Learning How Factors Interact: Conditioned Tensor Products for Unsupervised Hyperspectral Super-Resolution

Hyperspectral image super-resolution (HSI-SR) aims to reconstruct a high-spatial-resolution hyperspectral image from a low-resolution hyperspectral observation and a registered high-resolution multispectral image (HR-MSI). Existing unsupervised factorized priors typically employ globally fixed factor interactions and discrete band-wise spectral parameterizations, limiting adaptation to spatially varying guidance and ordered spectral variation. To address these limitations, we propose CPF-RFJ, a unified test-time framework that jointly adapts factor interactions and spectral representations. We first propose the Conditioned Tensor Product (CTP), which allows auxiliary observations to select the multiplication law between latent factors, thereby shifting conditioning from feature representations to the algebraic interaction itself. Building upon CTP, the Conditioned Product Factorization (CPF) enables the local HR-MSI observation at each spatial location to govern spectral–spatial factor coupling. We further develop a Pole-Free Rational Fractional-Jacobi Kolmogorov–Arnold Network (PF-RFJ-KAN), which models the spectral factor as a coordinate-defined function through signed fractional spectral reparameterization, an adaptive Jacobi basis family, and a structurally pole-free rational representation. The complete CPF-RFJ model is optimized directly from the observations without external training data or target HR-HSI supervision. Extensive experiments demonstrate state-of-the-art spatial–spectral reconstruction performance against representative training-data-free methods.