Edge-preserving smoothing using the truncated lp minimization

Edge-preserving smoothing is a fundamental task in visual processing and computational photography. This paper presents a nonconvex variational optimization model for edge-preserving smoothing, using a truncated l(p) function as the regularization term and the weighted l(2) norm as the fidelity term. The truncated l(p) function penalizes gradients below a given threshold, while the weighted l(2) norm is preferred over the l(1) and l(2) norms. The proposed model can preserve the salient edges of the input image and eliminate insignificant details. To solve the proposed nonconvex model, we design an effective algorithm based on the alternating direction method of multipliers (ADMM). The effectiveness of the proposed method is demonstrated by variety of applications, including texture smoothing, clip-art compression artifact removal, image abstraction, image denoising, high dynamic range (HDR) tone mapping, detail enhancement, and flash and no-flash image restoration.