Hilbert transform pairs of wavelet bases

By Ivan W. Selesnick. IEEE Signal Processing Letters, 2001

374 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/f760b1a439e92dc72afc8f003b8e05f83abef08b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. José M. Bioucas-Dias
2. Richard Baraniuk
3. Mário A. T. Figueiredo
4. Ivan W. Selesnick
5. Manya V. Afonso
6. Miguel López-Benítez
7. Fei Ma
8. Enggee Lim

In Computer Vision and Pattern Recognition

1. Ivan W. Selesnick
2. Richard Baraniuk
3. José M. Bioucas-Dias
4. Mário A. T. Figueiredo
5. Manya V. Afonso
6. N. Kingsbury
7. Miguel López-Benítez
8. Fei Ma

In Signal Processing

1. Richard Baraniuk
2. Miguel López-Benítez
3. Fei Ma
4. Enggee Lim
5. Tiantian Guo
6. Tongpo Zhang
7. Limin Yu
8. N. Kingsbury

Citations in the corpus

• A Review of Wavelet Analysis and Its Applications: Challenges and Opportunities (2022, methodology): “Selesnick further pointed out that the necessary conditions given by Selesnick in [32] are still sufficient [35].”
• The dual-tree complex wavelet transform (2005, background): “In [87] it is shown that ifG0(e ) = e−j 0.”
• Restoration of Poissonian Images Using Alternating Direction Optimization (2010, neutral): “Yet another example of a redundant Parseval frame is provided by complex wavelets, with the corresponding direct and inverse transforms havin g O(n) cost [24], [34].”
• An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems (2009, background): “Yet another example of a redundant Parseval frame is the complex wavelet transform, which has O(n) computational cost [38], [48].”
• The design of approximate Hilbert transform pairs of wavelet bases (2002, methodology): “Using the infinite product formula, it was shown in [18] that for two orthogonal wavelets to form a Hilbert transform pair,”
• The double-density dual-tree DWT (2004, methodology): “The design of wavelets for the dual-tree DWTs described in relied on filter coefficient optimization to minimize aliasing in a multistage filter bank.”
• Fast Image Recovery Using Variable Splitting and Constrained Optimization (2009, neutral): “Yet another example of a redundant Parseval frame is the complex wavelet transform, which hasO(n) computational cost [31], [41].”