Abstract: The total variation (TV) model is widely employed to remove salt and pepper noise. However, there is a serious staircase effect on the TV model. Recently, low-order overlapping group sparsity (LOGS) has received increasing attention due to the great performance in the suppression of the staircase effect. It is necessary to point out that there is still room for the improvement of LOGS total variation denoising model. In fact, the LOGS-based denoising model only takes into account the prior of the first-order image gradients and ignores the prior of the high-order image gradients. To further improve the quality of the recovery image, the author proposed a high-order OGS with the Lp-pseudo-norm. On the one hand, the overlapping group sparsity constraint of the high-order gradient can better describe the prior sparsity of image. On the other hand, the Lp-pseudo-norm was adopted to describe the sparsity of the salt and pepper noise, because of the strong sparsity inducing capacity. The alternating direction method of multipliers was employed to separate the proposed model into several sub-problems for the solving process. Finally, the numerical experiments were carried out to verify the proposed model, while the peak signal to noise ratio (PSNR), structural similarity (SSIM), and gradient magnitude similarity deviation (GMSD) were incorporated to evaluate the recovery performance. The experimental results prove that the proposed method is more competitiveness than some state-of-the-art denoising models. 

Key words:  , image denoising, overlapping group sparsity, Lp-pseudo-norm, high order gradient, regular term