonal and dual tree complex wavelet transforms. Expand
Wavelet Transform With Tunable Q-Factor
  • I. Selesnick
  • Mathematics, Computer Science
  • IEEE Transactions on Signal Processing
  • 1 August 2011
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. Expand
The design of approximate Hilbert transform pairs of wavelet bases
  • I. Selesnick
  • Mathematics, Computer Science
  • IEEE Trans. Signal Process.
  • 1 May 2002
TLDR
Design procedures, based on spectral factorization, for the design of pairs of dyadic wavelet bases where the two wavelets form an approximate Hilbert transform pair are described. Expand
The slantlet transform
  • I. Selesnick
  • Mathematics, Computer Science
  • IEEE Trans. Signal Process.
  • 1 May 1999
TLDR
This paper discusses the implementation and properties of an orthogonal DWT, with two zero moments and with improved time localization, with a piecewise linear basis that is reminiscent of the slant transform. Expand
The double-density dual-tree DWT
  • I. Selesnick
  • Mathematics, Computer Science
  • IEEE Transactions on Signal Processing
  • 1 May 2004
TLDR
The paper develops a design procedure to obtain finite impulse response (FIR) filters that satisfy the numerous constraints imposed and have vanishing moments, compact support, a high degree of smoothness, and are nearly shift-invariant. Expand
Hilbert transform pairs of wavelet bases
  • I. Selesnick
  • Computer Science, Mathematics
  • IEEE Signal Processing Letters
  • 1 June 2001
TLDR
This paper gives an alternative derivation and explanation for the result by Kingsbury (1999), that the dual-tree DWT is (nearly) shift-invariant when the scaling filters satisfy the same offset. Expand
Sparse Regularization via Convex Analysis
  • I. Selesnick
  • Mathematics, Computer Science
  • IEEE Transactions on Signal Processing
  • 1 September 2017
TLDR
A class of nonconvex penalty functions that maintain the convexity of the least squares cost function to be minimized, and avoids the systematic underestimation characteristic of L1 norm regularization are proposed. Expand
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