Fast algorithm for image denoising with different boundary conditions

In recent works several authors have considered the L1 fidelity term, the L2 fidelity term and the combined L1 and L2 fidelity term for denoising models, and they used the fast Fourier transform (FFT) algorithm which can only use periodic boundary conditions (BCs). In this paper, we combine the augmented Lagrangian method (ALM) and the symmetric Red-Black Gauss-Seidel (SRBGS) method to propose three algorithms that are suitable for different BCs. Experimental results show that the proposed algorithms are effective and the model with the combined L1 and L2 fidelity term demonstrates more advantages in efficiency and accuracy than other models with the L1 fidelity term or the L2 fidelity term.