Color image restoration and inpainting via multi-channel total curvature

The multi-channel total variation (MTV) based on L2 norm is capable of preserving object edges and smoothing flat regions in color images. However, it will lead to loss of image contrast, smear object corners, and produce staircase artifacts in the restored images. In order to remedy these side effects, we propose a new multi-channel total curvature model based on L1 norm (MTC-L1) for vector-valued image restoration in this paper. By introducing some auxiliary variables and Lagrange multipliers, we develop a fast algorithm based alternating direction method of multipliers (ADMM) for the proposed model, which allows the use of the fast Fourier transform (FFT), generalized soft threshold formulas and projection method. Extensive experiments have been conducted on both synthetic and real color images, which validate the proposed approach for better restoration performance, and show advantages of the proposed ADMM over algorithms based on traditional gradient descent method (GDM) in terms of computational efficiency.