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

Polyharmonic Smoothing Splines for Multi-Dimensional Signals with 1 ⁄ ||ω||τ-Like Spectra

S. Tirosh, D. Van De Ville, M. Unser

Proceedings of the Twenty-Ninth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'04), Montréal QC, Canada, May 17-21, 2004, pp. III-297–III-300.

Motivated by the fractal-like behavior of natural images, we propose a new smoothing technique that uses a regularization functional which is a fractional iterate of the Laplacian. This type of functional has previously been introduced by Duchon in the context of radial basis functions (RBFs) for the approximation of non-uniform data. Here, we introduce a new solution to Duchon's smoothing problem in multiple dimensions using non-separable fractional polyharmonic B-splines. The smoothing is performed in the Fourier domain by filtering, thereby making the algorithm fast enough for most multi-dimensional real-time applications. 

@INPROCEEDINGS(http://bigwww.epfl.ch/publications/tirosh0401.html,
AUTHOR="Tirosh, S. and Van De Ville, D. and Unser, M.",
TITLE="Polyharmonic Smoothing Splines for Multi-Dimensional Signals with
	$1/\|\omega\|^{\tau}$-Like Spectra",
BOOKTITLE="Proceedings of the Twenty-Ninth {IEEE} International
	Conference on Acoustics, Speech, and Signal Processing
	({ICASSP'04})",
YEAR="2004",
editor="",
volume="{III}",
series="",
pages="297--300",
address="Montr{\'{e}}al QC, CA",
month="May 17-21,",
organization="",
publisher="",
note="")

© 2004 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.