Hyperspectral Image Fusion via a Novel Generalized Tensor Nuclear Norm Regularization

Recently, low-rank tensor regularization has received more and more attention in hyperspectral and multispectral fusion (HMF). However, these methods often suffer from inflexible low-rank tensor definition and are highly sensitive to the permutation of tensor modes, which hinder their performance. To tackle this problem, we propose a novel generalized tensor nuclear norm (GTNN)-based approach for the HMF. First, we define a novel GTNN by extending the existing third-mode-based tensor nuclear norm (TNN) to arbitrary mode, which conducts the Fourier transform on an arbitrary single mode and then computes the TNN for each mode. In this way, we can not only capture more extensive correlations for the three modes of a tensor, and also omit the adverse effect of permutation of tensor modes. To utilize the correlations among spectral bands, the high-resolution hyperspectral image (HSI) is approximated as low-rank spectral basis multiplication by coefficients, and we estimate the spectral basis by conducting singular-value decomposition (SVD) on HSI. Then, the coefficients are estimated by addressing the proposed GTNN regularized optimization. In specific, to exploit the non-local similarities of the HSI, we first cluster the patches of the coefficient into a 3-D, which contains spatial, spectral, and non-local modes. Since the collected tensor contains the strong non-local spatial–spectral similarities of the HSI, the proposed low-rank tensor regularization is imposed on these collected tensors, which fully model the non-local self-similarities. Fusion experiments on both simulated and real datasets prove the advantages of this approach. The code is available at https://github.com/renweidian/GTNN.