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Design of Nearly-Orthogonal Symmetric Wavelet Filter Banks Based on the Wavelet Orthogonalization Process

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Abstract

This work proposes a new method for nearly-orthogonal wavelet filter banks design based on the wavelet orthogonalization process. A new procedure to extract semi-conjugate filters from non-orthogonal wavelets is used for such purposes. The proposed methodology allows the design of symmetrical odd length nearly-orthogonal wavelet filters according to the frequency domain specifications. Finite impulse response wavelet filters with linear phase are obtained, not implying significant gain distortions and satisfying perfect reconstruction condition as accurately as possible. A signal decomposition example is presented and the wavelet coefficients results are compared with orthogonal and biorthogonal wavelet filter banks. Considering such an example, the best result was obtained by one of the proposed nearly-orthogonal wavelet filter banks. Some nearly-orthogonal wavelet filter banks designed in this work are applied in the context of image compression, involving the reconstruction process. Image compression results from a nearly-orthogonal wavelet filter designed in this work are superior to those from some classical wavelet filters.

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Data Availability

The datasets used during the current study are available in the Public-domain test images for homeworks and projects repository, available at https://homepages.cae.wisc.edu/ece533/images.

Code Availability

Not applicable.

Materials Availability

Not applicable.

Notes

  1. Space of finite energy functions.

  2. Note that \(\omega \) is used as the discrete-time signal frequency parameter, in contrast to the continuous-time signal frequency parameter, where \(\Omega \) is the referent notation.

  3. Space of finite energy discrete signals

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Funding

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance code 001.

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Authors and Affiliations

  1. Department of Electrical Engineering, UNESP-São Paulo State University, Brasil Avenue 56, Ilha Solteira, Brazil

    Fabrício Ely Gossler

  2. Department of Mathematics, UEMS-State University of Mato Grosso do Sul, MS 306 Road, KM 06, Cassilândia, Brazil

    Marco Aparecido Queiroz Duarte

  3. Department of Mathematics, UNESP-São Paulo State University, Brasil Avenue 56, Ilha Solteira, Brazil

    Francisco Villarreal

Authors
  1. Fabrício Ely Gossler
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  2. Marco Aparecido Queiroz Duarte
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  3. Francisco Villarreal
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Correspondence to Fabrício Ely Gossler.

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Gossler, F.E., Duarte, M.A.Q. & Villarreal, F. Design of Nearly-Orthogonal Symmetric Wavelet Filter Banks Based on the Wavelet Orthogonalization Process. Circuits Syst Signal Process 42, 234–254 (2023). https://doi.org/10.1007/s00034-022-02111-6

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