EPFL
 Biomedical Imaging GroupSTI
EPFL
  Publications
English only   BIG > Publications > Subband Regression


 CONTENTS
 Home Page
 News & Events
 People
 Publications
 Tutorials and Reviews
 Research
 Demos
 Download Algorithms

 DOWNLOAD
 PDF
 Postscript
 All BibTeX References

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

M. Unser, D. Van De Ville

IEEE Transactions on Image Processing, vol. 17, no. 11, pp. 2040-2052, November 2008.



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 (γ⁄2)th Laplacian of a Gaussian.


@ARTICLE(http://bigwww.epfl.ch/publications/unser0814.html,
AUTHOR="Unser, M. and Van De Ville, D.",
TITLE="The Pairing of a Wavelet Basis with a Mildly Redundant Analysis
        via Subband Regression",
JOURNAL="{IEEE} Transactions on Image Processing",
YEAR="2008",
volume="17",
number="11",
pages="2040--2052",
month="November",
note="")

© 2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from IEEE.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.