Why Daubechies wavelets are so successful

Issue title: Soft Computing and Advances in Intelligent Systems

Guest editors: Ildar Batyrshin, Fernando Gomide, Vladik Kreinovich and Shahnaz Shahbazova

Article type: Research Article

Authors: Cortez, Solymar Ayala^a | Bokati, Laxman^b | Velasco, Aaron^a | Kreinovich, Vladik^{c; *}

Affiliations: [a] Department of Geological Sciences, University of Texas at El Paso, 500 W. University, El Paso, TX, USA | [b] Computational Science Program, University of Texasat El Paso, 500 W. University, El Paso, TX, USA | [c] Department of Computer Science, University of Texas at El Paso, 500 W. University, El Paso, TX, USA

Correspondence: [*] Corresponding author. Vladik Kreinovich, Department of Computer Science, University of Texas at El Paso, 500 W. University, El Paso, TX 79968, USA. E-mail: [email protected].

Abstract: In many applications, including analysis of seismic signals, Daubechies wavelets perform much better than other families of wavelets. In this paper, we provide a possible theoretical explanation for the empirical success of Daubechies wavelets. Specifically, we show that these wavelets are optimal with respect to any optimality criterion that satisfies the natural properties of scale- and shift-invariance.

Keywords: Daubechais wavelets, seismology, invariance

DOI: 10.3233/JIFS-212021

Journal: Journal of Intelligent & Fuzzy Systems, vol. 43, no. 6, pp. 6933-6938, 2022