Abstract: Y. Meyer’s oscillatory pattern decomposition theory is taken as the starting point in this paper. The existence and uniqueness of a class (B_V,E) model are first discussed. And then, a related multiscale decomposition of an image is proposed to reduce the dependence of the balance parameter on the priori information on the oscillatory component. At the same time, its convergence is analyzed. Finally, its algorithm in the wavelet domain is presented by using Lorenz’s project approach. Numerical experiments show that the algorithm can effectively separate the structure component and the oscillatory component from the image, moreover, a hierarchical multiscale representation of the image is also achieved

Key words: image decomposition, total variation, Besov space, low semi-continuous