目的 由于高光谱遥感数据携带丰富的光谱和空间信息，使其在许多领域得以广泛关注和应用。但是高光谱遥感数据在获取过程中受到各种因素的影响，存在多种不同程度的退化，进而影响到后续的处理和应用。因此，提出一种基于低秩矩阵近似和混合全变差正则化方法来复原退化的高光谱遥感数据。方法 首先分析高光谱遥感数据的两种低秩先验：光谱低秩先验和空间低秩先验；然后利用光谱低秩先验建立低秩矩阵近似表示模型，有效抑制稀疏噪声，例如脉冲噪声、条纹噪声、死线噪声等；再利用空间低秩先验建立混合全变差正则化模型，有效去除高密度噪声，例如强高斯噪声、泊松噪声等；最后结合两种模型的优势，建立基于低秩矩阵近似和混合全变差正则化模型。结果 利用多组高光谱遥感数据，和多种相关的高光谱复原方法进行对比仿真实验，表明新模型的结果在视觉质量有很大改进。与目前最新的复原模型相比，提出的模型的平均峰值信噪比能提高1.8 dB，而平均结构相似数值指标能提高0.05。结论 新模型充分利用高光谱遥感数据的空间和光谱低秩先验，针对含有高密度噪声和稀疏异常值的高光谱遥感数据，能够有效复原出高质量的高光谱遥感数据。

Objective With the wealth of available spatial and spectral information,hyperspectral remote sensing images have been used for many remote sensing applications and have attracted considerable attention.However,most hyperspectral remote sensing images suffer from degradation because of the distortion of atmospheric transmission,the limitation of electronic devices,and the influence of poor illumination.The degraded data can lead to seriously inaccurate results in the subsequent applications.Thus,on the basis of the low-rank representation and the mixture total variation regularization in this study,a new model is proposed to restore hyperspectral remote sensing images.Method First,two types of low rank-based priori information in the hyperspectral remote sensing images,i.e.,the low rank-based priori information in the spectral domain and the low rank-based priori information in the spatial domain,are explored.Then,on the basis of the low rank-based priori information in the spectral domain,a low-rank representation model is proposed to suppress sparse noises,such as impulse,stripe,and dead line noises.Subsequently,on the basis of the low rank-based priori information in the spatial domain,the mixture total variation regularization method is proposed to suppress density noises,such as Gaussian and Poisson noises.The mixture total variation is the linear combination of the anisotropic and isotropic total variations and is more approximate to the zero norm than the anisotropic and isotropic total variations.The restoration results of the mixture total variation regularization method are better than those of the traditional total variation-based methods.Finally,the low-rank representation and mixture total variation regularization models are integrated.As such,the new restoration model based on the low-rank representation and mixture total variation regularization possesses the advantages of the two aforementioned models.Result This study tests the performance of the proposed method with a set of challenging hyperspectral remote sensing images.The simulated noises are Gaussian,Poisson,salt-and-pepper,and dead line noises.The intensities of the mixture noise in each band are different,thereby enabling the simulation of the real situations as approximately as possible.The restoration results of the proposed method are compared with those of several related methods.After restoring the image,the peak signal-to-noise ratio and structural similarity indices are adopted to provide quantitative assessments of the results of the experiments.All the experiments prove that the proposed method achieves better visual quality and quantitative indices than those of several existing related methods.Conclusion The proposed model relies on the low rank-based priori knowledge in the spectral and spatial domains,efficiently suppresses the sparse and density noises in the degraded hyperspectral remote sensing images,and finally restores better hyperspectral remote sensing images than those of existing methods.The proposed model can be extended to other fields of remote sensing applications.