Two-dimensional nonseparable perfect reconstruction (PR) filter bank design based on the Bernstein polynomial approximation

Kerem A. Harmanci; Emin Anarim; Hakan Caglar; Bulent Sankur

doi:10.1117/12.186043

16 September 1994 Two-dimensional nonseparable perfect reconstruction (PR) filter bank design based on the Bernstein polynomial approximation

Kerem A. Harmanci, Emin Anarim, Hakan Caglar, Bulent Sankur

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Proceedings Volume 2308, Visual Communications and Image Processing '94; (1994) https://doi.org/10.1117/12.186043
Event: Visual Communications and Image Processing '94, 1994, Chicago, IL, United States

Abstract

This study presents design of 2D nonseparable Perfect Reconstruction Filter Bank (PRFB) for two different sampling lattices: the quincuncial and rectangular. In quincunx case z-domain PR conditions are mapped into Bernstein-x domain. Desired power spectrum of 2D nonseparable filter is approximated by using Bernstein polynomial. Since we introduce mapping from complex periodic domain to real polynomial domain, PRFB design in Bernstein-x domain is much easier to handle. The parametric solution for 2D nonseparable design technique is obtained with desired regularity for quincunx sampling lattices. This technique allows us to design of 2D wavelet transform. For rectangular downsampling, the use of signed shuffling operations to obtain a PRFB from a low pass filter enables the reduction of PR conditions. This design technique leads us to efficient implementation structure since all the filters in the bank have the same coefficients with sign and position changes. This structure overcomes the high complexity problem that is the major shortcoming of 2D nonseparable filter banks. Designed filter banks are tested on 2D image models and real images in terms of compaction performance. It has been shown that nonseparable design can outperform separable ones in the application of data compression.

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Kerem A. Harmanci, Emin Anarim, Hakan Caglar, and Bulent Sankur "Two-dimensional nonseparable perfect reconstruction (PR) filter bank design based on the Bernstein polynomial approximation", Proc. SPIE 2308, Visual Communications and Image Processing '94, (16 September 1994); https://doi.org/10.1117/12.186043

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KEYWORDS

Linear filtering

Optical filters

Image compression

Holmium

Image filtering

Performance modeling

Wavelet transforms

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