结合高阶非凸全变差与重叠组稀疏性去除脉冲噪声

Removal of Impulse Noise by Combining Higher Order Non-Convex Total Variation and Overlapping Group Sparsity

摘要: 为了消除脉冲噪声，一种有效的方法是采用L1范数全变差模型。然而，图像恢复总是会产生阶梯状伪影，此外，L1范数容易对解进行过度惩罚，且对脉冲噪声中的异常特征缺乏鲁棒性。因此，本文提出了一种混合正则化方法，旨在有效去除脉冲噪声并消除阶梯效应的同时，又能保留更多边缘细节。本文方法使用L0范数数据保真项有效去除脉冲噪声，重叠组稀疏全变差正则化项消除阶梯效应，而非凸高阶全变差正则化项用于保持恢复图像的清晰度。为了求解这个模型，我们分别采用了具有平衡约束的数学规划方法、逐次逼近最小化方法以及迭代重加权L1算法，并配合交替方向乘子法进行求解。实验结果表明，相较于几种现有方法，在峰值信噪比和结构相似性两项指标上均取得了具有竞争力的性能结果。

Abstract: For eliminating impulse noise, an effective way is to use the L1-norm total variation model. However, the image restoration always yields staircase artifacts. Additionally, the L1-norm tends to over penalize solutions and is not robust to outlier characteristics of impulse noise. Therefore, this paper proposes a hybrid regularization scheme aimed at effectively removing impulse noise and eliminating staircase artifacts while preserving more edge details. The method uses the L0-norm data fidelity to effectively remove impulse noise, the overlapping group sparse total variation regularization to eliminate the staircase artifacts, and the non-convex higher order total variation regularization is used to maintain the sharp restored image. To achieve the goal, we use mathematical program with equilibrium constraints method, the majorization-minimization method, and the iterative re-weighted L1 algorithm, combined with the alternating direction method of multipliers for solving. Experimental results show that, compared with several existing methods, competitive performance results are achieved in terms of both peak signal-to-noise ratio and structural similarity index measure.