Quaternion wavelet analysis and application in image denoising (Q1954840)

Summary: 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 \(L^2(\mathbb{R}^2)\), proves and presents quaternion wavelet's scale basis function and wavelet basis function concepts in spatial scale space \(L^2(\mathbb{R}^2; H)\), 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.