⚡ electrical engineering

Physical prior guided cooperative learning framework for joint turbulence degradation estimation and infrared video restoration

This paper proposes the Physical Prior Guided Cooperative Learning (P2GCL) framework, which employs a cyclic collaboration between a turbulence measurement network and a restoration network guided by physical constraints to simultaneously achieve state-of-the-art performance in estimating atmospheric turbulence strength and restoring infrared video sequences.

Original authors: Ziran Zhang, Yuhang Tang, Zhigang Wang, Yueting Chen, Bin Zhao

Published 2026-07-31

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CC BY 4.0

Original authors: Ziran Zhang, Yuhang Tang, Zhigang Wang, Yueting Chen, Bin Zhao

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine trying to take a clear photo of a distant mountain, but the air between you and the peak is shimmering like a hot road on a summer day. This shimmering is called "atmospheric turbulence." It happens because pockets of air at different temperatures mix together, bending light in chaotic ways. For infrared cameras—which see heat instead of visible light—this effect is like looking through a wavy, distorted window. It makes hot objects look blurry, wobbly, and hard to measure. Scientists and engineers need sharp images and accurate measurements of how strong this turbulence is to do everything from tracking weather patterns to monitoring industrial equipment. The big challenge has always been a catch-22: to fix the blurry image, you need to know exactly how strong the turbulence is; but to measure the turbulence accurately, you need a clear image to start with. It's a classic "chicken and egg" problem where both sides are stuck in the mud.

This paper introduces a clever new team-up called the Physical Prior Guided Cooperative Learning (P2GCL) framework to solve this standoff. Think of it as two detectives working on the same case, but they take turns helping each other get smarter. One detective, named TMNet, is an expert at measuring the "turbulence strength" (specifically a value called the refractive index structure constant, or $C_n^2$ ). The other detective, TRNet, is a master at cleaning up blurry infrared videos.

Here is how their secret handshake works: First, TMNet takes a blurry video and guesses the turbulence strength ( $C_n^2$ ). It hands this number to TRNet like a secret clue. TRNet uses this clue to fix the video, making the image much clearer. But instead of stopping there, TRNet feeds this newly restored, clearer image back to TMNet. Because the image is now less distorted, TMNet can re-measure the turbulence strength with much higher accuracy. They keep looping through this cycle, constantly refining each other's work.

To make sure they aren't just guessing wildly, the researchers gave them a strict rulebook based on real-world physics. They created special "loss functions" (which are like scorecards for the computer) that check if the results match the laws of nature. One scorecard, the $C_n^2$ -guided frequency loss, ensures the restored video looks right in terms of its wave patterns, while another physical constraint loss keeps the whole process grounded in scientific reality.

The results of this cooperative dance are quite promising. In their tests, this two-model team outperformed previous methods. For measuring turbulence strength, they improved the accuracy (measured by Mean Absolute Error) by 0.0156 and boosted the correlation score ( $R^2$ ) by 0.1065. For cleaning up the images, the restored videos became sharper, with a quality score (PSNR) increasing by 0.2775 dB. By letting the two models teach each other while sticking to the rules of physics, the paper suggests that we can get both better measurements and clearer pictures than ever before.

Technical Summary: Physical Prior Guided Cooperative Learning Framework for Joint Turbulence Degradation Estimation and Infrared Video Restoration

Problem Statement
Atmospheric turbulence significantly degrades the quality of infrared imaging, leading to blurred and distorted video sequences. This degradation poses a critical challenge for applications requiring high-fidelity infrared data. Furthermore, accurately measuring turbulence strength, specifically the refractive index structure constant ( $C_n^2$ ), is essential for understanding these distortions but remains difficult due to the complex, non-linear nature of atmospheric effects. Existing approaches often treat turbulence estimation and image restoration as separate tasks, failing to leverage the inherent physical relationship between the two. There is a need for a unified framework that can simultaneously enhance turbulence strength estimation and restore infrared video quality by exploiting their mutual dependencies.

Methodology
The paper proposes the Physical Prior Guided Cooperative Learning (P2GCL) framework, which establishes a cyclic collaboration between two specialized deep learning models to solve the joint problem of turbulence estimation and image restoration.

Dual-Model Architecture:
- TMNet (Turbulence Measurement Network): This network is responsible for measuring turbulence strength. It takes degraded infrared image sequences as input and outputs the refractive index structure constant ( $C_n^2$ ). The output $C_n^2$ serves as a physical prior.
- TRNet (Turbulence Restoration Network): This network utilizes the $C_n^2$ value provided by TMNet as a physical constraint to guide the restoration of the infrared image sequence.
Cooperative Learning Mechanism:
The framework operates on a cyclic feedback loop. TMNet provides the $C_n^2$ physical prior to TRNet to aid in restoration. In turn, TRNet outputs restored images, which are fed back into TMNet. This feedback mechanism is designed to boost the measurement accuracy of TMNet, creating a synergistic effect where better restoration leads to better estimation, and better estimation leads to better restoration.
Loss Functions and Physical Constraints:
To ensure the models adhere to physical laws rather than just statistical patterns, the training process incorporates specific loss functions:
- $C_n^2$ -Guided Frequency Loss: A novel loss function introduced to align the restoration process with the frequency characteristics dictated by the turbulence strength ( $C_n^2$ ).
- Physical Constraint Loss: This loss function enforces consistency with physical theories regarding turbulence degradation, ensuring the learned representations remain physically plausible.

Key Contributions

Joint Framework: The introduction of P2GCL, a novel framework that unifies turbulence strength estimation and infrared image restoration through a cyclic cooperative learning strategy.
Physical Prior Integration: The effective utilization of the refractive index structure constant ( $C_n^2$ ) not just as an output metric, but as an active physical prior to guide the image restoration process.
Feedback Loop: The design of a bidirectional feedback mechanism where restored images refine turbulence estimation, and estimated turbulence parameters refine image restoration.
Physics-Informed Training: The development of a $C_n^2$ -guided frequency loss and a physical constraint loss to ground the deep learning models in atmospheric physics.

Experimental Results
Extensive experiments were conducted to validate the performance of P2GCL against existing methods. The results demonstrate that the framework achieves state-of-the-art performance in both tasks:

Turbulence Strength Estimation: The framework improved the Mean Absolute Error (MAE) for $C_n^2$ estimation by 0.0156 and enhanced the coefficient of determination ( $R^2$ ) by 0.1065.
Image Restoration: The framework improved the Peak Signal-to-Noise Ratio (PSNR) by 0.2775 dB.

Significance
The paper claims that these results validate the significant impact of physical prior-guided cooperative learning. By integrating physical theories directly into the learning loop, the P2GCL framework successfully bridges the gap between accurate turbulence measurement and high-quality image restoration. The work suggests that treating these two tasks as interdependent rather than isolated problems, and grounding them in physical constraints, yields superior performance for infrared imaging systems operating under atmospheric turbulence.

Technical Summary: Physical Prior Guided Cooperative Learning Framework for Joint Turbulence Degradation Estimation and Infrared Video Restoration

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