Hyperspectral Band Selection via Tensor Low Rankness and Generalized 3DTV

Hyperspectral band selection plays a key role in reducing the high dimensionality of data while maintaining essential details. However, existing band selection methods often encounter challenges, such as high memory consumption, the need for data matricization that disrupts inherent data structures, and difficulties in preserving crucial spatial–spectral relationships. To address these challenges, we propose a tensor-based band selection model using Generalized 3D Total Variation (G3DTV), which utilizes the ℓ1p norm to promote smoothness across spatial and spectral dimensions. Based on the Alternating Direction Method of Multipliers (ADMM), we develop an efficient hyperspectral band selection algorithm, where the tensor low-rank structure is captured through tensor CUR decomposition, thus significantly improving computational efficiency. Numerical experiments on benchmark datasets have demonstrated that our method outperforms other state-of-the-art approaches. In addition, we provide practical guidelines for parameter tuning in both noise-free and noisy data scenarios. We also discuss computational complexity trade-offs, explore parameter selection using grid search and Bayesian Optimization, and extend our analysis to evaluate performance with additional classifiers. These results further validate the proposed robustness and accuracy of the model.