Alternating Iterative Optimization With Matrix Decomposition for Calibration-Free Rotation Angle Estimation and Polarization Reconstruction

Accurate estimation of rotation angles in polarimetric imaging is critical for high-precision polarimetric measurements. While existing least-squares-based methods avoid complex instrument calibration, they often suffer from high computational complexity, limited accuracy, and poor robustness. To address these challenges, we propose a novel alternating iterative optimization (AIO) framework based on matrix decomposition, which enables automatic, fast, and robust retrieval of rotation angles and reconstruction of polarization parameters. The method formulates the estimation as a matrix decomposition problem and solves it through a least-squares-based alternating update strategy. Its main advantage lies in avoiding strict uniformity assumptions, complex nonlinear approximations, and extra parameter tuning, thereby enhancing convergence stability and reducing computational complexity. Numerical simulation results demonstrate that the proposed method achieves a mean absolute error (MAE) of only 0.21° in rotation angle estimation, significantly outperforming the Levenberg–Marquardt (LM, 1.35°), Gauss–Newton (GN, 1.78°), and least-squares iterative (LSI, 1.56°) methods. Experimental validation across four real-world birefringent scenes further confirms its superior accuracy and computational efficiency, with the average MAE reduced from 14.81° to 0.39°, and the entire reconstruction process completed within 2 s per scene. In addition, the effects of noise, initial estimation errors, and the number of polarization channels are systematically evaluated. This work provides a generalized, low-cost, and high-precision solution for rotation angle retrieval in polarimetric systems, serving as a critical foundation for subsequent polarization measurement tasks, such as accurate stress analysis, polarization navigation, and medical diagnostics.