The paper addresses structural decomposition of images by using a family of non-linear and non-convex objective functions. These functions rely on ℓ p quasi-norm estimation costs in a piecewise constant regularization framework. These objectives make image decomposition into constant cartoon levels and rich textural patterns possible. The paper shows that these regularizing objectives yield image texture-versus-cartoon decompositions that cannot be reached by using standard penalized least square regularizations associated with smooth and convex objectives. 
High order structural image decomposition by using non-linear and non-convex regularizing objectives