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.
Abstract (translated)
高度非线性的退化过程、复杂的物理交互以及各种不确定性来源，使得单图像超分辨率（SR）成为一个特别具有挑战性的任务。现有的可解释的SR方法，无论是基于先验学习还是深度优化框架，通常依赖于黑盒式的深层网络来建模潜在变量，这使得退化过程难以理解和控制。 受Kolmogorov-Arnold定理(KAT)启发，我们首次提出了一种新的、用于图像超分辨率的可解释操作符，称为Kolmogorov-Arnold神经算子（KANO）。KANO提供了对潜在退化适应过程的一种透明且结构化的表示。具体而言，我们采用一个由有限数量的B样条函数组成的加性结构来分段逼近连续光谱曲线。通过学习和优化这些样条函数在定义区间内的形状参数，我们的KANO能够精确捕捉关键的光谱特征，如局部线性趋势以及非线性拐点处的峰值-谷值结构，从而使超分辨率结果具有物理可解释性。 此外，我们通过理论建模和跨自然图像、航拍照片及卫星遥感数据进行实验评估，在处理复杂序列拟合任务时系统地比较了多层感知器（MLP）与Kolmogorov-Arnold网络（KAN）。这项对比研究揭示了这些模型在表征复杂退化机制方面的各自优势和局限性，为开发可解释的SR技术提供了宝贵的见解。
URL
https://arxiv.org/abs/2512.22822
