BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Shift-Orthogonal Wavelet Bases

M. Unser, P. Thévenaz, A. Aldroubi

IEEE Transactions on Signal Processing, vol. 46, no. 7, pp. 1827–1836, July 1998.

Shift-orthogonal wavelets are a new type of multiresolution wavelet bases that are orthogonal with respect to translation (or shifts) within one level, but not with respect to dilations across scales. In this paper, we characterize these wavelets and investigate their main properties by considering two general construction methods. In the first approach, we start by specifying the analysis and synthesis function spaces, and obtain the corresponding shift-orthogonal basis functions by suitable orthogonalization. In the second approach, we take the complementary view and start from the digital filterbank. We present several illustrative examples, including a hybrid version of the Battle-Lemarié spline wavelets. We also provide filterbank formulas for the fast wavelet algorithm. A shift-orthogonal wavelet transform is closely related to an orthogonal transform that uses the same primary scaling function; both transforms have essentially the same approximation properties. One experimentally confirmed benefit of relaxing the inter-scale orthogonality requirement is that we can design wavelets that decay faster than their orthogonal counterpart. 

@ARTICLE(http://bigwww.epfl.ch/publications/unser9802.html,
AUTHOR="Unser, M. and Th{\'{e}}venaz, P. and Aldroubi, A.",
TITLE="Shift-Orthogonal Wavelet Bases",
JOURNAL="{IEEE} Transactions on Signal Processing",
YEAR="1998",
volume="46",
number="7",
pages="1827--1836",
month="July",
note="")

© 1998 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.