$L_{1}$-Regularized Reconstruction Model for Edge-Preserving Filtering

Smoothing images while preserving salient edges is a crucial task in computational photography. Existing edge-preserving filters suffer from various artifacts, such as halos, gradient reversals, and intensity shifts. Observing that various artifacts are strongly related to salient edges with large gradients, we propose a continuous mapping function to process the gradients. The proposed function is literally edge-preserving, i.e., it keeps large gradients intact while attenuating small gradients. We propose an L₁-regularized reconstruction model based on the processed gradients for edge-preserving image filtering. The L₁-regularization facilitates the edge-preserving property in the reconstructed results. To solve the proposed L₁-regularized model, we implement an efficient algorithm based on the alternating direction method of multipliers (ADMM) and Fourier domain optimization. We have conducted qualitative and quantitative experiments to evaluate the proposed filter. The results demonstrate that our filter better handles various artifacts and delivers superior image quality on various applications. The proposed filter is highly efficient, our GPU implementation takes 70ms to process a color image with 1 megapixel on an NVIDIA GTX 1070 GPU.