Two-Dimensional Wavelets with Complementary Filter Banks

Authors

  • M.G. Almeida

DOI:

https://doi.org/10.5540/tema.2000.01.01.0001

Abstract

In this paper, the Two-Dimensional (2D) Complementary Filter (CF) Banks, a signal processing technique which can be used to get scaling and wavelets functions, are presented. The 2D multirate signal processing theory and complementary filters properties are the base of CF Banks, permitting us to consider different types of sampling and filters. Two-dimensional nonseparable quincunx, rectangular and circular complementary filters are designed for an alias free decimation and interpolation. When CF bank is implemented with quincunx sampling and filters, perfect reconstruction is achieved and although it is not reached in others cases, the analysis and synthesis are performed without aliasing. The CF banks are related with wavelet theory and procedures to get 2D scaling and bandpass wavelets functions from the L-level filter bank tree structure iteratively are shown. We illustrate scaling and wavelets functions convergence as the level of decomposition increases.

References

[1] M.G. Almeida, “Two-Dimensional Complementary Filter Bank in the Wavelet Representation Context: Theory, Design and Applications”, Ph.D. Dissertation, University of Pittsburgh, 1994.

S. Mallat, A Theory for Multiresolution Signal Decomposition: The Wavelet epresentation, IEEE Transactions on Pattern, Analysis, and Machine Intelligence, 11 No.7 (1989), 674-692.

S. Mallat, Multifrequency Channel Decompositions of Images and Wavelet Models, IEEE Transactions on Acoustic, Speech, and Signal Processing, 37 No.12 (1991), 2091-2110.

J. Kovaˇcevi´c, M. and Vetterli, Nonseparable Multidimensional Perfect Reconstruction Filter Banks and Wavelet Bases for Rn, IEEE Transactions on Information Theory, 38 No.2 (1992), 533-555.

P.P. Vaidyanathan, “Multirate Systems and Filter Banks”, Englewood Cliffs, NJ: Prentice Hall, 1993.

J.S. Lim, “Two-Dimensional Signal Processing and Image Processing”, Prentice Hall Signal Processing Series, A. Oppenheim, 1990.

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Published

2000-06-01

How to Cite

Almeida, M. (2000). Two-Dimensional Wavelets with Complementary Filter Banks. Trends in Computational and Applied Mathematics, 1(1), 1–8. https://doi.org/10.5540/tema.2000.01.01.0001

Issue

Vol. 1 No. 1 (2000)

Section

Original Article

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