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

Abstract

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 thus have trouble capturing the latent high-order structure of hyperspectral data cube. To address that, a novel Anisotropicly Sparse (AS) tensor norm is developed to make the rank minimization a learnable process under Tucker decomposition. The AS norm enables the model to minimize the multi-linear 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 current time. Additionally, piece-wise smooth prior of the Tucker factors is employed by extra regularizers as supplement to the loss 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 low computational cost.