Title :
Optimal Isotropic Wavelets for Localized Tight Frame Representations
Author :
Ward, John Paul ; Pad, Pedram ; Unser, Michael
Author_Institution :
Biomed. Imaging Group, Ecole Polytech. Fed. de Lausanne (EPFL), Lausanne, Switzerland
Abstract :
In this letter, we aim to identify the optimal isotropic mother wavelet for a given spatial dimension based on a localization criterion. Within the framework of the calculus of variations, we specify an Euler-Lagrange equation for this problem, and we find the unique analytic solutions. In the one- and two-dimensional cases, the derived wavelets are well known.
Keywords :
signal representation; wavelet transforms; Euler-Lagrange equation; localized tight frame representations; optimal isotropic mother wavelet; spatial dimension; Biomedical imaging; Calculus; Europe; Fourier transforms; Wavelet analysis; Wavelet transforms; Calculus of variations; Simoncelli wavelets; localization; wavelet tight frames;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2015.2448233
