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Based on the basic characteristic that the spectral library can contain the spectral information about the whole types of ground-surface objects in the observation area of hyperspectral images, the optimized dictionary learning via spectral library refers to the process of constructing optimized spectral dictionary under strict theoretical derivation, in which the spectra in the spectral library are used as training samples. The above process enables the spectra in the hyperspectral image to be sparsely represented under the learned spectral dictionary. To this end, a new spectral super-resolution method using optimized dictionary learning via spectral library is proposed in this paper, which uses only one high-spatial multispectral image to reconstruct high-spatial hyperspectral image. The above problem is formulated in the framework of sparse representation, as an estimation of the band matching matrix, the optimized spectral dictionary and the corresponding sparse coefficients. Specifically, a band matching method is proposed for mapping the common spectral library to a specific spectral library corresponding to the reconstructed high-spatial hyperspectral image. Then, by using both this specific spectral library and the high-spatial multispectral image, an optimization of spectral dictionary and its corresponding sparse coefficients is derived theoretically using the alternating direction method of multipliers (ADMM) algorithm. Comparison results with the relative methods demonstrated that, even only using one high-spatial multispectral image, our method cannot only achieve a high quality reconstruction of the high-spatial hyperspectral image, but also significantly improved the classification accuracy of multispectral images.