The total variation (TV) regularization has been widely used in various applications related to hyperspectral (HS) signal and image processing due to its potential in modeling the underlying smoothness of HS data. However, most existing TV norms usually tend to generate spatial oversmoothing or artifacts. To this end, we propose a novel $l_{0}$ - $l_{1}$ hybrid TV ( $l_{0}$ - $l_{1}$ HTV) regularization with the applications to HS mixed noise removal and compressed sensing (CS). More specifically, $l_{0}$ - $l_{1}$ HTV can be regarded as a globally and locally integrated TV regularizer, where the $l_{0}$ gradient constraint is incorporate into the $l_{1}$ spatial–spectral TV ( $l_{1}$ -SSTV). $l_{1}$ -SSTV is capable of exploiting the local structure information across both spatial and spectral domains, while the $l_{0}$ gradient can promote a globally spectral–spatial smoothness by directly controlling the number of nonzero gradients of HS images. This efficient combination considers more comprehensive prior knowledge of HS images, yielding sharper edge preservation and resolving the above drawbacks of existing pure TV norms. More significantly, $l_{0}$ - $l_{1}$ HTV can be easily injected into HS-related processing models, and an effective algorithm based on the alternating direction method of multipliers (ADMM) is developed to solve the optimization problems. Extensive experiments conducted on several HS data sets substantiate the superiority and effectiveness of the proposed method in comparison with many state-of-the-art methods.

中文翻译：

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l₀-l₁混合总变异正则化及其在高光谱图像混合降噪和压缩感知上的应用

总变差 (TV) 正则化因其在建模 HS 数据的潜在平滑度方面的潜力，已广泛用于与高光谱 (HS) 信号和图像处理相关的各种应用中。然而，大多数现有的电视规范通常倾向于产生空间过度平滑或伪影。为此，我们提出了一部小说 $l_{0}$ —— $l_{1}$ 混合电视（ $l_{0}$ —— $l_{1}$ HTV) 正则化与 HS 混合噪声去除和压缩感知 (CS) 的应用。进一步来说， $l_{0}$ —— $l_{1}$ HTV 可以看作是一个全局和局部集成的 TV 正则化器，其中 $l_{0}$ 梯度约束被纳入 $l_{1}$ 空间光谱电视（ $l_{1}$ -SSTV）。 $l_{1}$ -SSTV 能够利用跨空间和光谱域的局部结构信息，而 $l_{0}$ 梯度可以通过直接控制 HS 图像的非零梯度的数量来促进全局光谱空间平滑度。这种有效的组合考虑了更全面的 HS 图像先验知识，产生了更清晰的边缘保留并解决了现有纯 TV 规范的上述缺点。更重要的是， $l_{0}$ —— $l_{1}$ HTV 可以很容易地注入到 HS 相关的处理模型中，并开发了一种基于乘法器交替方向法 (ADMM) 的有效算法来解决优化问题。与许多最先进的方法相比，在几个 HS 数据集上进行的大量实验证实了所提出的方法的优越性和有效性。