Nonconvex regularization for convex image smoothing

• Published in: Signal processing 2023-04, Vol.205, p.108862, Article 108862
• Main Authors: Zhu, Guoliang, Lv, Xiaoguang, Jiang, Le, Sun, Xueman, Fang, Biao
• Format: Article
• Language: English
• Subjects: Convergence; Convex; Image smoothing; MM Algorithm; Nonconvex regularization
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2022.108862

•We propose using three nonconvex penalty functions for image smoothing.•A sufficient condition on the nonconvex regularizers is derived for the strict convexity of the objective functions.•The majorization-minimization algorithm is employed for solving the convex image smoothing models with global convergence.•The comprehensive experiments and comparisons show that the proposed method can achieve high-quality smoothing results. Image smoothing is a fundamental part of many computer vision and graphics. In this paper, to improve the sparsity of the gradient norm of the smoothing image, we use nonconvex penalty functions as regularization terms. A condition on nonconvex regularizers is given to ensure that the objective functions are strictly convex. We apply the powerful majorization-minimization (MM) algorithm for solving the convex image smoothing models. Proof of global convergence for the MM algorithm is provided. The superiority of the proposed method in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM) and visual quality is verified through comprehensive experiments in a variety of applications such as image abstraction, artifact removal, detail enhancement, texture removal, image denoising and high dynamic range (HDR) tone mapping.