To reconstruct hyperspectral image (HSI) accurately from a few noisy compressive measurements, we present a novel manifold-structured sparsity prior based hyperspectral compressive sensing (HCS) method in this study. A matrix based hierarchical prior is first proposed to represent the spectral structured sparsity and spatial unknown manifold structure of HSI simultaneously. Then, a latent variable Bayes model is introduced to learn the sparsity prior and estimate the noise jointly from measurements. The learned prior can fully represent the inherent 3D structure of HSI and regulate its shape based on the estimated noise level. Thus, with this learned prior, the proposed method improves the reconstruction accuracy significantly and shows strong robustness to unknown noise in HCS. Experiments on four real hyperspectral datasets show that the proposed method outperforms several state-of-the-art methods on the reconstruction accuracy of HSI.
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