  Infrared imaging and turbulence strength measurements are in widespread
demand in many fields. This paper introduces a Physical Prior Guided
Cooperative Learning (P2GCL) framework to jointly enhance atmospheric
turbulence strength estimation and infrared image restoration. P2GCL involves a
cyclic collaboration between two models, i.e., a TMNet measures turbulence
strength and outputs the refractive index structure constant (Cn2) as a
physical prior, a TRNet conducts infrared image sequence restoration based on
Cn2 and feeds the restored images back to the TMNet to boost the measurement
accuracy. A novel Cn2-guided frequency loss function and a physical constraint
loss are introduced to align the training process with physical theories.
Experiments demonstrate P2GCL achieves the best performance for both turbulence
strength estimation (improving Cn2 MAE by 0.0156, enhancing R2 by 0.1065) and
image restoration (enhancing PSNR by 0.2775 dB), validating the significant
impact of physical prior guided cooperative learning.
