I. Introduction
A FEW years ago, the second author proposed several image decomposition models which are aimed to split an image into three components. The first component should describe the objects contained in the image, the second one is given by the textured components and the third one is an additive noise. The structures are modelized as functions belonging to the -space (the space of bounded variations functions) and the textures as oscillating functions belonging to a space, called by the second author, which is close to the dual of the -space. Many papers deal with numerical implementation [1], [5], [4], extensions to other cases (like color images [12]) and some applications [13] but few of them study the theoretical behavior of this model.