Image Smoothing via a Novel Adaptive Weighted $L_0$ Regularization

Image smoothing has been extensively used in various fields, e.g., edge extraction, image abstraction, and image detail enhancement. Many existing optimization-based image smoothing methods have been proposed in recent years. The downside of these methods is that the results often have unclear edges and missing structures. To obtain satisfactory smoothing results, we design a novel optimization model by introducing an anisotropic $L_0$ gradient intensity. Specifically, a weighted matrix $T$ is imposed to control further the sparsity of the gradient measured by $L_0$-norm. Since the proposed model is non-convex and non-smooth, we apply the half quadratic splitting (HQS) algorithm to solve it effectively. In addition, to obtain a more suitable regularization parameter $λ,$ we utilize an adaptive parameter selection method based on Morozovs discrepancy principle. Finally, we conduct numerical experiments to illustrate the superiority of our method over some state-of-the-art methods.