t-Linear Tensor Subspace Learning for Robust Feature Extraction of Hyperspectral Images

Subspace learning has been widely applied for feature extraction of hyperspectral images (HSIs) and achieved great success. However, the current methods still leave two problems that need to be further investigated. First, those methods mainly focus on finding one or multiple projection matrices for mapping the high-dimensional data into a low-dimensional subspace, which can only capture the information from each direction of high-order hyperspectral data separately. Second, the performance of feature extraction is barely satisfactory when the hyperspectral data is severely corrupted by noise. To address these issues, this article presents a t-linear tensor subspace learning (tLTSL) model for robust feature extraction of HSIs based on t-product projection. In the model, t-product projection is a new defined tensor transformation way similar to linear transformation in vector space, which can maximally capture the intrinsic structure of tensor data. The integrated tensor low-rank and sparse decomposition can effectively remove the noise corruption and the learned t-product projection can directly transform the high-order hyperspectral data into a subspace with information from all modes comprehensively considered. Moreover, a proposition related to tensor rank is proofed for interpreting the meaning of the tLTSL model. Extensive experiments are conducted on two different kinds of noise (i.e., simulated and real noise) corrupted HSI data, which validate the effectiveness of tLTSL.