Title: Physics-informed Neural Operator for Pansharpening
Venue: NeurIPS 2025
Accepted: yes
Keywords: Pan-sharpening; Neural Operator; Multispectral and hyperspectral image fusion
Abstract: Over the past decades, pansharpening has contributed greatly to numerous remote sensing applications, with methods evolving from theoretically grounded models to deep learning approaches and their hybrids. Though promising, existing methods rarely address pansharpening through the lens of underlying physical imaging processes. In this work, we revisit the spectral imaging mechanism and propose a novel physics‐informed neural operator framework for pansharpening, termed PINO, which faithfully models the end‐to‐end electro‐optical sensor process. Specifically, PINO operates as: (1) First, a spatial-spectral encoder pair is introduced to aggregate multi-granularity high-resolution panchromatic (PAN) and low-resolution multispectral (LRMS) features.
(2) Subsequently, an iterative neural integral process utilizes these fused spatial-spectral characteristics to learn a continuous radiance field $L_i(x, y, \lambda)$ over spatial coordinates and wavelength, effectively emulating band-wise spectral integration. (3) Finally, the learned radiance field is modulated by the sensor’s spectral responsivity  $R_b(\lambda)$ to produce physically consistent spatial–spectral fusion products. This physics-grounded fusion paradigm offers a principled solution for reconstructing high-resolution multispectral and hyperspectral images in accordance with sensor imaging physics, effectively harnessing the unique advantages of spectral data to better uncover real-world characteristics. Experiments on multiple benchmark datasets show that our method surpasses state-of-the-art fusion algorithms, achieving reduced spectral aberrations and finer spatial textures. Furthermore, extension to hyperspectral (HS) data demonstrates its generalizability and universality. The code will be available upon potential acceptance.


Peer reviews:
comments: SUMMARY:
This paper proposes a novel physics-informed neural operator framework for pansharpening, termed PINO. A spatial-spectral encoder is introduced to aggregate multi-granularity high-resolution panchromatic (PAN) and low-resolution multi-spectral (LRMS) features. An iterative neural integral process utilizes these fused spatial-spectral characteristics to learn a continuous radiance field. The learned radiance field is modulated by the sensor’s spectral responsivity to produce the desired fusion products.

STRENGTHS AND WEAKNESSES:
Strengths 
1, this paper proposed a novel physics-informed neural operator framework for pansharpening, termed PINO.
2, A spatial-spectral encoder is introduced to aggregate multi-granularity high-resolution panchromatic (PAN) and low-resolution multi-spectral (LRMS) features.
3, An iterative neural integral process utilizes these fused spatial-spectral characteristics to learn a continuous radiance field. 
Weaknesses
1, It would be better to describe section 3.1 in the background section.
2, It seems that the contribution of this paper comes from the utilization of PIOO for Pansharpening. Theoretical analysis is encouraged to investigate.

QUESTIONS:
See the weakness.

LIMITATIONS:
N/A
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-06-29

comments: SUMMARY:
This paper presents an interesting model called PINO for pansharpening, which combines deep learning with the underlying physics of spectral imaging. The approach is implemented using implicit neural representations and neural operators, offering a novel perspective on the problem. Given that physics-driven methods are still relatively rare in remote sensing (RS) research, this work could inspire more explorations in this direction. Overall, the paper is well-structured, and the experimental results are compelling.

STRENGTHS AND WEAKNESSES:
# Strengths
1. The paper introduces an interesting method for pansharpening that integrates physical imaging using implicit neural representation and neural operators. The idea is innovative compared with existing pansharpening works. 
2. The experiment results are significantly improved over the existing methods, while the ablation studies show the effectiveness of the core designs.
3. The motivation and presentation of the paper are clear.

# Weaknesses 
1. While combining pansharpening with physical imaging is reasonable, the paper needs deeper theoretical analysis of the proposed model, particularly regarding its physical modeling components.
2. The physical interpretability of the proposed model remains unclear. Additional experiments or in-depth analysis would help demonstrate whether it properly captures physical imaging properties.
3. The discussion should include more relevant physically-driven pansharpening works, such as those presented in DOI: 10.1109/TGRS.2024.3523865, for better contextualization.

