Optimal Isotropic Wavelets for Localized Tight Frame Representations

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John Paul Ward, Pedram Pad, Michael Unser

Published: 2015, Last Modified: 13 Nov 2024IEEE Signal Process. Lett. 2015EveryoneRevisionsBibTeXCC BY-SA 4.0
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.