A Multiscale Hierarchical Model for Sparse Hyperspectral Unmixing

Due to the complex background and low spatial resolution of the hyperspectral sensor, observed ground reflectance is often mixed at the pixel level. Hyperspectral unmixing (HU) is a hot-issue in the remote sensing area because it can decompose the observed mixed pixel reflectance. Traditional sparse hyperspectral unmixing often leads to an ill-posed inverse problem, which can be circumvented by spatial regularization approaches. However, their adoption has come at the expense of a massive increase in computational cost. In this paper, a novel multiscale hierarchical model for a method of sparse hyperspectral unmixing is proposed. The paper decomposes HU into two domain problems, one is in an approximation scale representation based on resampling the method’s domain, and the other is in the original domain. The use of multiscale spatial resampling methods for HU leads to an effective strategy that deals with spectral variability and computational cost. Furthermore, the hierarchical strategy with abundant sparsity representation in each layer aims to obtain the global optimal solution. Both simulations and real hyperspectral data experiments show that the proposed method outperforms previous methods in endmember extraction and abundance fraction estimation, and promotes piecewise homogeneity in the estimated abundance without compromising sharp discontinuities among neighboring pixels. Additionally, compared with total variation regularization, the proposed method reduces the computational time effectively