, Volume 100, Issue 7, pp 715–739 | Cite as

Inverse formulas of parameterized orthogonal wavelets

  • Oscar Herrera-AlcántaraEmail author
  • Miguel González-Mendoza


We review the parameterization of orthogonal wavelet based filters of length 4, 6, 8, and 10, and present their inverse formulas, which means to determine the parameter values from filter coefficients. Experimental results support the validity of these inverse formulas when parameters are restricted to \([0, 2\pi )\) for practical applications, such as image processing where parameters are optimized to maximize the number of negligible wavelet coefficients.


Wavelets Filter parameterization Orthogonality Image processing 

Mathematics Subject Classification

65T60 94A12 94A08 


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Copyright information

© The Author(s) 2018
corrected publication September 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Universidad Autónoma MetropolitanaAzcapotzalcoMéxico
  2. 2.Instituto Tecnológico y de Estudios Superiores de MonterreyAtizapán de ZaragozaMéxico

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