Superpixel-Informed Continuous Low-Rank Tensor Representation for Multi-Dimensional Data Recovery

Low-rank tensor representation (LRTR) has emerged as a powerful tool for multidimensional data processing. However, classical LRTR methods face two critical limitations: (1) they assume holistic data is low-rank, which is often violated in real-world scenarios with significant spatial variations; and (2) they are constrained to discrete meshgrid data, limiting flexibility. To overcome these limitations, we propose a Superpixel-informed Continuous Low-Rank Tensor Representation (SCTR) framework. Our approach introduces two innovations: First, motivated by the observation that semantically coherent regions exhibit stronger low-rank characteristics than holistic data, we employ superpixels as basic modeling units. Second, we propose a novel model where superpixel-specific factor matrices are parameterized by a shared neural network with specialized heads. This framework efficiently captures both cross-superpixel commonalities and within-superpixel variations, yielding compact yet expressive representations. Extensive experiments demonstrate that SCTR achieves state-of-the-art performance, with PSNR gains of 3-5 dB on multispectral images. Notably, compared to leading hybrid methods, SCTR reduces peak memory consumption by ∼37× while maintaining superior reconstruction quality.