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, whilst image noise is filtered out. At each resolution level, the image edges are estimated by gradient magnitudes (obtained from the wavelet coefficients), which are modeled probabilistically, and a shrinkage function is assembled based on the model obtained. Joint use of space and scale consistency is applied for better preservation of edges. The shrinkage functions are combined to preserve edges that appear simultaneously at several resolutions, and geometric constraints are applied to preserve edges that are not isolated. The proposed technique produces a filtered version of the original image, where homogeneous regions appear separated by well-defined edges. Possible applications include image presegmentation, and image denoising.