Ward, J.P.Pad, P.Unser, M.2015-07-282015-07-282015-07-28201510.1109/Lsp.2015.2448233https://infoscience.epfl.ch/handle/20.500.14299/116720WOS:000356970700003In 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.Calculus of variationslocalizationSimoncelli waveletswavelet tight framestext::journal::journal article::research article