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A Copula-Guided Temporal Dependency Method for Multitemporal Hyperspectral Images Unmixing

Multitemporal hyperspectral unmixing (MTHU) aims to model variable endmembers and dynamical abundances, which emphasizes the critical temporal information. However, existing methods have limitations in modeling temporal dependency, thus fail to capture the dynamical material evolution. Motivated by the ability of copula theory in modeling dependency structure explicitly, in this paper, we propose a copula-guided temporal dependency method (Cog-TD) for multitemporal hyperspectral unmixing. Cog-TD defines new mathematical model, constructs copula-guided framework and provides two key modules with theoretical support. The mathematical model provides explicit formulations for MTHU problem definition, which describes temporal dependency structure by incorporating copula theory. The copula-guided framework is constructed for utilizing copula function, which estimates dynamical endmembers and abundances with temporal dependency. The key modules consist of copula function estimation and temporal dependency guidance, which computes and employs temporal information to guide unmixing process. Moreover, the theoretical support demonstrates that estimated copula function is valid and the represented temporal dependency exists in hyperspectral images. The major contributions of this paper include redefining MTHU problem with temporal dependency, proposing a copula-guided framework, developing two key modules and providing theoretical support. Our experimental results on both synthetic and real-world datasets demonstrate the utility of the proposed method.

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