Hyperspectral and Multispectral Image Fusion Using Factor Smoothed Tensor Ring Decomposition

Fusing a pair of low-spatial-resolution hyperspectral image (LR-HSI) and high-spatial-resolution multispectral image (HR-MSI) has been regarded as an effective and economical strategy to achieve HR-HSI, which is essential to many applications. Among existing fusion models, the tensor ring (TR) decomposition-based model has attracted rising attention due to its superiority in approximating high-dimensional data compared to other traditional matrix/tensor decomposition models. Unlike directly estimating HR-HSI in traditional models, the TR fusion model translates the fusion procedure into an estimate of the TR factor of HR-HSI, which can efficiently capture the spatial–spectral correlation of HR-HSI. Although the spatial–spectral correlation has been preserved well by TR decomposition, the spatial–spectral continuity of HR-HSI is ignored in existing TR decomposition models, sometimes resulting in poor quality of reconstructed images. In this article, we introduce a factor smoothed regularization for TR decomposition to capture the spatial–spectral continuity of HR-HSI. As a result, our proposed model is called factor smoothed TR decomposition model, dubbed FSTRD . In order to solve the suggested model, we develop an efficient proximal alternating minimization algorithm. A series of experiments on four synthetic datasets and one real-world dataset show that the quality of reconstructed images can be significantly improved by the introduced factor smoothed regularization, and thus, the suggested method yields the best performance by comparing it to state-of-the-art methods.