Generalized Welsch penalty for edge-aware image decomposition

Edge-aware image decomposition is an essential topic in the field of multimedia signal processing. In this paper, we propose a novel non-convex penalty function, which we name the generalized Welsch function. We show that the proposed penalty function is more than a generalization of most existing penalty functions for edge-aware regularization, thus, it better facilitates edge-awareness. We embed the proposed penalty function into a novel optimization model for edge-aware image decomposition. To solve the optimization model with non-convex penalty function, we propose an efficient algorithm based on the additive quadratic minimization and Fourier domain optimization. We have experimented with the proposed method in a variety of tasks, including image smoothing, detail enhancement, HDR tone mapping, and JPEG compression artifact removal. Experiment results show that our method outperforms the state-of-the-art image decomposition methods. Furthermore, our method is highly efficient, it is able to render real-time processing of 720P color images on a modern GPU.