Weighted sparse gradient reconstruction model with a robust fidelity for edge-aware image smoothing

Smoothing out image details while preserving the salient edges is of significance to the field of computational photography. In this paper, we propose a novel optimization model for edge-aware image smoothing, which consists of a regularization term and a fidelity term. The regularization term is based on the idea of weighted sparse gradient reconstruction, which ensures edge-awareness. The fidelity term is based on an \(L_1\) $L_1$ loss, which is robust to outliers. Our model is sophisticated and thus can be non-trivial to solve. In this paper, we propose an iterative solution based on the augmented Lagrange multiplies, where the computational cost in each iteration is dominated by a least square problem that can be efficiently solved in the Fourier domain. We have conducted extensive experiments to evaluate the proposed filter. Both quantitative and qualitative results indicate that our filter is advantageous to the state-of-the-art filters on a variety of image processing and vision tasks. Furthermore, the proposed filter is efficient, it takes approximately 2 s to process images with 1 megapixel on a modern CPU.