Robust GBM hyperspectral image unmixing with superpixel segmentation based low rank and sparse representation

Abstract

Abstract Generalized bilinear model (GBM) has been one of the most representative models for nonlinear unmixing of hyperspectral image (HSI), which can take the second-order scattering of photons into consideration. However, the GBM is implicitly developed for the additive white Gaussian noise. Besides, the performances of traditional GBM based unmixing methods are not that satisfying since the spatial correlation of HSI is not considered. In this paper, to overcome the two problems mentioned above, we propose a robust GBM (RGBM) for nonlinear unmixing of HSI, which can simultaneously take the Gaussian noise and sparse noise into account. Besides, we propose a new unmixing method with superpixel segmentation (SS) and low-rank representation (LRR) based on RGBM, which can take the spatial correlation of HSI into consideration. First, we adopt the principal component analysis (PCA) to get the first principal component of HSI, which contains the most information for the whole HSI. Then we adopt the SS in the first principal component of HSI to get the homogeneous regions, and the abundances in each homogeneous region have the underlying low-rank property. Finally, we unmix the pixels in each homogeneous region of HSI according to the low-rank property of abundances and the sparse property of sparse noise, and the proposed RGBM based unmixing method can be solved by the alternative direction method of multipliers (ADMM). Experiments on both synthetic datasets and real HSIs demonstrate that the proposed RGBM and corresponding method are efficient compared with some other popular GBM based unmixing methods.