Abstract
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.
Abstract (translated)
超分辨率成像（HSI）在遥感中是一个重要的技术。然而，高维度和数据量通常会带来显著的计算挑战。带选择对于在超分辨率图像中减少光谱重叠并保留固有关键信息至关重要。在这项工作中，我们提出了一种新的超分辨率带选择模型，通过将数据分解为低秩和平滑组件和稀疏组件。特别，我们通过应用$\ell_1^p$范数来保留空间-频谱平滑性，开发了一个通用的3D总方差（G3DTV）。通过采用交替方向乘子法（ADMM），我们推导出一种高效的算法，其中张量低秩性隐含于张量CUR分解。我们通过与各种最先进的带选择技术进行比较，证明了所提出方法的有效性。此外，我们还为噪声无党和噪声场景提供了参数选择的实际建议。
URL
https://arxiv.org/abs/2405.00951
