Non‐Local Sparse and Low‐Rank Regularization for Structure‐Preserving Image Smoothing

This paper presents a new image smoothing method that better preserves prominent structures. Our method is inspired by the recent non‐local image processing techniques on the patch grouping and filtering. Overall, it has three major contributions over previous works. First, we employ the diffusion map as the guidance image to improve the accuracy of patch similarity estimation using the region covariance descriptor. Second, we model structure‐preserving image smoothing as a low‐rank matrix recovery problem, aiming at effectively filtering the texture information in similar patches. Lastly, we devise an objective function, namely the weighted robust principle component analysis (WRPCA), by regularizing the low rank with the weighted nuclear norm and sparsity pursuit with L1 norm, and solve this non‐convex WRPCA optimization problem by adopting the alternative direction method of multipliers (ADMM) technique. We experiment our method with a wide variety of images and compare it against several state‐of‐the‐art methods. The results show that our method achieves better structure preservation and texture suppression as compared to other methods. We also show the applicability of our method on several image processing tasks such as edge detection, texture enhancement and seam carving.