目的 高光谱图像距具有较高的光谱分辨率，从而具备区分诊断性光谱特征地物的能力，但高光谱数据经常会受到如环境、设备等各种因素的干扰，导致数据污染，严重影响高光谱数据在应用中的精度和可信度。方法 根据高光谱图像光谱维度特征值大小与所包含信息的关系，利用截断核范数最小化方法表示光谱低秩先验，从而有效抑制稀疏噪声；再利用高光谱图像的空间稀疏先验建立正则化模型，达到去除高密度噪声的目的；最终，结合上述两种模型的优势，构建截断核范数全变差正则化模型去除高斯噪声、稀疏噪声及其他混合噪声等。结果 将本文与其他三种近期发表的主流去噪方法进行对比，模型平均峰信噪比提高3.20 dB，平均结构相似数值指标提高0.22，并可以应用到包含各种噪声、不同尺寸的图像，其模型平均峰信噪比提高1.33 dB。结论 本文方法在光谱低秩中更加准确地表示了观测数据的先验特征，利用高光谱遥感数据的空间和低秩先验信息，能够对含有高密度噪声以及稀疏异常值的图像进行复原。

Objective Hyperspectral remote sensing is a technique based on the principle of spectrometry to obtain some very narrow and continuous image data in the ultraviolet, visible, near-infrared and mid-infrared regions of the electromagnetic spectrum. Hyperspectral imaging technology combines the traditional two-dimensional image remote sensing technology and spectral technology to obtain the surface image and the spectral information at the same time. Hyperspectral images(HSI) can not only classify and recognize ground objects with high spectral diagnostic ability, but also contain rich information, which makes them widely used in many fields. The unique characteristics of hyperspectral images bring convenience and advantages to the acquisition of geographic information and the identification of ground objects. Unfortunately, there are also some difficulties in hyperspectral technology:the amount of data obtained by hyperspectral sensors is large, but it is often interfered by various factors during the acquisition process,such as environment and equipment, so that the data is polluted, which reduces the data availability and limits the subsequent application of hyperspectral sensors in various fields. Therefore, reducing noise pollution of data, obtaining more effective image information and increasing the utilization rate of image data are important links to ensure that hyperspectral images can play an important role in subsequent applications. Method Hundreds of continuous spectral bands image the target region at the same time, so that the hyperspectral image can provide spatial and spectral domain information. Moreover, the continuity of hyperspectral images in spatial domain and spectral domain makes the correlation between adjacent channels strong, that is a low-rank property. Based on this feature, spectral low-rank priors or spatial low-rank priors are considered to establish the restoration model for hyperspectral data restoration. Undoubtedly, the combination of the two models can achieve better recovery effect. But now, although the recovery method based on nuclear norm has a strong theory to ensure that excellent results can be obtained, due to the defects in the application, the second-best results can be obtained in the actual application. In the rank function, different eigenvalues contain different information of the observation data, among which the larger eigenvalues mainly contain the original data information, while the smaller eigenvalues mainly contain the noise information of the observation data. However, the restoration method based on nuclear norm minimization treats all the eigenvalues equally, and the corresponding model algorithm uses the same threshold to shrink the eigenvalues, thus losing a large amount of image information under the premise of false noise, which is an important defect of current mainstream denoising methods. In addition, some theoretical requirements of the nuclear norm are hardly satisfactory in practice. Considering truncated nuclear norm regularization is more robust and accurate than nuclear norm for the rank function's approximation, the application of truncated norm in hyperspectral denoising is still in the stage of using the low-rank priori information of hyperspectral spectrum for denoising, and the spatial low-rank priori information of hyperspectral is not used. The results of the existing methods are not satisfactory. We improve the current low rank based prior information in the spatial domain and based on the low rank based priori information in the spectral domain, a low rank representation model is proposed to depress the sparse noises. Based on the low rank based priori information in the spatial domain, the total variation regularization method is proposed to depress the density noises. Finally combined with the advantages of the two model we propose the model with truncated nuclear norm minimization and total variation regularization. This model not only retains the processing advantages of current mainstream models, but also makes full use of the truncated nuclear norm. As for the algorithm, alternating direction method of multipliers(ADMM) is a simple and effective method for distributed convex optimization. This method can decompose the original function and the amplification function, so as to optimize in parallel under more general assumptions. Therefore, the paper chooses ADMM method to solve the model. In order to verify the denoising effect of the model proposed in this paper, as well as the universality and generalization of the model, two truly collected hyperspectral sets were selected for the experiment. Gaussian noise, salt-pepper noise and dead line noise with different intensity are added to simulate noise pollution in real situation. In addition, different size images are selected for experiments to test the denoising effect of various methods. Result The restoration results of the proposed method are compared with the latest method, the peak signal to noise ratio (PSNR) index and the structure similarity (SSIM) index are improved 3.2 dB and 0.22. It can be seen from the experimental results that the gaussian white noise is still left after the traditional method is processed, while the image processed by the method in this paper effectively restrains the mixed noise. Not only the visual image shows that the de-noising result of the model proposed in this paper is more detailed than that recovered by total variation-regularized low-rank matrix factorization (LRTV) and other methods. PSNR and SSIM index of each channel also confirmed this result.In addition, the method proposed in this paper has stronger image restoration ability under higher noise, and no outliers appear. It can effectively improve the image quality, and get good recovery results for images containing various noises and images of different sizes, the peak signal to noise ratio is improved 1.33 dB, which shows that the model has good generalization and universality. Conclusion The low rank based priori information in the spectral domain is more robust and the model in this paper relies on the low rank based priori knowledge in both spectral and spatial domain tightly so that it can efficiently depresses the sparse noise and the density noise in the degraded hyperspectral remote sensing images. Experiments show that truncated nuclear norm can better control noise error by using the sum of smaller eigenvalues, so as to better represent the characteristics of data. Experiments with different noises added to hyperspectral data of different sizes also show that this method has excellent denoising effect.