High-order TVL1-based images restoration and spatially adapted regularization parameter selection

The total variation (TV) model with an L1L1-fidelity term (TVL1) is a famous model to recover blurred and impulse noisy image with edges-preserving. However, it usually causes some staircase effects. In this paper, we propose a hybrid model combining the TV regularizer and the high-order TV regularizer with the TVL1 model (HTVL1) for blurred and salt-and-pepper impulse noisy image restoration. The solving algorithm is under the frame-work of alternating direction method of multipliers (ADMM). In addition, a spatially adapted regularization parameter selection scheme is also used. Numerical results show that the quality of restored images by the proposed methods is competitive with the quality of restored images by some other existing methods.