In this study, a novel noise reduction algorithm for hyperspectral imagery (HSI) is proposed based on high-order rank-1 tensor decomposition. The hyperspectral data cube is considered as a three-order tensor that is able to jointly treat both the spatial and spectral modes. Subsequently, the rank-1 tensor decomposition (R1TD) algorithm is applied to the tensor data, which takes into account both the spatial and spectral information of the hyperspectral data cube. A noise-reduced hyperspectral

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... age is then obtained by combining the rank-1 tensors using an eigenvalue intensity sorting and reconstruction technique. Compared with the existing noise reduction methods such as the conventional channel-by-channel approaches and the recently developed multidimensional filter, the spatial-spectral adaptive total variation filter, experiments with both synthetic noisy data and real HSI data reveal that the proposed R1TD algorithm significantly improves the HSI data quality in terms of both visual inspection and image quality indices. The subsequent image classification results further validate the effectiveness of the proposed HSI noise reduction algorithm. Ó