TRT: Harnessing Tensor Ring Transformer for Hyperspectral Image Super-Resolution

Deep unfolding networks (DUNs) have recently emerged as a promising approach for hyperspectral image super-resolution (HSISR) by combining the benefits of nonlinear deep learning architectures with interpretable optimization techniques. Despite their advantages, current DUNs face significant challenges, particularly in approximating degradation matrices across both spatial and spectral dimensions, which results in complex and cumbersome model construction. By analyzing the difference between the upsampled low-resolution hyperspectral images (LRHS) and the true target image, we observed that the residual image exhibits strong sparsity, akin to noise. Leveraging this insight, we reformulate the HSISR problem as a robust principal component analysis (RPCA)-based denoising task, effectively eliminating the need for the complex approximation of spatial degradation matrix and its transpose. In addition, we introduce a Tensor Ring Transformer based on multilinear products as the prior term, wherein tokens are mapped to a tensor ring factor domain and the traditional dot product is replaced with a multilinear tensor ring product. This significantly reduces the computational complexity of the Transformer model, from O(N 2 d) to O(N r 2 ), where the tensor ring rank r is significantly smaller than d, while maintaining the expressive power. The proposed Tensor Ring Transformer integrates both Softmax and linear attention mechanisms, striking a balance between interpretability-characteristic of model-based approaches-and the efficiency inherent in deep learning techniques. Experimental results across multiple remote sensing datasets demonstrate the superiority of the designed Tensor Ring Transformer, achieving substantial improvements in image quality and computational efficiency compared to current state-of-the-art methods.