Chan, Wai LamChoi, HyeokhoBaraniuk, Richard G.2007-10-312007-10-312004-10-012004-10-01W. L. Chan, H. Choi and R. G. Baraniuk, "Quaternion Wavelets for Image Analysis and Processing," vol. 5, 2004.https://hdl.handle.net/1911/19774Conference PaperUsing the concepts of two-dimensional Hubert transform and analytic signal, we construct a new quaternion wavelet transform (QWT). The QWT forms a tight frame and can be efficiently computed using a-2-D dual-tree filter bank. The QWT and the 2-D complex wavelet transform (CWT) are related by a unitary transformation, but the former inherits the quaternion Fourier-transform (QFT) phase properties, which are desirable for image analysis. The quaternion magnitude-phase representation of the QWT directly leads to near shift-invariance and the ability to encode phase shifts in an absolute x-y-coordinate system, which we can use for applications such as edge estimation and statistical image modeling.engDSP for CommunicationsConference paperhttp://dx.doi.org/10.1109/ICIP.2004.1421758