Bridging and Unified Understanding of Huynen Decomposition and H/A/alpha Decomposition for PolSAR Data Based on SU Group Theory

Polarimetric decomposition is a crucial technique for interpreting targets from full polarimetric synthetic aperture radar (PolSAR) data. In recent years, the special unitary (SU) group theory has garnered widespread attention: not only have model-based polarimetric decomposition methods increasingly adopted SU matrices to model some polarimetric features of targets, but also Paladini et al. have proposed an algorithm that completely extracts polarimetric information of targets entirely based on SU matrices. Furthermore, we found that the classic algorithms Huynen decomposition and H/A/alpha decomposition can be related based on SU group theory, although they have always been considered entirely distinct methods. In this paper, we elucidate the relationship between Huynen decomposition and H/A/alpha decomposition based on their mathematical representations in the SU decomposition model. A comparative analysis of their similarities and differences reveals that Huynen decomposition represents an incomplete SU decomposition. Conversely, H/A/alpha decomposition redundantly extracts noise information (termed by Huynen) compared to SU decomposition. Additionally, the information about the single target extracted by both methods exhibits an SU transformation relationship. Theoretical validation is performed using PolSAR data acquired by Radarsat-2 in San Francisco, along with the experimental analysis of their preferences in extracting target polarimetric characteristics. In conclusion, polarimetric decomposition based on SU group theory not only ensures completeness in information extraction but also possesses explicit physical meanings. More importantly, it offers theoretical connections among diverse polarimetric decomposition approaches, promising a more unified framework for target interpretation.