Quaternion Wavelets for Image Analysis and Processing (WP-L3)

Author(s) : Wai Lam Chan (Rice University, USA) Hyeokho Choi (Rice University, USA) Richard Baraniuk (Rice University, USA)

Abstract : We apply the concepts of 2-D Hilbert transform and analytic function to build a new quaternion wavelet transform (QWT). The resulting transform is a 4x redundant tight frame and the wavelet bases can be efficiently generated using a 2-D dual-tree filter bank. The QWT and the 2-D CWT are equivalent under a unitary transformation but the former also inherits the QFT phase properties desirable for image analysis. The quaternion magnitude-phase representation in the QWT directly leads to its shift-invariance and its ability to encode phase shifts in absolute xy-coordinate system.

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