Hyperspectral Imaging (HSI) serves as an important technique in remote sensing. However, high dimensionality and data volume typically pose significant computational challenges. Band selection is essential for reducing spectral redundancy in hyperspectral imagery while retaining intrinsic critical information. In this work, we propose a novel hyperspectral band selection model by decomposing the data into a low-rank and smooth component and a sparse one. In particular, we develop a generalized 3D total variation (G3DTV) by applying the $\ell_1^p$-norm to derivatives to preserve spatial-spectral smoothness. By employing the alternating direction method of multipliers (ADMM), we derive an efficient algorithm, where the tensor low-rankness is implied by the tensor CUR decomposition. We demonstrate the effectiveness of the proposed approach through comparisons with various other state-of-the-art band selection techniques using two benchmark real-world datasets. In addition, we provide practical guidelines for parameter selection in both noise-free and noisy scenarios.

翻译：高光谱成像（HSI）是遥感领域的重要技术。然而，高维度和大数据量通常带来显著的计算挑战。波段选择对于降低高光谱影像中的光谱冗余，同时保留内在关键信息至关重要。本文提出一种新颖的高光谱波段选择模型，将数据分解为低秩平滑分量与稀疏分量。具体而言，我们通过将$\ell_1^p$-范数应用于导数，发展了一种广义三维全变差（G3DTV）方法来保持空间-光谱平滑性。采用交替方向乘子法（ADMM），我们推导出一种高效算法，其中张量低秩性由张量CUR分解隐含实现。通过与多种其他先进波段选择技术在两个基准真实世界数据集上的对比，我们展示了所提方法的有效性。此外，我们为无噪声和含噪声场景下的参数选择提供了实用指南。