Existence of uncertainty minimizers for the continuous wavelet transform

Simon Halvdansson, Jan‐Fredrik Olsen, Nir Sochen and Ron Levie

Mathematische Nachrichten, 2023, vol. 296, issue 3, 1156-1172

Abstract: Continuous wavelet design is the endeavor to construct mother wavelets with desirable properties for the continuous wavelet transform (CWT). One class of methods for choosing a mother wavelet involves minimizing a functional, called the wavelet uncertainty functional. Recently, two new wavelet uncertainty functionals were derived from theoretical foundations. In both approaches, the uncertainty of a mother wavelet describes its concentration, or accuracy, as a time‐scale probe. While an uncertainty minimizing mother wavelet can be proven to have desirable localization properties, the existence of such a minimizer was never studied. In this paper, we prove the existence of minimizers for the two uncertainty functionals.

Date: 2023
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