Zhaojie Pan

Chenyu Li, Danfeng Hong, Bing Zhang et al.

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.

Chenyu Li, Danfeng Hong, Bing Zhang et al.

Image super-resolution (SR) is a critical technology for overcoming the inherent hardware limitations of sensors. However, existing approaches mainly focus on directly enhancing the final resolution, often neglecting effective control over error propagation and accumulation during intermediate stages. Recently, Mamba has emerged as a promising approach that can represent the entire reconstruction process as a state sequence with multiple nodes, allowing for intermediate intervention. Nonetheless, its fixed linear mapper is limited by a narrow receptive field and restricted flexibility, which hampers its effectiveness in fine-grained images. To address this, we created a nonlinear state predictive control model \textbf{MambaX} that maps consecutive spectral bands into a latent state space and generalizes the SR task by dynamically learning the nonlinear state parameters of control equations. Compared to existing sequence models, MambaX 1) employs dynamic state predictive control learning to approximate the nonlinear differential coefficients of state-space models; 2) introduces a novel state cross-control paradigm for multimodal SR fusion; and 3) utilizes progressive transitional learning to mitigate heterogeneity caused by domain and modality shifts. Our evaluation demonstrates the superior performance of the dynamic spectrum-state representation model in both single-image SR and multimodal fusion-based SR tasks, highlighting its substantial potential to advance spectrally generalized modeling across arbitrary dimensions and modalities.