Nonlinear approximation with redundant dictionaries

Lasse Borup; M. Nielsen; R. Gribonval

doi:10.1109/ICASSP.2005.1415995

Nonlinear approximation with redundant dictionaries

Lasse Borup, M. Nielsen, R. Gribonval

Department of Mathematical Sciences

Research output: Contribution to journal › Conference article in Journal › Research › peer-review

1 Citation (Scopus)

Abstract

In this paper we study nonlinear approximation and data representation with redundant function dictionaries. In particular, approximation with redundant wavelet bi-frame systems is studied in detail. Several results for orthonormal wavelets are generalized to the redundant case. In general, for a wavelet bi-frame system the approximation properties are limited by the number of vanishing moments of the system. In some cases this can be overcome by oversampling, but at a price of replacing the canonical expansion by another linear expansion. Moreover, for special non-oversampled wavelet bi-frames we can obtain good approximation properties not restricted by the number of vanishing moments, but again without using the canonical expansion.

Original language	English
Journal	I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings
Volume	1-5
Pages (from-to)	261-264
Number of pages	4
ISSN	1520-6149
DOIs	https://doi.org/10.1109/ICASSP.2005.1415995
Publication status	Published - 2005
Event	IEEE International Conference on Acoustics, Speech, and Signal Processing - Philadelphia, United States Duration: 18 Mar 2005 → 23 Sept 2005

Conference

Conference	IEEE International Conference on Acoustics, Speech, and Signal Processing
Country/Territory	United States
City	Philadelphia
Period	18/03/2005 → 23/09/2005

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10.1109/ICASSP.2005.1415995

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Cite this

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title = "Nonlinear approximation with redundant dictionaries",

abstract = " In this paper we study nonlinear approximation and data representation with redundant function dictionaries. In particular, approximation with redundant wavelet bi-frame systems is studied in detail. Several results for orthonormal wavelets are generalized to the redundant case. In general, for a wavelet bi-frame system the approximation properties are limited by the number of vanishing moments of the system. In some cases this can be overcome by oversampling, but at a price of replacing the canonical expansion by another linear expansion. Moreover, for special non-oversampled wavelet bi-frames we can obtain good approximation properties not restricted by the number of vanishing moments, but again without using the canonical expansion.",

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year = "2005",

doi = "10.1109/ICASSP.2005.1415995",

language = "English",

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AU - Nielsen, M.

AU - Gribonval, R.

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N2 - In this paper we study nonlinear approximation and data representation with redundant function dictionaries. In particular, approximation with redundant wavelet bi-frame systems is studied in detail. Several results for orthonormal wavelets are generalized to the redundant case. In general, for a wavelet bi-frame system the approximation properties are limited by the number of vanishing moments of the system. In some cases this can be overcome by oversampling, but at a price of replacing the canonical expansion by another linear expansion. Moreover, for special non-oversampled wavelet bi-frames we can obtain good approximation properties not restricted by the number of vanishing moments, but again without using the canonical expansion.

AB - In this paper we study nonlinear approximation and data representation with redundant function dictionaries. In particular, approximation with redundant wavelet bi-frame systems is studied in detail. Several results for orthonormal wavelets are generalized to the redundant case. In general, for a wavelet bi-frame system the approximation properties are limited by the number of vanishing moments of the system. In some cases this can be overcome by oversampling, but at a price of replacing the canonical expansion by another linear expansion. Moreover, for special non-oversampled wavelet bi-frames we can obtain good approximation properties not restricted by the number of vanishing moments, but again without using the canonical expansion.

U2 - 10.1109/ICASSP.2005.1415995

DO - 10.1109/ICASSP.2005.1415995

M3 - Conference article in Journal

SN - 1520-6149

VL - 1-5

SP - 261

EP - 264

JO - I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings

JF - I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings

T2 - IEEE International Conference on Acoustics, Speech, and Signal Processing

Y2 - 18 March 2005 through 23 September 2005

ER -