<p>Global optimization models can be advantageous to structure- and edge-preserving image decomposition. However, existing global image decomposition models put relatively strong assumptions on the probability distributions. In this paper, we propose a novel global optimization model for edge-preserving image decomposition, where both the fidelity and regularization terms are built upon the Barron’s penalty function. The function caters to various probability distributions as it generalizes existing popular penalty functions and beyond. Furthermore, we extend our model with spatial scale support, which is shown to be particularly useful for structure-preserving image decomposition. Therefore, our model provides a general framework for various structure- and edge-preserving image processing tasks. Finally, existing models adapt the balancing parameter to the weight. We propose to further adapt the bandwidth of the non-convex function to improve structure- and edge-awareness. The proposed model is non-convex, thus can be non-trivial to solve. We propose an iterative solution based on the additive half quadratic minimization method, where the main computational burden in each iteration is a least square problem that can be solved efficiently in the Fourier domain. We have experimented with the proposed method in a variety of applications. Both quantitative and qualitative results indicate the superiority over the state-of-the-art methods. Moreover, our method is highly efficient, it is able to process 720P color images in real time on a modern GPU.</p>