Efficient Arbitrary-Scale Image Super-Resolution via Functional Tensor Decomposition

Existing arbitrary-scale super-resolution (ASSR) methods suffer from quadratic computational complexity w.r.t. image scale due to the reliance on multi-layer perceptrons (MLPs) to query dense spatial coordinate matrices. The inefficiency becomes particularly pronounced when extending to high-dimensional imaging modalities. To address these limitations, we propose a novel functional tensor decomposition (FTD) framework that fundamentally reconfigures the computational paradigm for ASSR. Specifically, we propose 1) a separation mechanism that employs distinct MLPs to query separable spatial coordinate vectors, substantially reducing decoder MLP invocations, and 2) functional tensor Tucker or CP decompositions for efficient factor matrix integration. The FTD framework delivers three key advantages: 1) Superior scalability to high-dimensional imaging modalities, such as hyperspectral images (HSIs), by virtue of the FTD design; 2) Significantly enhanced inference speed across scales; 3) Faster convergence towards a desired training model. Extensive experiments validate FTD's exceptional performance in HSI joint spatial-spectral ASSR, achieving up to 90.04% reduction in inference time and substantial performance improvements. For conventional image ASSR, our method improves both inference speed and convergence efficiency, achieving up to 88.82% inference time reduction and superior few-shot generalization capabilities due to faster convergence.