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Higher-density dual tree discrete wavelet transform. (English) Zbl 1213.42152

Summary: This paper introduces the higher-density dual-tree (HDDT) discrete wavelet transform (DWT). A new MRA is introduced to describe higher-density DWT and used to obtain the sufficient condition for the HDDT Hilbert transform pair. For designing HDDT filters, we use the extended common-factor method which not only includes the common-factor method but also provides exact linear phase bi-frame filters. Both HDDT tight frame and bi-frame (anti)symmetric filter design methods are given. Finally, the results of denoising experiments by our newly designed HDDT filters in this paper prove the effectiveness of higher-density dual-tree DWT in the application of image processing.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
44A15 Special integral transforms (Legendre, Hilbert, etc.)

Software:

DT-CWT
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Full Text: DOI

References:

[1] DOI: 10.1109/TSP.2006.875388 · Zbl 1373.94520 · doi:10.1109/TSP.2006.875388
[2] DOI: 10.1109/TSP.2004.826174 · Zbl 1370.94234 · doi:10.1109/TSP.2004.826174
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[5] DOI: 10.1109/97.923042 · doi:10.1109/97.923042
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[7] DOI: 10.1109/MSP.2005.1550194 · doi:10.1109/MSP.2005.1550194
[8] DOI: 10.1109/79.482137 · doi:10.1109/79.482137
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