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Processing and applications of hyperspectral images (HSI) are limited by the noise component. This paper establishes an HSI denoising algorithm by applying dictionary learning and sparse coding theory, which is extended into the spectral domain. First, the HSI noise model under additive noise assumption was studied. Considering the spectral information of HSI data, a novel dictionary learning method based on an online method is proposed to train the spectral dictionary for denoising. With the spatial–contextual information in the noisy HSI exploited as a priori knowledge, the total variation regularizer is introduced to perform the sparse coding. Finally, sparse reconstruction is implemented to produce the denoised HSI. The performance of the proposed approach is better than the existing algorithms. The experiments illustrate that the denoising result obtained by the proposed algorithm is at least 1 dB better than that of the comparison algorithms. The intrinsic details of both spatial and spectral structures can be preserved after significant denoising.

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