Existence of uncertainty minimizers for the continuous wavelet transform

Simon Halvdansson*, Jan Fredrik Olsen, Nir Sochen, Ron Levie

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1156-1172
Number of pages17
JournalMathematische Nachrichten
Issue number3
StatePublished - Mar 2023


FundersFunder number
Israeli Ministry of Agriculture's Kandel Program20‐12‐0030
Deutsche ForschungsgemeinschaftSPP 1798
Ministry of Health, State of Israel3‐13898


    • continuous wavelet
    • uncertainty minimizer
    • uncertainty principle
    • wavelet design


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