Adaptive image denoising in scale-space using the wavelet transform

This paper proposes a new method for image denoising with edge preservation, based on image multiresolution decomposition by a redundant wavelet transform. In our approach, edges are implicitly located and preserved in the wavelet domain, while noise is filtered out. At each resolution, the coefficients associated to noise and coefficients associated to edges are modeled by Gaussians, and a shrinkage function is assembled. The shrinkage functions are combined in consecutive resolution, and geometric constraints are applied to preserve edges that are not isolated. Finally, the inverse wavelet transform is applied to the modified coefficients. This method is adaptive, and performs well for images contaminated by natural and artificial noise.