Image denoising using selective neighboring quaternionic wavelet coefficients

Removing noise for image is a classical problem in image processing but it is still relevant issue. In this paper, we adopt an innovative and original approach, which is combined between a recent quaternionic wavelet transform and selective neighbouring coefficients to image denoising. The choice of quaternionic transformation is justified by the fact that it gives a very good separation of the coefficients in terms of amplitude and 3-angles phase. This representation generalizes better the concept of analytic signal to the image. Quaternionic transformation retains property of shift invariant but it allows the introduction of a true 2D analysis compared with the traditional complex wavelet transform. After decomposition, selective neighbouring coefficients are used for denoising. Interesting results are obtained by comparing in term of PSNR with the complex wavelet transform and the discrete wavelet transform.