The problem of multispectral and hyperspectral image fusion (MHF) is to reconstruct images by fusing the spatial information of multispectral images and the spectral information of hyperspectral images. Focusing on the problem that the hyperspectral canonical polyadic decomposition model and the Tucker model cannot introduce the physical interpretation of the latent factors into the framework, it is difficult to use the known properties and abundance of endmembers to generate high-quality fusion images. This paper proposes a new fusion algorithm. In this paper, a coupled non-negative block-term tensor model is used to estimate the ideal high spatial resolution hyperspectral images, its sparsity is characterized by adding 1-norm, and total variation (TV) is introduced to describe piecewise smoothness. Secondly, the different operators in two directions are defined and introduced to characterize their piecewise smoothness. Finally, the proximal alternating optimization (PAO) algorithm and the alternating multiplier method (ADMM) are used to iteratively solve the model. Experiments on two standard datasets and two local datasets show that the performance of this method is better than the state-of-the-art methods.

Multispectral and hyperspectral image fusion (MHF) aims to reconstruct high-resolution hyperspectral images by fusing spatial and spectral information. Unlike the traditional canonical polyadic decomposition and Tucker decomposition models, the block-term tensor decomposition model is able to improve the quality of fused images using known endmember and abundance information. This paper presents an improved hyperspectral image fusion algorithm. Firstly, the two abundance matrices are combined into a single bulk matrix to promote structural sparsity by introducing the $L_{2,1}$-norm to eliminate the scaling effects present in the model. Secondly, the counter-scaling effect is eliminated by adding the $L_2$-norm to the endmember matrix. Finally, the chunk matrix and the endmember matrix are coupled together, and the matrix is reorganized by adding the $L_{2,1}$-norm to the matrix to facilitate chunk elimination and solved using an extended iterative reweighted least squares (IRLS) method, focusing on the problem of the inability to accurately estimate the tensor rank in the chunk-term tensor decomposition model and the noise/artifact problem arising from overestimation of rank. Experiments are conducted on standard and local datasets, and the fusion results are compared and analyzed in four ways: visual result analysis, metric evaluation, time of the algorithm, and classification results, and the experimental results show that the performance of the proposed method is better than the existing methods. An extensive performance evaluation of the algorithms is performed by conducting experiments on different datasets. The experimental results show that the proposed algorithm achieves significant improvements in terms of reconstruction error, signal-to-noise ratio, and image quality compared with the existing methods. Especially in the case of a low signal-to-noise ratio, the proposed algorithm shows stronger robustness and accuracy. These results show that the proposed algorithm has significant advantages in dealing with multispectral high-resolution hyperspectral data.

The multispectral and hyperspectral image fusion (MHF) technique is designed to address the challenge of integrating the spatiotemporal characteristics of multispectral images with those of hyperspectral images. In the initial stages, the image to be fused is primarily decomposed into endmembers and abundances using a matrix decomposition method. This approach, however, may disrupt the correlation of spectral data. Subsequently, tensor decomposition-based methods emerged, with the most representative being canonical polyadic decomposition and Tucker decomposition. These methods are widely applied to the MHF problem due to their good recoverability. However, they lack the ability to introduce the physical interpretation of potential factors into the framework, and it is difficult to improve the quality of the fused image by utilizing the physical properties of the endmembers. Consequently, we employ a block term tensor decomposition algorithm based on sparse regularization to estimate the optimal high spatial resolution hyperspectral image. First, the abundance information is reconstructed into a chunk matrix, and its sparsity is characterized by introducing the l2,1 norm to eliminate the scaling effect present in the model. Second, the endmembers’ matrix sparsity is facilitated by the introduction of the row sparsity of the l2,1 norm regularization, which eliminates the inverse scaling effect present in the model. Finally, the model is solved using the conjugate alternating iteration algorithm. Experiments on three standard datasets and two local datasets demonstrate that this method outperforms state-of-the-art methods.