# Radiative-Structured Neural Operator for Continuous Spectral Super-Resolution

arXiv: https://arxiv.org/abs/2511.17895 · HTML: https://mlsanity.com/paper/2511.17895/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 54 references that are in the map.
- First posted on arXiv 22 Nov 2025.

## Builds on (most cited first, 15 of 15)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [U-NO: U-shaped Neural Operators](https://mlsanity.com/paper/2204.11127/) (2022)
- [MST++: Multi-stage Spectral-wise Transformer for Efficient Spectral Reconstruction](https://mlsanity.com/paper/2204.07908/) (2022)
- [Super-Resolution Neural Operator](https://mlsanity.com/paper/2303.02584/) (2023)
- [Implicit Neural Representation Learning for Hyperspectral Image Super-Resolution](https://mlsanity.com/paper/2112.10541/) (2021)
- [Spectral-wise Implicit Neural Representation for Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2312.01061/) (2023)
- [Dual-Stage Approach Toward Hyperspectral Image Super-Resolution](https://mlsanity.com/paper/2204.04387/) (2022)
- [Deep Physics-Guided Unrolling Generalization for Compressed Sensing](https://mlsanity.com/paper/2307.08950/) (2023)
- [Continuous Spectral Reconstruction from RGB Images via Implicit Neural Representation](https://mlsanity.com/paper/2112.13003/) (2021)
- [HPRN: Holistic Prior-embedded Relation Network for Spectral Super-Resolution](https://mlsanity.com/paper/2112.14608/) (2021)
- [Space-Time Video Super-resolution with Neural Operator](https://mlsanity.com/paper/2404.06036/) (2024)
- [Learning to Recover Spectral Reflectance from RGB Images](https://mlsanity.com/paper/2304.02162/) (2023)
- [Mixed-granularity Implicit Representation for Continuous Hyperspectral Compressive Reconstruction](https://mlsanity.com/paper/2503.12783/) (2025)

## Built on by (most cited first, 1 of 1)

- [Spectral Super-Resolution using Spatial-Spectral Residual Operator Networks](https://mlsanity.com/paper/2609.35410/) (2026)

## Abstract (arXiv)

Spectral super-resolution (SSR) aims to reconstruct hyperspectral images (HSIs) from multispectral observations, with broad applications in computer vision and remote sensing. Deep learning-based methods have been widely used, but they often treat spectra as discrete vectors learned from data, rather than continuous curves constrained by physics principles, leading to unrealistic predictions and limited applicability. To address this challenge, we propose the Radiative-Structured Neural Operator (RSNO), which learns a continuous mapping for spectral super-resolution while enforcing physical consistency under the radiative prior. The proposed RSNO consists of three stages: upsampling, reconstruction, and refinement. In the upsampling stage, we leverage prior information to expand the input multispectral image, producing a physically plausible hyperspectral estimate. Subsequently, we adopt a neural operator backbone in the reconstruction stage to learn a continuous mapping across the spectral domain. Finally, the refinement stage imposes a hard constraint on the output HSI to eliminate color distortion. The upsampling and refinement stages are implemented via the proposed angular-consistent projection (ACP), which is derived from a non-convex optimization problem. Moreover, we theoretically demonstrated the optimality of ACP by null-space decomposition. Various experiments validate the effectiveness of the proposed approach in both discrete and continuous spectral super-resolution.