Paper Info
Title
The pairing of a wavelet basis with a mildly redundant analysis via subband regression.
Abstract
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 (Step 3) which computes a wavelet expansion that is maximally consistent in the least squares sense with the redundant wavelet analysis. We demonstrate that this approach significantly improves the performance of soft-threshold wavelet denoising with a moderate increase in computational cost. We also show that the analysis filters in the proposed framework can be adjusted for improved feature detection; in particular, a new quincunx Mexican-hat-like wavelet transform that is fully reversible and essentially behaves the (gamma/2)th Laplacian of a Gaussian.
Year
DOI
Venue
2008
10.1109/TIP.2008.2004607
IEEE Transactions on Image Processing
Keywords
Field
DocType
filtering theory,image reconstruction,image representation,least squares approximations,regression analysis,signal denoising,wavelet transforms,Mallat filterbank algorithm,mildly redundant analysis,quincunx Mexican-hat-like wavelet transform,signal reconstruction,signals representation,soft-threshold wavelet denoising,subband regression filter,wavelet analysis,wavelet bases,wavelet channels,wavelet frames,wavelet-domain processing,Denoising,Mexican-hat filter,feature detection,fractals,frames,isotropy,pyramid,wavelets
Computer vision,Pattern recognition,Lifting scheme,Second-generation wavelet transform,Artificial intelligence,Discrete wavelet transform,Cascade algorithm,Stationary wavelet transform,Wavelet packet decomposition,Mathematics,Wavelet,Wavelet transform
Journal
Volume
Issue
ISSN
17
11
1057-7149
Citations 
PageRank 
References 
15
0.91
33
Authors
2
Name
Order
Citations
PageRank
Unser, M.13438442.40
Dimitri Van De Ville21656118.48