Several methods based on Total Variation (TV) have been proposed for Hyperspectral Image (HSI) denoising. However, the TV terms of these methods just use various $l_1$ norms and penalize image gradient magnitudes, having a negative influence on the preprocessing of HSI denoising and further HSI classification task. In this paper, a novel $l_0$ Total Variation ( $l_0$ TV) is first introduced and analyzed for the HSI noise removal framework to preserve more information for classification. We propose a novel Tensor low-rank constraint and $l_0$ Total Variation (TLR- ${l_0}\text{TV}$ ) model in this paper. $l_0$ TV directly controls the number of non-zero gradients and focuses on recovering the sharp image edges. The spectral-spatial information among all bands is exploited uniformly for removing mixed noise, which facilitates the subsequent classification after denoising. Including the Weighted Sum of Weighted Nuclear Norm (WSWNN) and the Weighted Sum of Weighted Tensor Nuclear Norm (WSWTNN), we propose two TLR- ${l_0}\text{TV}$ -based algorithms, namely WSWNN- ${l_0}\text{TV}$ and WSWTNN- ${l_0}\text{TV}$ . The Alternating Direction Method of Multipliers (ADMM) and the Augmented Lagrange Multiplier (ALM) are employed to solve the $l_0$ TV model and TLR- ${l_0}\text{TV}$ model, respectively. In both simulated and real data, the proposed models achieve superior performances in mixed noise removal of HSI. Especially, HSI classification accuracy is improved more effectively after denoising by the proposed TLR- ${l_0}\text{TV}$ method.

中文翻译：

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张量低秩约束和 $ l_0 $ 高光谱图像混合噪声去除的总变化

已经提出了几种基于总变化量（TV）的高光谱图像（HSI）去噪方法。但是，这些方法的电视术语只能使用各种$ l_1 $规范和惩罚图像梯度幅度，对HSI去噪的预处理和进一步的HSI分类任务产生负面影响。在本文中，一本小说$ l_0 $ 总变化（ $ l_0 $ 首先介绍并分析了HSI噪声消除框架，以保留更多信息以进行分类。我们提出了一种新颖的Tensor低秩约束和$ l_0 $ 总差异（TLR- $ {l_0} \ text {TV} $ ）模型。 $ l_0 $ 电视直接控制非零渐变的数量，并专注于恢复清晰的图像边缘。统一利用所有频段之间的频谱空间信息来去除混合噪声，这有助于在降噪后进行后续分类。包括加权核规范的加权和（WSWNN）和加权张量核规范的加权和（WSWTNN），我们提出了两种TLR- $ {l_0} \ text {TV} $ 的算法，即WSWNN- $ {l_0} \ text {TV} $ 和WSWTNN- $ {l_0} \ text {TV} $ 。交替方向乘数法（ADMM）和增强拉格朗日乘数（ALM）用于求解$ l_0 $ 电视型号和TLR- $ {l_0} \ text {TV} $模型。在仿真数据和实际数据中，所提出的模型在消除HSI的混合噪声方面均具有出色的性能。特别是，通过提出的TLR- $ {l_0} \ text {TV} $ 方法。