**Yulei Qian \* and Daiyin Zhu**

Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, College of Electronic Information Engineering, Nanjing University of Aeronautics and Astronautics, 29 Jiangjun Avenue, Nanjing 211100, China; zhudy@nuaa.edu.cn

**\*** Correspondence: qian\_yulei@nuaa.edu.cn; Tel.: +86-025-8489-2410

Received: 3 October 2019; Accepted: 15 November 2019; Published: 18 November 2019

**Abstract:** The phenomenon of periodical gapping in Synthetic Aperture Radar (SAR), which is induced in various ways, creates challenges in focusing raw SAR data. To handle this problem, a novel method is proposed in this paper. Complex deconvolution is utilized to restore the azimuth spectrum of complete data from the gapped raw data in the proposed method. In other words, a new approach is provided by the proposed method to cope with periodically gapped raw SAR data via complex deconvolution. The proposed method provides a robust implementation of deconvolution for processing azimuth gapped raw data. The proposed method mainly consists of phase compensation and recovering the azimuth spectrum of raw data with complex deconvolution. The gapped data become sparser in the range of the Doppler domain after phase compensation. Then, it is feasible to recover the azimuth spectrum of the complete data from gapped raw data via complex deconvolution in the Doppler domain. Afterwards, the traditional SAR imaging algorithm is capable of focusing the reconstructed raw data in this paper. The effectiveness of the proposed method was validated via point target simulation and surface target simulation. Moreover, real SAR data were utilized to further demonstrate the validity of the proposed method.

**Keywords:** Synthetic Aperture Radar (SAR); focusing; periodically gapped data; complex deconvolution
