IEEE Trans Image Process. 2014 Dec;23(12):5531-44. doi: 10.1109/TIP.2014.2364141.
Nonlocal total variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the structure tensor (ST) resulting from the gradient of a multicomponent image. The proposed approach allows us to penalize the nonlocal variations, jointly for the different components, through various l(1, p)-matrix-norms with p ≥ 1. To facilitate the choice of the hyperparameters, we adopt a constrained convex optimization approach in which we minimize the data fidelity term subject to a constraint involving the ST-NLTV regularization. The resulting convex optimization problem is solved with a novel epigraphical projection method. This formulation can be efficiently implemented because of the flexibility offered by recent primal-dual proximal algorithms. Experiments are carried out for color, multispectral, and hyperspectral images. The results demonstrate the interest of introducing a nonlocal ST regularization and show that the proposed approach leads to significant improvements in terms of convergence speed over current state-of-the-art methods, such as the alternating direction method of multipliers.
非局部全变差（NLTV）已成为图像恢复问题变分方法中的一种有用工具。在本文中，我们通过利用多分量图像的梯度产生的结构张量（ST），将基于 NLTV 的正则化方法扩展到多分量图像。通过使用各种 p≥1 的 l(1, p)-矩阵范数，我们可以对不同分量的非局部变化进行联合惩罚。为了方便选择超参数，我们采用了一种约束凸优化方法，在该方法中，我们最小化数据保真项，同时满足涉及 ST-NLTV 正则化的约束。通过一种新的图论投影方法来解决这个凸优化问题。由于最近的原始对偶近端算法提供的灵活性，这种公式可以有效地实现。针对彩色、多光谱和高光谱图像进行了实验。结果表明，引入非局部 ST 正则化是有意义的，并表明与交替方向乘子法等现有最先进方法相比，所提出的方法在收敛速度方面有显著的提高。
