Multiscale Image Representation and Texture Extraction Using Hierarchical Variational Decomposition

In order to achieve a mutiscale representation and texture extraction for textured image, a hierarchical (BV, Gp, L ) decomposition model is proposed in this paper. We firstly introduce the proposed model which is obtained by replacing the fixed scale parameter of the original (BV, Gp, L 2 ) decomposition with a varying sequence. And then, the existence and convergence of the hierarchical decomposition are proved. Furthermore, we show the nontrivial property of this hierarchical decomposition. Finally, we introduce a simple numerical method for the hierarchical decomposition, which utilizes gradient decent for energy minimization and finite difference for the associated gradient flow equations. Numerical results show that the proposed hierarchical (BV, Gp, L 2 ) decomposition is very appropriate for multiscale representation and texture extraction of textured image.