BCUN: Bayesian Fully Convolutional Neural Network for Hyperspectral Spectral Unmixing

Spectral unmixing (SU) plays a fundamental role in hyperspectral image (HSI) processing. Effective SU relies on the accurate and efficient characterization of the noise effect, the endmembers, and the spatial correlation effect in abundances, as well as efficient optimization techniques to estimate these effects. To address these issues, this article presents a Bayesian fully convolutional hyperspectral unmixing network (BCUN) with the following key characteristics. First, a fully convolutional neural network (FCNN)-based deep image prior (DIP) is designed for enhanced characterization and estimation of the spatial context information in abundance maps, leading to more efficient and accurate abundance modeling than the traditional nonnegative least squares (NNLS) approaches. Second, a multivariate Gaussian distribution with an anisotropic covariance matrix is designed to characterize the conditional distribution of the spectral observations, leading to a novel Mahalanobis distance-based loss for FCNN training that is better capable of addressing the noise heterogeneous effect in HSI than the Euclidean distance-based mean squared error (MSE) loss in traditional deep neural networks. Third, the designed conditional distribution of spectral observations also enables the incorporation of the spectral mixture model (SMM) into the FCNN training process for effectively leveraging the knowledge in the forward spectral model. Fourth, the endmembers are modeled and estimated by a “purified means” approach that is capable of better characterizing endmembers. Finally, the above key components are coherently integrated into a Bayesian framework, and the resulting maximum a posteriori (MAP) problem is solved by a designed expectation–maximization (EM) algorithm. Experimental results on both simulated and real HSIs demonstrate that the proposed BCUN approach outperforms the other classical and state-of-the-art methods on both endmember estimation and abundance estimation.