Spectral Variability Bayesian Unmixing for Hyperspectral Sequence in Wavelet Domain

For unmixing (UN) of the sequence of hyperspectral images (SHS), spectral variability is an important factor to be considered. However, most existing UN methods tend to model the endmember and its variability in the spatial domain rather than the transform domain. In fact, the intrinsic and invariant features of the spectral curve can be effectively represented by wavelet transform. Therefore, this article proposes to perform SHS UN in the wavelet domain by combining the Bayesian method. First, the assumption of abundance being invariability in both the spatial and wavelet domains is made, and then, the formulation of UN in the wavelet domain using the perturbed linear mixing model (PLMM) is presented. Second, based on the Bayesian framework, the likelihood and prior are both given, in which the parameter priors are divided into two parts: low- and high-frequency wavelet coefficients. Moreover, by considering the sparsity of the high-frequency wavelet coefficients of endmembers, a noninformative prior with zero mean is designed. Meanwhile, for the coefficients of endmember variability, Gaussian distributions are utilized to represent the steady fluctuation along the temporal dimension. Finally, using the maximum a posteriori (MAP) rule, a hierarchical spectral variability UN model in the wavelet domain is built and solved by the Markov chain Monte Carlo (MCMC) sampling algorithm. Numerical experiments show that the proposed method generates more accurate estimates for endmembers and their variation.