Integrated Spatio-Spectral–Temporal Fusion via Anisotropic Sparsity Constrained Low-Rank Tensor Approximation

Although spatio-spectral and spatio-temporal fusion has been well explored, few efforts are made on integrating spatio-spectral–temporal features. As an intrinsic prior, low tensor rank has been successfully taken into effect by current fusion models, most of which, however, resort to establishing an overall low-rank norm without performing factorization techniques and thus have trouble capturing the latent high-order structure of hyperspectral data cube. To address that, a novel anisotropic sparsity (AS) tensor norm is developed to make the rank minimization a learnable process under the Tucker decomposition. The AS norm enables the model to minimize the multilinear tensor ranks if imposed on the core tensor after factorization; hence, it significantly improves the model’s fusion performance. In the temporal domain, a Hadamard-product-based variability descriptor is incorporated into the fusion model to map the former information to the current time. In addition, piecewise smooth prior of the Tucker factors is employed by extra regularizers as supplement to the loss of spatial information. With the proximal differential matrix being developed for optimization, the proposed method reaches state-of-the-art results on both spatio-spectral and spatio-spectral–temporal fusion at a low computational cost.