Relaxed Low Tensor Train Rank Representation with Structural Smoothness for Hyperspectral Image Super-resolution

We propose a super-resolution method for hyperspectral image (HSI) that utilizes relaxed low tensor train (TT) rank representation with structural smoothness in this paper. Nonlocal similarity is exploited by grouping the similar HSI cubes. The 4D tensor formed by similar cubes is highly low-rank. The good balanced matricisation scheme of TT and rational shrinkage strategy of log-sum norm motivated us to design the relaxed low TT rank regularization in the model. It can learn the spatial and spectral correlations hidden in these 4-D tensors. The structural smoothness is captured by the three-dimensional total variation (3DTV) regularization in the model. We solve our model via ADMM. Compared with existing state-of-art super-resolution approaches, quantitative and qualitative reconstruct results on typical HSI data indicate that our method is effective.