基于Lp伪范数和高阶OGS全变分的椒盐噪声去除

Salt and pepper noise denoising using high-order overlapping group sparsity with Lp-pseudo-norm

全变分(TV)模型广泛应用于椒盐噪声的去除。然而,TV模型中存在着严重的阶梯效应。近年来,由于低阶交叠组稀疏(LOGS)全变分能够很好地抑制阶梯效应,受到了越来越多的关注,但仍有改进空间。实际上,其只考虑一阶图像梯度的先验信息,而忽略了高阶图像梯度的先验信息。为了进一步提高恢复图像的质量,提出了一种结合Lp伪范数的高阶OGS全变分,在利用高阶梯度的OGS约束更好地描述图像梯度稀疏先验的同时,还利用Lp伪范数的强稀疏诱导能力更好地描述椒盐噪声的稀疏性。该模型采用交替方向乘子法求解,并将模型分解为若干个子问题求解。最后,通过实验验证了该模型的正确性,并结合峰值信噪比、结构相似性度和梯度幅值相似性偏差对模型的恢复性能进行了评价。实验结果表明,该方法相比一些先进的去噪模型具有很强的竞争力。

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.