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Hyperspectral compressed sensing (HCS) is a new imaging method that effectively reduces the power consumption of data acquisition. In this article, we present a novel HCS algorithm by incorporating spatial-spectral hybrid compressed sensing, followed by a reconstruction based on spectral unmixing. At the sampling stage, the measurements are acquired by a spatial-spectral hybrid compressive sampling scheme to preserve the necessary information for the following spectral unmixing, where spatial compressive sampling mainly retains the endmember information, and spectral compressive sampling mainly retains the abundance information. Due to the limitations of the traditional linear mixed model, an improved mixed model is proposed for HCS reconstruction, which considers spectral variability, nonlinear mixing, and other factors. At the reconstruction stage, based on the improved mixed model, semi-nonnegative matrix factorization is introduced to realize spectral unmixing on the measurements to achieve the final reconstruction by using an alternate iteration manner. The proposed algorithm is tested on real hyperspectral data, and the selection of parameters is fully analyzed. Experimental results demonstrate that the proposed algorithm can significantly outperform state-of-the-art HCS algorithms in terms of reconstruction performance.