Low-Rank Tensor Decomposition With Smooth and Sparse Regularization for Hyperspectral and Multispectral Data Fusion

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.