Weighted quasi-elastic net gradient regularization for image smoothing

The L0 filter is a prevalent edge-preserving image filter in computer vision and image processing due to its strong edge-preserving ability. However, due to the extremely sparse gradient regularization, it suffers from severe gradient reversal artifacts, and it tends to keep undesired high-contrast oscillations. Furthermore, the original L0 filter does not support joint image filtering, i.e., it can only smooth the input under the guidance of itself, rather than another image. We propose a quasi-elastic net gradient regularization. It imposes an extra L2-regularization to the original model of the L0 filter to suppress high-contrast oscillations. Furthermore, we introduce a weighted scheme to the model so that our filter supports the joint image filtering scheme. We show that our model can be solved efficiently with an iterative algorithm based on half-quadratic splitting and Fourier domain optimization. We have conducted extensive experiments across multiple applications to evaluate the proposed filter, and both quantitative and qualitative results indicate the effectiveness of the proposed filter. Finally, the proposed filter is efficient and able to process 720P color images at interactive rates on a modern GPU.