各向异性全变分图像去噪算法

图像去噪是图像复原问题中的重要研究内容之一，在此过程中图像的高频部分易受到破坏。针对这一情况，通过引入不同的权重参数惩罚x与y方向上的梯度算子，提出修正的各向异性全变分去噪模型。引入的权重参数具有局部自适应性，可以使模型对应欧拉方程在图像切线与法向方向的扩散具有更鲁棒的各向异性扩散能力，可以达到保护图像细节的目的。另外，提出的模型是具有可分裂结构的非光滑凸优化问题，采用算子分裂技术将其转化为多个易求解的子问题，并在交替方向乘子法的框架下求解，从而保证了算法在理论上的收敛性。与现阶段其他变分型的复原模型相比，所提出的模型在有效抑制噪声的同时能有效地保持图像的局部结构特征。对于分块效果明显，噪声水平较低的图像去噪结果十分显著；对于分块效果不明显，图像细节较多的图像，该模型依然有效。

Image Denoising via Anisotropic Total-Variation-Based Method

Image denoising is an important filed in the image restoration problems. However, the information with the high frequency is easily destroyed in this process. In order to overcome it, this paper proposes a new anisotropic total-variatrion-based denoising mode by introducing a weighted parameter to penalty the gradient operator along with the x-axis and y-axis directions. Since the weighted parameters are locally adaptive, which can enhance the diffusion of the corresponding Euler-Lagrangian of the proposed model along with the edge direction, the proposed model can preserve the image details. In addition, the proposed model is nonconvex and separable, the alternating direction multiplier method can be employed to solve it and the convergence can be also kept from the analysis theory. Some numerical comparisons show that the proposed model can suppress the noise and preserve local structure effectively by comparing with other well-known total-variation-based models.