Hilbert-like tight frame wavelets with symmetric envelope

A. Farras Abdelnour

doi:10.1117/12.733192

20 September 2007 Hilbert-like tight frame wavelets with symmetric envelope

A. Farras Abdelnour

Proceedings Volume 6701, Wavelets XII; 67011B (2007) https://doi.org/10.1117/12.733192
Event: Optical Engineering + Applications, 2007, San Diego, California, United States

Abstract

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 tight frame wavelets and scaling functions {φh, ψh1, ψh2, ψh3} and {φg, ψg1, ψg2, ψg3} based on FIR filterbanks of four filters, and downsampling by 2. Such wavelets closely approximate shift invariance. Moreover, the resulting complex wavelets are smooth and lead to exactly symmetric envelope. The filters in this paper enjoy vanishing moments property.

Citation Download Citation

A. Farras Abdelnour "Hilbert-like tight frame wavelets with symmetric envelope", Proc. SPIE 6701, Wavelets XII, 67011B (20 September 2007); https://doi.org/10.1117/12.733192

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