Edge-aware image smoothing via weighted sparse gradient reconstruction

Edge-ware image smoothing, which aims at removing fine details while respecting salient edges, is a prevalent topic in the field of computational imaging and photography. In this paper, we propose a novel weighted sparse gradient reconstruction model for edge-aware image smoothing. The proposed method first suppresses the low-amplitude gradients with an edge-aware mapping function. The processed gradients are then fed into a weighted L_1 gradient reconstruction model to derive the output. The L_1 regularization enforces the sparsity on the output gradients, thus facilitating the edge-aware property. The weighted scheme further promotes the edge awareness of the filter. In order to solve the proposed model, we propose an efficient solution based on the combination of the augmented Lagrange multipliers and the Fourier domain optimization. The GPU implementation of our filter takes 39ms to process a 720P color image on an NVIDIA RTX 3070. We have applied the proposed filter in various tasks, including edge-aware smoothing, edge extraction, image abstraction, and low-light image enhancement. Both the qualitative and quantitative results validate the superiority of the proposed filter.