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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
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Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency
Most simple nonlinear thresholding rules for wavelet-based denoising assume that the wavelet coefficients are independent. However, wavelet coefficients of natural images have significantExpand
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Wavelet Transform With Tunable Q-Factor
  • I. Selesnick
  • Computer Science, Mathematics
  • IEEE Transactions on Signal Processing
  • 1 August 2011
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 isExpand
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The design of approximate Hilbert transform pairs of wavelet bases
  • I. Selesnick
  • Mathematics, Computer Science
  • IEEE Trans. Signal Process.
  • 1 May 2002
Several authors have demonstrated that significant improvements can be obtained in wavelet-based signal processing by utilizing a pair of wavelet transforms where the wavelets form a HilbertExpand
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The slantlet transform
  • I. Selesnick
  • Computer Science, Mathematics
  • IEEE Trans. Signal Process.
  • 1 May 1999
The discrete wavelet transform (DWT) is usually carried out by filterbank iteration; however, for a fixed number of zero moments, this does not yield a discrete-time basis that is optimal withExpand
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The double-density dual-tree DWT
  • I. Selesnick
  • Mathematics, Computer Science
  • IEEE Transactions on Signal Processing
  • 1 May 2004
This paper introduces the double-density dual-tree discrete wavelet transform (DWT), which is a DWT that combines the double-density DWT and the dual-tree DWT, each of which has its ownExpand
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The Double Density DWT
This chapter tak es up the design of discret e wavelet transforms ba sed on oversampled filter b anks. In t his case t he wavelet s form an overcom plete basis, or frame. In par ticul ar , weExpand
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A bivariate shrinkage function for wavelet-based denoising
  • L. Sendur, I. Selesnick
  • Computer Science, Mathematics
  • IEEE International Conference on Acoustics…
  • 13 May 2002
Most simple nonlinear thresholding rules for wavelet-based denoising assume the wavelet coefficients are independent. However, wavelet coefficients of natural images have significant dependency. InExpand
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Resonance-based signal decomposition: A new sparsity-enabled signal analysis method
  • I. Selesnick
  • Computer Science, Mathematics
  • Signal Process.
  • 1 December 2011
Abstract Numerous signals arising from physiological and physical processes, in addition to being non-stationary, are moreover a mixture of sustained oscillations and non-oscillatory transients thatExpand
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Sparse Regularization via Convex Analysis
  • I. Selesnick
  • Mathematics, Computer Science
  • IEEE Transactions on Signal Processing
  • 1 September 2017
Sparse approximate solutions to linear equations are classically obtained via L1 norm regularized least squares, but this method often underestimates the true solution. As an alternative to the L1Expand
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