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Hyperspectral (HS) super-resolution reconstruction is an ill-posed inversion problem, for which the solution from reconstruction constraint is not unique. To address this, an HS image super-resolution method is proposed to first utilize the joint regulation of spatial and spectral nonlocal similarities. We then fused the HS and panchromatic images with sparse regulation. With these two regulation terms, edge sharpness and spectrum consistency are preserved and noises are suppressed. The proposed method is tested with Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) and Hyperion images and evaluated by quantitative measures. The resulting enhanced images from the proposed method are superior to the results obtained by other well-known methods.