Spectral Super-Resolution using Spatial-Spectral Residual Operator Networks

Achieving cross-sensor generalization and arbitrary-scale reconstruction with a single model remains challenging in hyperspectral super-resolution (HSR). Although recent methods support arbitrary-scale reconstruction, applying them to new sensors or scales beyond the training range often requires additional data and computation to maintain reconstruction quality. To address these challenges, we propose OmniHSR, which predicts band-shared spatial operators rather than spectral values. Cross-Spectral Mapping (CSM) resamples inputs with any number of bands to fixed reference positions and predicts local operators with Gaussian supports. Continuous Operator-Field Reconstruction (COFR) composes these operators into a continuous field and applies them to all original bands for arbitrary-scale reconstruction. Experiments demonstrate that operator prediction outperforms direct spectral-value prediction on all seven datasets. Trained solely on ARAD with only 0.538M parameters, OmniHSR outperforms all directly transferred baselines on six unseen datasets without target-domain training data or adaptation. Across twelve upsampling factors from $\times2$ to $\times48$, it improves average PSNR on Pavia U and Chikusei by 0.55 dB over the strongest baseline. It also surpasses baselines trained from scratch or adapted on the target sensor and achieves up to $36\times$ faster inference. Our code will be publicly released soon.

Hyperspectral image super-resolution (HSI-SR) aims to recover spatial detail while preserving the spectral shape on which quantitative analysis relies. Recent HSI-SR methods, from repurposed RGB super-resolution backbones to dedicated spectral-spatial architectures, have greatly improved spatial reconstruction. However, overlooking the compact spectral structure of hyperspectral data leaves residual spectral errors, while binding the spectral treatment to each architecture forces it to be rebuilt for every new backbone. Yet the low-dimensional structure of spectra belongs to the data, not to any backbone. Backbones differ in the errors they leave, but not in the structure of the true spectra. One rectifier design can therefore serve any backbone. Building on this insight, we propose the \textbf{S}pectral \textbf{R}ectification \textbf{S}uper-\textbf{R}esolution Network (\textbf{SR$^{2}$-Net}), a model-agnostic rectifier that needs nothing from the backbone but its output, leaves its internal architecture untouched, and is trained per backbone. SR$^{2}$-Net follows an \emph{enhance-then-rectify} pipeline in which Hierarchical Spectral-Spatial Synergy Attention (\textbf{H-S$^{3}$A}) reinforces cross-band interactions, while Mode-Constrained Rectification (\textbf{MCR}) confines the correction to a learned compact spectral subspace. A degradation-consistency constraint further ties the output to the observed low-resolution input. Experiments with five backbones spanning CNN, Transformer, and diffusion families show that one fixed configuration improves spectral fidelity in every reported setting while preserving or improving spatial quality. Averaged over thirty in-domain settings, SR$^{2}$-Net removes 22.6% of the residual spectral error at a backbone-independent cost of 0.048M parameters.

Neural operators are often reported to exhibit zero-shot super-resolution, a phenomenon in which a model trained on coarse grids produces accurate predictions on finer testing grids without additional retraining. Despite strong empirical evidence, the theoretical foundations of this phenomenon remain unclear. In this work, we provide a systematic theoretical study of zero-shot super-resolution in operator learning. We first show that zero-shot super-resolution can be information-theoretically impossible even in benign settings such as when the input functions are available over the entire continuum and the ground truth is a simple rank-one linear operator. We then identify H{" o}lder smoothness of the output functions as a sufficient condition for zero-shot super-resolution and derive corresponding generalization bounds. Finally, we also validate the identified failure modes through experimental results.