  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.
