Superpixel-Based Graph Laplacian Regularized and Weighted Robust Sparse Unmixing

The sparse unmixing (SU) technique is widely used in hyperspectral image (HSI) unmixing because it does not need to estimate the number of pure endmembers but directly obtains the spectra from known spectral libraries to construct the endmember matrix, which avoids the influence of endmember extraction on unmixing. However, some existing SU algorithms still have problems, such as insufficient consideration of abundance details and sensitivity to noise. In order to solve the above issues, this article proposes a graph Laplacian weighted robust SU (RSU) algorithm based on superpixels, which can better reconstruct abundance details and reduce sensitivity to noise. The coarse abundance is calculated based on the superpixel results, and then the global spatial prior weight is calculated. Then, weighted RSU is applied to each superpixel to achieve a combination of local and global cooperation to reduce sensitivity to noise. On this basis, in order to better reconstruct the abundance details, the spatial position information and spectral information between pixels within superpixels are used to construct a weighted map to represent the similarity between pixels. Finally, the alternating direction multiplier method (ADMM) is used to perform structural optimization on the superpixel scale, retaining the structural information of abundance and reducing the amount of calculation. Experiments are conducted on three simulated datasets and three real datasets, and the results show that the proposed algorithm outperforms state-of-the-art SU algorithms.