卫星平台振动和反射镜震颤会引起遥感图像中的振荡畸变。这类畸变难以通过常用的几何校正方法消除。对此，提出了一种使用压缩感知的几何校正方法。该方法基于有理函数模型（RFM）进行几何校正。在校正过程中，利用初始的RFM 计算出地面控制点(GCPs)在图像中的投影坐标与实际成像坐标之间的偏差（称为投影偏差），以地面控制点处的投影偏差作为采样值，使用压缩感知技术重构出所有像元处的投影偏差，并据此对RFM 进行像方补偿；利用经过补偿的RFM 进行遥感图像纠正。通过补偿，消除了振荡畸变引起的RFM 模型误差，进而提高校正性能。利用实测数据验证了该方法的有效性，并通过仿真数据分析了地标点的数量与分布对该几何校正方法性能的影响。

Satellite vibration and scan mirror oscillation can cause oscillation distortions of remote sensing imagery. These distortions are difficult to be corrected by common geometric correction methods. A geometric correction method using compressive sampling is proposed. In this method, geometric correction is performed with rational function model (RFM). The biases between the image coordinates and project coordinates of ground control points (GCPs) are calculated with the original RFM. The bias is called projection bias. The projection biases at the GCPs are regarded as measurements. By using the technique of compressive sampling, the projection biases of every pixel can be reconstructed, and the RFM is compensated according to projection biases. The remote sensing imagery is rectified with the compensated RFM. Through compensation, the errors of RFM which caused by oscillation distortions are eliminated and the performance of geometric correction is improved. The method is proved effective by using real remote sensing images. Based on simulated images, the effect of GCPs distribution and number on geometric correction is also analyzed.