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-variationbased 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.
Fusion of hyperspectral and multispectral imagery data is utilized to reconstruct a superresolution image with high spectral and spatial resolution, which plays a significant role in remote sensing image processing. Conversely, hyperspectral and multispectral data can be modeled as two low-dimensional subspaces by respectively spatially and spectrally degrading the desired image. A representative method is called coupled non-negative matrix factorization (CNMF) based on a Gaussian observation model, but it is an ill-posed inverse problem. In addition, from the perspective of matrix factorization, the matrixing process of hyperspectral and multispectral cube data generally results in the loss of structural information and performance degradation. To address these issues, this article proposes a proximal minimum-volume expression to regularize the convex simplex, enclosing all reconstructed image pixels instead of lowdimensional subspace data. Then, we incorporate sparse and proximal regularizers into the original CNMF to reformulate the fusion problem as a dynamical system via proximal alternating optimization. Finally, the alternating direction method of multipliers is adopted to split the variables for the closed-form solutions that are further reduced in computational complexity. The experimental results show that the proposed algorithm in this paper performs better than the state-of-the-art fusion methods in most cases, which verifies the effectiveness and efficiency of this proposed algorithm in yielding high-fidelity reconstructed images.
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