Physical Realizability Test for 3x4 Partial Mueller Matrix Using Supervised Learning Algorithms

Translating wide-field imaging Mueller polarimetry to clinical settings requires fast image acquisition and post-processing. The former can be achieved using polarization-sensitive cameras. However, such detectors typically measure only linear polarization states, which limited to capturing only first three rows of a complete 4x4 Mueller matrix. Testing for physical realizability-a critical step in Mueller polarimetric data post-processing-requires knowledge of all coefficients of the complete Mueller matrix. We developed a machine learning framework based on supervised learning algorithms (XGBoost, CatBoost, and Multi-Layer Perceptron) to directly test the physical realizability of partial 3x4 Mueller matrices. The models were trained and validated on experimental Mueller matrix images of brain tissue specimens measured in reflection geometry, achieving accuracies above 98% when compared to ground truth. Robustness testing on isolated samples and Monte Carlo simulated data confirmed reliable performance across different tissue types and imaging conditions. The framework is sufficiently fast to ensure compatibility with real-time data post-processing requirements.