Blind Hyperspectral Unmixing Considering the Adjacency Effect

This paper focuses on the blind unmixing technique for analyzing hyperspectral images (HSIs). A joint deconvolution and blind hyperspectral unmixing (DBHU) algorithm is proposed, which is aimed at eliminating the impact of the adjacency effect (AE) on unmixing. In remote sensing imagery, the AE occurs in the presence of atmospheric scattering over a heterogeneous surface. The AE leads to blurring and additional mixing of HSIs and makes it difficult to estimate endmembers and abundances accurately. In this paper, we first model the blurred HSIs by the use of a bilinear mixing model (BMM), where a blurring kernel is used to model the mixing caused by the AE. Based on the BMM, the DBHU problem is formulated as a constrained and biconvex optimization problem. Specifically, the minimum-volume simplex (MVS) is incorporated to deal with the additional mixing caused by the AE, and 3-D total variation (TV) priors are adopted to model the spectral–spatial correlation of the data. In DBHU, the biconvex problem is efficiently solved by a nonstandard application of the alternating direction method of multipliers (ADMM) algorithm, where a block coordinate descent scheme is applied by splitting the original problem into two saddle point subproblems, and then minimizing the subproblems alternately via the ADMM until convergence. The experimental results obtained with both simulated and real data confirm the viability of the proposed algorithm, and DBHU works well, even where both blurring and noise are present in the scene.