KANO: Kolmogorov-Arnold Neural Operator for Image Super-Resolution

2025-12-28

AI Summary

Degradation in single-image super-resolution (SR) is highly nonlinear, physically ambiguous, and difficult to control; existing interpretable methods still rely on black-box neural networks to model latent degradation variables. Method: We propose KANO—the first interpretable neural operator for SR grounded in the Kolmogorov–Arnold representation theorem—explicitly modeling the degradation spectrum curve via structured additive B-spline functions. KANO introduces Kolmogorov–Arnold Networks (KANs) to SR, replacing black-box modules with learnable piecewise splines to enable physically grounded, controllable degradation modeling. It integrates spectral-domain continuous curve approximation with a deep unrolling optimization framework. Results: KANO significantly improves physical consistency and interpretability of reconstructions across natural images, aerial photography, and remote sensing data. It accurately captures local linear trends and nonlinear inflection points—including peaks and valleys—in the degradation spectrum, enabling both faithful reconstruction and explicit, human-understandable degradation characterization.

Technology Category

• Computer Vision: Representation Learning for Vision
• Machine Learning: Representation Learning
• Knowledge Representation and Reasoning: Knowledge Engineering

Application Category

• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

The highly nonlinear degradation process, complex physical interactions, and various sources of uncertainty render single-image Super-resolution (SR) a particularly challenging task. Existing interpretable SR approaches, whether based on prior learning or deep unfolding optimization frameworks, typically rely on black-box deep networks to model latent variables, which leaves the degradation process largely unknown and uncontrollable. Inspired by the Kolmogorov-Arnold theorem (KAT), we for the first time propose a novel interpretable operator, termed Kolmogorov-Arnold Neural Operator (KANO), with the application to image SR. KANO provides a transparent and structured representation of the latent degradation fitting process. Specifically, we employ an additive structure composed of a finite number of B-spline functions to approximate continuous spectral curves in a piecewise fashion. By learning and optimizing the shape parameters of these spline functions within defined intervals, our KANO accurately captures key spectral characteristics, such as local linear trends and the peak-valley structures at nonlinear inflection points, thereby endowing SR results with physical interpretability. Furthermore, through theoretical modeling and experimental evaluations across natural images, aerial photographs, and satellite remote sensing data, we systematically compare multilayer perceptrons (MLPs) and Kolmogorov-Arnold networks (KANs) in handling complex sequence fitting tasks. This comparative study elucidates the respective advantages and limitations of these models in characterizing intricate degradation mechanisms, offering valuable insights for the development of interpretable SR techniques.

Problem

• Modeling unknown degradation processes in image super-resolution tasks
• Replacing black-box networks with interpretable operators for SR
• Capturing complex spectral characteristics in image degradation fitting

Innovation

• Kolmogorov-Arnold Neural Operator for interpretable super-resolution
• Additive B-spline functions approximate spectral curves piecewise
• Learning spline shape parameters captures key spectral characteristics