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Abstract: The more a priori knowledge we encode into a signal processing algorithm, the better performance we can expect. In this paper, we overview several approaches to capturing the structure of singularities (edges, ridges, etc.) in wavelet-based signal processing schemes. Leveraging results from approximation theory, we discuss nonlinear approximations on trees and point out that an optimal tree approximant exists and is easily computed. The optimal tree approximation inspires a new hierarchical... (Update)
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...image features like edges cause high coecients at several resolutions. More sophisticated methods exploit this multiscale structure [37, 12, 3]. In the case of correlated noise [22] or a non orthogonal transform, the multiresolution structure of a wavelet transform justi es the...
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BibTeX entry: (Update)
R. Baraniuk. Optimal tree approximation with wavelets. In M. A. Unser, A. Aldroubi, and Laine A. F., editors, Wavelet Applications in Signal and Image Processing VII, volume 3813 of SPIE Proceedings, pages 206-214, July 1999. http://citeseer.ist.psu.edu/baraniuk99optimal.html More
@misc{ baraniuk99optimal,
author = "R. Baraniuk",
title = "Optimal tree approximation with wavelets",
text = "R. Baraniuk. Optimal tree approximation with wavelets. In M. A. Unser,
A. Aldroubi, and Laine A. F., editors, Wavelet Applications in Signal and
Image Processing VII, volume 3813 of SPIE Proceedings, pages 206-214, July
1999.",
year = "1999",
url = "citeseer.ist.psu.edu/baraniuk99optimal.html" }
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519 A Wavelet Tour of Signal Processing (context) - Mallat - 1998
385 A new, fast, and efficient image codec based on set partitio.. - Said, Pearlman - 1996
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109 Image coding based on mixture modeling of wavelet coefficien.. - LoPresto, Ramchandran et al. - 1997
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87 Introduction to Wavelets and Wavelet Transforms: A Primer (context) - Burrus, Gopinath et al. - 1998
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67 Nonlinear approximation - DeVore - 1998
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47 A signal-dependent time-frequency representation: Fast algor.. (context) - Baraniuk, Jones - 1994
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24 Elements of Pattern Theory (context) - Grenander - 1996
22 Layered representations for image coding - Adelson - 1991
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14 Shear Madness: Signal-Dependent and Metaplectic Time-Frequen.. (context) - Baraniuk - 1992
13 The dual-tree complex wavelet transform: A new technique for.. - Kingsbury - 1998
13 CART and best-ortho-basis: A connection - Donoho - 1997
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8 Multiscale hidden Markov models for Bayesian image analysis - Nowak - 1999
7 A simple wavelet approach to nonparametric regression from r.. (context) - Engel - 1994
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3 Constrained stochastic language models - Mark, Miller et al. - 1994
3 Tree approximation and encoding - Cohen, Dahmen et al. - 1999
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