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2008

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

9 years 6 months ago
The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression
A distinction is usually made between wavelet bases and wavelet frames. The former are associated with a one-to-one representation of signals, which is somewhat constrained but most efficient computationally. The latter are over-complete, but they offer advantages in terms of flexibility (shape of the basis functions) and shift-invariance. In this paper, we propose a framework for improved wavelet analysis based on an appropriate pairing of a wavelet basis with a mildly redundant version of itself (frame). The processing is accomplished in four steps: 1) redundant wavelet analysis, 2) wavelet-domain processing, 3) projection of the results onto the wavelet basis, and 4) reconstruction of the signal from its nonredundant wavelet expansion. The wavelet analysis is pyramid-like and is obtained by simple modification of Mallat's filterbank algorithm (e.g., suppression of the down-sampling in the wavelet channels only). The key component of the method is the subband regression filter (...
Michael Unser, Dimitri Van De Ville
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2008
Where TIP
Authors Michael Unser, Dimitri Van De Ville
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