A Bayesian Approach of Hyperanalytic Wavelet Transform Based Denoising

The property of shift-invariance associated with a good directional selectivity is important for the application of a wavelet transform, (WT), in many fields of image processing. Generally, complex wavelet transforms, like for example the double tree complex wavelet transform, (DTCWT), have these good properties. In this paper we propose the use of a new implementation of such a WT, recently introduced, namely the hyperanalytic wavelet transform, (HWT), in denoising applications. The proposed denoising method is very simple, implying three steps: the computation of the forward WT, the filtering in the wavelets domain and the computation of the inverse WT, (IWT). The goal of this paper is the association of a new implementation of the HWT, recently proposed, with a maximum a posteriori (MAP) filter. Some simulation examples and comparisons prove the performances of the proposed denoising method.