QUESTIONS:
See the Weaknesses.

LIMITATIONS:
Yes.
TITLE: Official Review
CLARITY: 2
IMPACT: 2
ORIGINALITY: 3
DATE: 2025-07-01

comments: SUMMARY:
This paper proposed a physics-informed neural operator framework, named PINO, which unified continuous radiance field modeling with learnable spectral responsivity, significantly boosting spatial spectral fidelity and enhancing generalization across heterogeneous sensors and varying imaging conditions.
The main contributions as follows:
1)	This paper proposed a physically-grounded pansharpening framework that established a new paradigm bridging neural representations with physical sensor model.
2)	It employed an iterative kernel integral operator that leverages multi-granularity spatial–spectral features to learn a continuous radiance field over spatial coordinates and wavelength, enabling sub-pixel and sub-band fusion of different modalities while effectively emulating band-wise spectral integration.
3)	Introduced a learnable band-wise spectral responsivity modulation to simulate the sensor’s spectral properties, allowing the simultaneous optimization of response functions.
4)	Experiments on multiple remote sensing benchmark datasets reveal that PINO consistently outperforms state-of-the-art methods in fusion capability, generaizalibity and adaptability.

STRENGTHS AND WEAKNESSES:
Strengths : 
The idea is novel, and the theoretical reasoning is correct.
Weaknesses:
1.Readers are not clear about why physical information neural operators are useful.
2. The experimental data set is small and insufficient.

QUESTIONS:
1.	Why implement analog imaging process operators in imaging products? From a physical principle perspective, why is this useful?
2.	Lack of more detailed experimental analysis.
3.	Will the approach used in this paper result in a significant increase in computational load and a significant decrease in training speed?

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 3
IMPACT: 2
ORIGINALITY: 3
DATE: 2025-07-02

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe PINO paper proposes a physics-based neural operator framework for pansharpening of remote sensing images. By simulating the physical imaging process, this framework provides a new solution that can significantly improve the quality and generalization ability of fused images. Although there are some challenges in terms of computational complexity and model complexity, PINO's outstanding performance on multiple benchmark datasets demonstrates its potential and value in the field of pansharpening. Future research can further optimize computational efficiency, explore cross-sensor generalization capabilities, and expand its application in other image fusion tasks.\n\nSTRENGTHS AND WEAKNESSES:\n# Strengths\n1. The continuous radiation field modeling $L_i(x,y,\\lambda)$ is combined with the learnable spectral response modulation $R_b(\\lambda)$ to explicitly simulate the physical process of sensor imaging, surpassing the traditional heuristic fusion method. The learned spectral response curve is consistent with the real sensor characteristics, enhancing the credibility of the model.\n\n2. Continuous radiation field modeling is achieved through Galerkin-type integration, preserving sub-pixel spatial details and sub-band spectral features. Pre-train the encoder (L1+SSIM) and then fine-tune the whole (L1+histogram loss) to alleviate the information degradation problem in implicit representation training.\n\n3. Multi-granularity feature aggregation (expanded spatial attention + grouped spectral attention) effectively fuses the HR details of PAN and the spectral information of LRMS.\n\n# Weaknesses\n1. The high computational cost caused by iterative neural integration and radiation field modulation makes training time-consuming (2000 rounds for CAVE), and the authors did not evaluate the inference speed.\n\nQUESTIONS:\n1. The encoder details are not detailed enough. The BDT architecture does not specify key parameters such as the number of layers/heads, and the appendix only mentions \"Bidirectional Dilated Transformer\".\n2. For the boundary conditions of the radiation field, Formula 1 does not discuss the boundary constraints of the scene radiation $L_i^s$, which may affect physical consistency.\n3. In the implementation of wavelength modulation, the discretization does not specify the sampling strategy (uniform/adaptive?).\n\nLIMITATIONS:\nSame weaknesses and problems as before.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}