Abstract: Image denoising and compression has been the classic image processing problem,
and traditional methods are difficult to reach both requirements. Quaternion wavelet transform is
the product of the combination of real wavelet, complex wavelet, quaternion theory and 2D-hilbert
transform, and it is a new kind of multiresolution analysis of image processing tools. After
quaternion wavelet transform, Image wavelet coefficients have certain intrascale and interscale
correlation. This paper presents a mixed statistical model, which includes interscale bivariate
non-Gaussian distribution and intrascale generalized Gaussian distribution. The minimum mean
square error (MMSE) is used to estimate original image coefficients from wavelet coefficients
with noise, so as to achieve the purpose of denoising. The experiment results show that this
method can not only get signal-to-noise ratio enhancement and better visual quality, but also
achieve high compression ratio.

Key words: quaternion wavelet, image denoising, image compression, bivariate non-
Gaussian distribution, generalized Gaussian distribution