Blind Spectral Unmixing Considering the Adjacent Effect

Abstract

Blind hyperspectral unmixing (HU) technique aims at identifying pure materials in a hyperspectral image (HSI), called endmembers, and quantifying the corresponding proportions, called abundances, with little prior knowledge. In this paper, the degradation mechanism during data collection—adjacent effect (AE), is considered in the process of blind HU. Since the AE leads to blurring (the loss of sharpness, contrast and apparent resolution) in scene, it blocks the quantitative analysis of HSI in sub-pixel level and makes the estimated endmembers and abundances inaccurate. To solve this problem, a bilinear mixing model is developed to simulate the AE, and a novel algorithm, termed joint deconvolution and blind HU (DBHU) is proposed. In DBHU, the bi-convex optimization 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 alternatively via ADMM until convergence. The experimental results on both simulated and real HSI illustrate the viability of the proposed algorithm.