Dual-Tree Tight Frame Wavelets with Symmetric Envelope

Wavelets based on Hilbert pairs have appealing properties when applied to image denoising and feature detection due to their directional sensitivity. In this paper we propose dual-tree 4-channel tight frame wavelets and scaling functions {phih, psih1, psih2, psih3} and {phig, psig1, psig2, psig3} based on FIR filterbanks of four filters, and downsampling by 2. Such wavelets closely approximate shift invariance, and the resulting complex wavelets lead to exactly symmetric envelope. The filters enjoy vanishing moments property.

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