Adaptive Image Denoising and Edge Enhancement in Scale-Space Using the Wavelet Transform Cl´audio Rosito Jung a Jacob Scharcanski b a UNISINOS - Universidade do Vale do Rio dos Sinos Centro de Ciˆ encias Exatas e Tecnol´ ogicas - C6/6 Av. UNISINOS, 950. S˜ ao Leopoldo, RS, Brasil, 93022-000 crjung@exatas.unisinos.br b UFRGS–Universidade Federal do Rio Grande do Sul Instituto de Inform´ atica Av. Bento Gon¸ calves, 9500. Porto Alegre, RS, Brasil 91501-970 jacobs@inf.ufrgs.br Abstract This paper proposes a new method for image denoising with edge preservation and enhancement, based on image multi-resolution decomposition by a redundant wavelet transform. At each resolution, the coefficients associated with noise and the coefficients associated with edges are modeled by Gaussians, and a shrinkage func- tion is assembled. The shrinkage functions are combined in consecutive resolutions, and geometric constraints are applied to preserve edges that are not isolated. Within the proposed framework, edge related coefficients may be enhanced and denoised simultaneously. 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. Key words: denoising, enhancement, multiresolution analysis, wavelet shrinkage Preprint submitted to Elsevier Science 23 December 2004