Sum-Product Unmixing for Hyperspectral Analysis With Endmember Variability

Models of endmember variability capture the notion that multiple spectra may represent a single class or material, and while these models are physically realistic, they often give rise to excessive computational complexity during the spectral unmixing process. In this letter, we present a computationally tractable supervised unmixing method that uses Gauss-Markov processes to model endmember variability and interband correlation properties within endmembers. We use a probabilistic graphical model over multiple Gauss-Markov processes to capture the mixing effects of a spectral sensor and employ sum-product message passing to develop an accelerated statistical unmixing algorithm. The computational complexity of the proposed unmixing algorithm is only linear in the number of bands, making it suitable for both hyperspectral (hundreds of hands) and ultraspectral (thousands of bands) applications. Unmixing examples with measured reflectance spectra show sizable performance improvements when accounting for interband correlation using the proposed method, and empirical results quantify orders of magnitude reduction in complexity compared to alternative methods.