Sparse Hyperspectral Unmixing Using Spectral Library Adaptive Adjustment

Sparse regression methods based on the spectral libraries have shown promise for hyperspectral unmixing, which assumes that the observed image can be represented linearly by a small subset of a known spectral library. However, the spectral mismatches are often assumed to occur between the actual endmembers and the corresponding signatures in the spectral library, which greatly limits the application of the sparse unmixing method. In this article, we address the abovementioned problem by adaptively adjusting the spectral library to match the current hyperspectral image during the unmixing procedure and propose a spectral library adaptive collaborative sparse unmixing model. In our model, we introduce both the spectral scaling factors and the spectral residual variables, which can adjust the spectral library in terms of spectral intensity and local spectral variations, respectively. Moreover, the first-order sparse property of the spectral difference is utilized to improve the accuracy of the spectral library adjustment. We solve our model by the alternating direction method of multipliers. Simulations and real-data experiments show that the proposed method is effective for reducing the impact of spectral library mismatches compared with state-of-the-art algorithms.