遥感图像在成像过程中，容易受到云层和雾霾天气的影响，形成带雾图像；同时在下传时，会受到多种因素影响（如发送接收误码、电离层和对流层的随机变化对信号形成扰动等），使图像信息丢失或掺杂噪声。本文针对信息丢失的带雾单色遥感图像，提出了基于矩阵复原和暗通道理论的单色遥感图像去雾算法，通过基于交替方向乘子法（Alternating Direction Method of Multipliers，ADMM）的矩阵复原算法与传统暗通道理论相结合，有效实现了信息丢失下的遥感雾图复原。通过主观评价和客观评价相结合的方式，将本文算法与经典算法对比。结果表明，本文算法得到的结果在直观视觉上效果更好，且相对于信息丢失30%的雾图，6个场景的平均信息熵提升1.665 2，平均峰值信噪比提升11.702 9，平均结构相似性提升0.814 6，客观评价指标结果优异。进一步在不同比例信息丢失情况下进行实验，结果表明，即使在信息大量丢失的情况下，依然能够得到清晰的复原去雾图像。

In the imaging process, the remote sensing images are easily affected by clouds and haze weather, and forms foggy images. At the same time, when the data are downloaded, they are affected by various factors (such as transmission and reception errors, signals disturbed by random changes in the ionosphere and troposphere, etc.) making the image information lost or doped with noise. This paper proposes a dehazing algorithm for monochrome remote sensing images based on matrix restoration and dark channel theory for foggy monochrome remote sensing images with information loss. Combined with the matrix restoration based on ADMM(Alternating Direction Method of Multipliers) and dark channel theory, the restoration of remote sensing fog map under the condition of information loss is effectively realized. By combining subjective evaluation and objective evaluation, the algorithm in this paper is compared with the classical algorithm. The results show that the results obtained by the algorithm in this paper are more intuitive and visually effective, and compared with the fog map with 30% information loss, the six scenes have better visual effects. The average information entropy is improved by 1.665 2, the average peak signal-to-noise ratio is improved by 11.702 9, and the average structural similarity is improved by 0.814 6. The objective evaluation index results are excellent. Further experiments are carried out in the case of different proportions of information loss, and the results show that the clear restoration and dehazing image can still be obtained even when a large amount of information is lost.