MATLAB Implementation for Polarimetric SAR Data Processing

Polarimetric SAR (Synthetic Aperture Radar) is an advanced remote sensing technology that captures surface information by measuring the polarization characteristics of electromagnetic waves. This article presents a MATLAB implementation for processing polarimetric SAR data and converting it into Müller matrices. Polarimetric SAR data is typically stored in complex number format, containing echo information from different polarization channels (such as HH, HV, VH, VV). In MATLAB, the standard processing workflow includes data reading, polarimetric covariance matrix calculation, and conversion to Müller matrix. First, read raw data from polarimetric SAR data files of the San Francisco area. MATLAB provides multiple functions (such as `load` or custom file reading functions) to load binary or specific-format polarimetric SAR data. Key implementation involves using `fread` for binary data or specialized toolboxes like `polsar` for standardized formats. After reading, the data is typically stored as complex matrices representing scattering coefficients for different polarization combinations. Next, construct the polarimetric covariance matrix or coherency matrix. This step involves calculating cross-correlation relationships between different polarization channels, typically achieved through outer product operations. Algorithm implementation uses MATLAB's matrix operations: for full polarimetric data, the covariance matrix C = k·k† where k is the scattering vector [HH, HV, VH, VV] and † denotes conjugate transpose. The `ctranspose` function and matrix multiplication efficiently handle this computation. Finally, convert the covariance matrix to a Müller matrix. The Müller matrix is a 4×4 real matrix describing polarimetric scattering characteristics of electromagnetic waves. The conversion process typically involves linear combinations and normalization of covariance matrix elements to satisfy physical constraints of Müller matrices. MATLAB's matrix manipulation functions like `reshape` for dimension transformation and `dot` for vector operations efficiently implement this transformation. Special attention should be paid to normalization factors to maintain energy conservation principles. Polarimetric SAR data processing finds wide applications in remote sensing, including terrain classification, target detection, and environmental monitoring. Implementing Müller matrix conversion in MATLAB provides a foundation for subsequent polarimetric decomposition or scattering mechanism analysis, leveraging MATLAB's built-in functions for eigenvalue decomposition (`eig`) and matrix transformations.