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

TL;DR

This paper introduces KANO, an interpretable neural operator based on Kolmogorov-Arnold theorem, to model complex degradation processes in image super-resolution, providing physical interpretability and improved understanding of the underlying mechanisms.

Contribution

The paper proposes the first interpretable operator for image super-resolution inspired by KAT, capturing spectral characteristics with B-spline functions for physical interpretability.

Findings

KANO accurately models spectral degradation features.

Comparative analysis shows advantages of KANO over MLPs.

Experimental results demonstrate improved interpretability in SR tasks.

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.