S\'eparation en composantes structures, textures et bruit d'une image, apport de l'utilisation des contourlettes

In this paper, we propose to improve image decomposition algorithms in the case of noisy images. In \cite{gilles1,aujoluvw}, the authors propose to separate structures, textures and noise from an image. Unfortunately, the use of separable wavelets shows some artefacts. In this paper, we propose to replace the wavelet transform by the contourlet transform which better approximate geometry in images. For that, we define contourlet spaces and their associated norms. Then, we get an iterative algorithm which we test on two noisy textured images.