Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 493976, 21 pages
Research Article

Quaternion Wavelet Analysis and Application in Image Denoising

School of Mathematics, Hefei University of Technology, Hefei, Anhui 230009, China

Received 11 June 2012; Revised 14 September 2012; Accepted 17 September 2012

Academic Editor: Carlo Cattani

Copyright © 2012 Ming Yin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The quaternion wavelet transform is a new multiscale analysis tool. Firstly, this paper studies the standard orthogonal basis of scale space and wavelet space of quaternion wavelet transform in spatial , proves and presents quaternion wavelet’s scale basis function and wavelet basis function concepts in spatial scale space , and studies quaternion wavelet transform structure. Finally, the quaternion wavelet transform is applied to image denoising, and generalized Gauss distribution is used to model QWT coefficients’ magnitude distribution, under the Bayesian theory framework, to recover the original coefficients from the noisy wavelet coefficients, and so as to achieve the aim of denoising. Experimental results show that our method is not only better than many of the current denoising methods in the peak signal to noise ratio (PSNR), but also obtained better visual effect.