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The analysis and design of two-dimensional nearly-orthogonal symmetric wavelet filter banks

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Abstract

The design and analysis of two-channel two-dimensional (2D) nonseparable nearly-orthogonal symmetric wavelet filter banks with quincunx decimation is studied. The basic idea is to impose multiple zeros at the aliasing frequency to a symmetric filter and minimize the deviation of the filter satisfying the orthogonal condition to obtain a nearly-orthogonal FIR filter bank. Since multiple zeros are imposed, a scaling function may be generated from the minimized filter. With this filter, a semi-orthogonal filter bank is constructed. Methods for analyzing the correlation of the semi-orthogonal filter banks are proposed. The integer translates of the wavelet and scaling function are nearly-orthogonal. The integer translates of the wavelet at different scale are completely orthogonal. The semi-orthogonal filter bank can be efficiently implemented using the corresponding nearly-orthogonal FIR filter bank.

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Authors and Affiliations

  1. The Key Lab of Integrated Microsystems, Shenzhen Graduate School, Peking University, Xili, 518055, Shenzhen, China

    Yong Zhao

  2. Centre for Signal Processing and Communications, Department of Electrical and Computer Engineering, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, QC, H3G 1M8, Canada

    M. N. S. Swamy

Authors
  1. Yong Zhao
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  2. M. N. S. Swamy
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Correspondence to Yong Zhao.

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Zhao, Y., Swamy, M.N.S. The analysis and design of two-dimensional nearly-orthogonal symmetric wavelet filter banks. Multidim Syst Sign Process 24, 199–218 (2013). https://doi.org/10.1007/s11045-011-0165-0

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  • DOI: https://doi.org/10.1007/s11045-011-0165-0

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