Nonlocal TV-L1 Inpainting Model and its Augmented Lagrangian Algorithm

Abstract

Nonlocal differential operators have been extensively applied to variational models for image restoration due to its texture-preserving capability. In this paper, we propose a nonlocal TV (total variation)-L1 model for texture image inpainting, which, technically, combines nonlocal operators for regularization term and L1 norm for data term. The former is used to regularize texture and the latter to preserve contrast of images. In addition, we develop augmented Lagrangian algorithm for proposed model by introducing nonlocal auxiliary variable and Lagrangian multiplier. Finally, extensive experiments on synthetic and real texture images are presented to validate the effectiveness and efficiency of our proposed model and algorithm.