A Multiscale Variational Model for Image Decomposition

This paper presents a novel multiscale variational image decomposition model. Based on the hierarchical multiscale variational model of Tadmor, a novel (BV, H-1) hierarchical multiscale image decomposition method is proposed, then the novel Integro-Differential Equation (IDE) is obtained by integrating in inverse scale space a succession of refined slices of the image and balancing a Laplacian of the curvature term at the finer scale. The IDE includes a monotone increasing scaling function which is shown to dictate the size of the residual image measured in the star-norm. Some theoretical properties of the novel IDE and its numerical implementation methods are given. Theoretical analysis and numerical experiments show the effectiveness of the IDE model.