Abstract
The fusion of hyperspectral and multispectral images is an effective way to obtain hyperspectral super-resolution images with high spatial resolution. A hyperspectral image is a datacube containing two spatial dimensions and a spectral dimension. The fusion methods based on non-negative matrix factorization need to reshape the three-dimensional data in matrix form, which will result in the loss of data structure information. Owing to the non-uniqueness of tensor rank and noise inference, there is a lot of redundant information in the spatial and spectral subspaces of tensor decomposition. To address the above problems, this article incorporates smooth and sparse regularization into low-rank tensor decomposition to reformulate a fusion method, in which the logarithmic sum function is adopted to eliminate the effect of redundant information and shadows in both spatial and spectral domains. Moreover, the total-variation-based regularizer is employed to vertically smooth the spectral factor matrix to suppress the noise. Then, the alternating direction multiplier method, as well as the conjugate gradient approach, is utilized to design a set of efficient algorithms by complexity reduction. The experimental results demonstrate that the proposed method can yield better performance than the state-of-the-art benchmark algorithms in most cases, which also verifies the effectiveness of incorporated regularizers in low signal-to-noise ratio environments for hyperspectral super-resolution images.
Highlights
Ahyper-spectral image (HSI) is a three-dimensional datacube with abundant spatial and spectral information, which is widely used to accurately identify substance and classification in remote sensing [1]–[3]
Because the non-uniqueness of tensor rank generally result in the redundant information, this article proposes a fusion method based on low-rank tensor decomposition to eliminate the redundancy and suppress the shadow and/or noise, in which smooth and sparse regularizers are imposed on the spectral factor matrix and the core tensor
To address the structure loss of hyperspectral and multispectral data cubes and suppress the effect of noise and redundant information, this article proposes a low-rank decomposition-based fusion method with total variation and sparse regularization to achieve the fusion of HSIs and MSIs for hyperspectral super-resolution images
Summary
Ahyper-spectral image (HSI) is a three-dimensional datacube with abundant spatial and spectral information, which is widely used to accurately identify substance and classification in remote sensing [1]–[3]. In order to preserve spatial–spectral structures in the LR-HSIs and the HR-MSIs effectively, Zhang et al [30] put forward an image fusion method based on spatial–spectral-graph-regularized low-rank tensor decomposition to preserve the spatial correlation and the spectral structure in the fused images by deriving two graphs in the spatial and spectral domains, respectively. Dian et al [39] developed a subspace-based low-tensor method with multi-rank regularization, which fully exploited the spectral correlations and non-local similarities in the HRHSI He et al [40], [41] developed a hyperspectral superresolution based on a coupled tensor ring model to decompose a higher-order tensor into a series of three-dimensional tensors. To address the effect of redundant information and noise, this article proposes a novel fusion method based on low-rank Tucker tensor decomposition to fuse the LR-HSI and HR-MSI for the hyperspectral super-resolution image. I stands for the identity matrix with proper dimensions. vec(C) stands for the vector of a tensor C. ⊗ represents the Kronecker product. [·]+ stands for the orthogonal projection onto the non-negative orthant of Euclidean space. represents the componentwise inequality operation. ×n denotes the mode-n product. · stands for the simplified form of mode-n product. · ∗ denotes the nuclear norm
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