**5. Conclusions**

Geometric calibration must be carried out before the application of raw images. This paper proposed a geometric calibration method using sparse recovery to remove linear array push-broom sensor bias. The errors in the imaging process were approximated to the equivalent bias angles in this method. By using the sparse recovery method, the proposed method exactly estimated long-period errors with a small number of GCPs available. Also, the proposed method effectively removed short-period errors by recognizing periodic wavy patterns in advance. The preliminary experimental results indicated the practicality and superior calibration performance of the proposed method when used for image data captured by the EO-1 and ALOS satellites. Compared with the traditional methods, the proposed method did well in situations with insufficient GCPs and short-period error calibration.

Future research will focus on the effects of GCP distribution on the proposed method. It is also important to apply the proposed method to other types of sensors.

**Author Contributions:** Z.S., J.Y., and W.A. conceived and designed the experiments; J.C. performed the experiments; J.C. and Z.S. analyzed the data; J.C. wrote the paper.

**Acknowledgments:** This work was supported in part by the National Natural Science Foundation of China under grant no. 61605242 and the Hunan Provincial Natural Science Foundation under grant no. 2016JJ3025. These foundations offered the cost of publishing this paper in an open access journal.

**Conflicts of Interest:** The authors declare no conflict of interest.
