Program for Pauli Decomposition of Covariance Matrix Data in Polarimetric SAR Images

Polarimetric SAR (Synthetic Aperture Radar) is a remote sensing technology capable of acquiring full polarimetric information of ground targets. In polarimetric SAR data processing, Pauli decomposition serves as a fundamental polarimetric target decomposition method that breaks down covariance matrix data into three basic scattering mechanisms, facilitating the analysis of target scattering characteristics. The core concept of Pauli decomposition involves decomposing the 3x3 covariance matrix into a linear combination of three fundamental scattering mechanisms: surface scattering, double-bounce scattering, and volume scattering. This decomposition approach, grounded in physical scattering mechanisms, provides intuitive visualization of target scattering properties. In program implementation, Pauli decomposition typically follows these key steps: First, the algorithm reads polarimetric SAR data and computes the covariance matrix C3 using polarization channel combinations (HH, VV, HV). The implementation often utilizes matrix operations to ensure numerical stability during covariance calculation. Next, the covariance matrix undergoes eigenvalue decomposition to extract scattering characteristics, where eigenvectors represent scattering mechanisms and eigenvalues indicate their relative magnitudes. The decomposition results are then converted into an RGB color composite image using a standard color mapping scheme - red for double-bounce scattering, blue for surface scattering, and green for volume scattering. This color transformation involves normalization and scaling operations to optimize visual representation. Pauli decomposition images play crucial roles in various remote sensing applications. In agricultural monitoring, they help distinguish different crop types based on their unique scattering signatures. For disaster assessment, the technique enables identification of damaged structures through characteristic double-bounce scattering patterns. In marine surveillance, it facilitates detection of oil spills on sea surfaces by analyzing surface scattering variations. The resulting color composite images allow researchers to intuitively analyze scattering characteristic differences among various ground targets through clear visual discrimination of dominant scattering mechanisms.