论文信息 - Construction of Quaternion-Valued Wavelets

Construction of Quaternion-Valued Wavelets

In this paper, we introduce quaternion-valued wavelets in the context of the duplex matrix-valued function. We then formulate quaternion scaling and wavelet functions using quaternion multiresolution analysis (QMRA).With these formulations, we obtain coefficients of highpass and lowpass filters of QMRA. Keywords: Quaternion-valued wavelets; quaternion multiresolution analysis; highpass and lowpass filters.

Mawardi Bahri

[1] Eckhard Hitzer,et al. Clifford Fourier Transform on Multivector Fields and Uncertainty Principles for Dimensions n = 2 (mod 4) and n = 3 (mod 4) , 2008 .

[2] Jun Zhou,et al. Quaternion wavelet phase based stereo matching for uncalibrated images , 2007, Pattern Recognit. Lett..

[3] Eduardo Bayro-Corrochano,et al. The Theory and Use of the Quaternion Wavelet Transform , 2005, Journal of Mathematical Imaging and Vision.

[4] Mawardi Bahri,et al. An uncertainty principle for quaternion Fourier transform , 2008, Comput. Math. Appl..

[5] Mawardi Bahri,et al. Clifford Algebra Cl3, 0-Valued Wavelet Transformation, Clifford Wavelet Uncertainty inequality and Clifford Gabor Wavelets , 2007, Int. J. Wavelets Multiresolution Inf. Process..

[6] Bo Yu,et al. Continuous wavelet transforms on the space L2(R, H;dx) , 2004, Appl. Math. Lett..

[7] Rémi Vaillancourt,et al. Windowed Fourier transform of two-dimensional quaternionic signals , 2010, Appl. Math. Comput..

[8] A. Walden,et al. Wavelet analysis of matrix–valued time–series , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[9] Xiang-Gen Xia,et al. Vector-valued wavelets and vector filter banks , 1996, IEEE Trans. Signal Process..

[10] Leonardo Traversoni. Image Analysis Using Quaternion Wavelets , 2001 .

[11] Klaus Gürlebeck,et al. Quaternionic and Clifford Calculus for Physicists and Engineers , 1998 .