Vector extension of quaternion wavelet transform and its application to colour image denoising

Abstract

In this study, the authors study and give a new framework for colour image representation based on colour quaternion wavelet transform (CQWT). The new colour quaternion filter bank is constructed by using radon transform. Starting from link with structure tensors, the authors propose a new multi-scale tool for vector-valued signals which can provide efficient analysis of local features by using the concepts of amplitude, phase, and orientation. To demonstrate the properties of CQWT, new colour image denoising algorithm is proposed by using CQWT and bivariate shrinkage function. The performance of the proposed algorithm is experimentally verified on a variety of noise levels. Experimental results show that the proposed algorithm achieves superior performance both in visual quality and objective peak-signal-to-noise ratio, mean square error, and structure similarity values, compared with other state-of-the-art denoising algorithms. 2 Quaternion wavelet transform In this section, we will review the basic concepts of quaternion wavelet transform. As it was shown in [14], the quaternion wavelet transform of 2D function f (x, y) can be represented as

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