Magnitude-phase of the dual-tree quaternionic wavelet transform for multispectral satellite image denoising

In this paper, we study the potential of the quaternionic wavelet transform for the analysis and processing of multispectral images with strong structural information. This new representation gives a very good division of the coefficients in terms of magnitude and three-phase angles and generalizes better the concept of analytic signal to image. Furthermore, it retains the property of shift invariant and directivity. We show an application of this transform in satellite image denoising. The proposed approach relies on the adaptation of thresholding procedures based on the dependency between magnitude quaternionic coefficients in local neighborhoods and phase regularization. In addition a non-marginal aspect of multispectral representation is introduced. Thanks to coherent analysis provided by the quaternionic wavelet transformation, the results obtained indicate the potential of this multispectral representation with magnitude thresholding and phase smoothing in noise reduction and edge preservation compared with classical wavelet thresholding methods that do not use phase or multiband information.