{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T03:24:44Z","timestamp":1770521084317,"version":"3.49.0"},"reference-count":40,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2021,10,30]],"date-time":"2021-10-30T00:00:00Z","timestamp":1635552000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Nature Science Foundation of China","award":["62001508"],"award-info":[{"award-number":["62001508"]}]},{"name":"National Nature Science Foundation of China","award":["62131020"],"award-info":[{"award-number":["62131020"]}]},{"name":"Natural Science Basic Research Program of Shaanxi","award":["2020JQ-480"],"award-info":[{"award-number":["2020JQ-480"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Ground moving target (GMT) is displaced and defocused in conventional synthetic aperture radar (SAR) image due to the residual phase error of non-cooperative GMT motion. In this study, a GMT imaging (GMTIm) method is proposed for highly squint SAR. As the squint angle become large, the displace and defocus effect of the GMT image become severe and the geometry distortion of the GMT image cannot be ignored. The proposed method first deduced the two-dimensional (2-D) frequency domain signal of the GMT and the bulk compression function of the Range Migration Algorithm (RMA) in highly squint SAR. Then GMT ROI data are extracted and a modified minimum entropy algorithm (MMEA) is proposed to refocus the GMT image. MMEA introduces the idea of bisection into the iteration process to converge more efficiently than the previous minimum entropy method. To overcome the geometry distortion of the GMT image, an equivalent squint angle spectrum rotation method is proposed. Finally, to suppress the GMT image sidelobe, the sparse characteristic of GMT is considered and a sparse enhancement method is adopted. The proposed method can realize GMTIm in highly squint SAR where the squint angle reaches to 75 degrees. The PSNR and ISLR of point target in highly squint SAR is close to that in side-looking SAR. The simulated point target data and ship data are used to validate the effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/rs13214373","type":"journal-article","created":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T22:24:22Z","timestamp":1635805462000},"page":"4373","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Ground Moving Target Imaging for Highly Squint SAR by Modified Minimum Entropy Algorithm and Spectrum Rotation"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2710-4630","authenticated-orcid":false,"given":"Shichao","family":"Xiong","sequence":"first","affiliation":[{"name":"Information and Navigation College, Air Force Engineering University, Xi\u2019an 710077, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4189-9206","authenticated-orcid":false,"given":"Jiacheng","family":"Ni","sequence":"additional","affiliation":[{"name":"Information and Navigation College, Air Force Engineering University, Xi\u2019an 710077, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2773-3437","authenticated-orcid":false,"given":"Qun","family":"Zhang","sequence":"additional","affiliation":[{"name":"Information and Navigation College, Air Force Engineering University, Xi\u2019an 710077, China"},{"name":"Key Laboratory of Wave Scattering and Remote Sensing Information, Fudan University, Shanghai 200433, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1460-4289","authenticated-orcid":false,"given":"Ying","family":"Luo","sequence":"additional","affiliation":[{"name":"Information and Navigation College, Air Force Engineering University, Xi\u2019an 710077, China"},{"name":"Key Laboratory of Wave Scattering and Remote Sensing Information, Fudan University, Shanghai 200433, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6311-7212","authenticated-orcid":false,"given":"Longqiang","family":"Yu","sequence":"additional","affiliation":[{"name":"Information and Navigation College, Air Force Engineering University, Xi\u2019an 710077, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1109\/7.53413","article-title":"Moving Target Imaging Algorithm for SAR Data","volume":"26","author":"Werness","year":"1990","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1109\/MSP.2014.2312834","article-title":"Sparsity-Driven Synthetic Aperture Radar Imaging: Reconstruction, Autofocusing, Moving targets, and Compressed Sensing","volume":"31","author":"Varshney","year":"2014","journal-title":"IEEE Signal. Process. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Graziano, M.D., D\u2019Errico, M., and Rufino, G. (2016). Wake Component Detection in X-band SAR Images for Ship Heading and Velocity Estimation. Remote Sens., 8.","DOI":"10.3390\/rs8060498"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zhao, Y., Han, S., Yang, J., Zhang, L., Xu, H., and Wang, J. (2018). A Novel Approach of Slope Detection Combined with Lv\u2019s Distribution for Airborne SAR Imagery of Fast Moving Targets. Remote Sens., 10.","DOI":"10.3390\/rs10050764"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Song, C., Wang, B., Xiang, M., Wang, Z., Xu, W., and Sun, X. (2020). A Novel Post-Doppler Parametric Adaptive Matched Filter for Airborne Multichannel Radar. Remote Sens., 12.","DOI":"10.3390\/rs12244017"},{"key":"ref_6","unstructured":"Chen, J., Xing, M., Yu, H., Liang, B., Peng, J., and Sun, G. (2021). Motion Compensation\/Autofocus in Airborne Synthetic Aperture Radar: A Review. IEEE Geosci Remote Sens. Mag., 2\u201323."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1109\/7.745691","article-title":"SAR Imaging of Moving Targets","volume":"35","author":"Perry","year":"1999","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1049\/ip-rsn:20030076","article-title":"Detection and Imaging of Arbitrarily Moving Targets with Single-Channel SAR","volume":"150","author":"Kirscht","year":"2003","journal-title":"IET Radar Sonar Navig."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4735","DOI":"10.1109\/TGRS.2012.2191561","article-title":"Moving-Target Tracking in Single-Channel Wide-Beam SAR","volume":"50","author":"Henke","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1949","DOI":"10.1109\/TGRS.2018.2870299","article-title":"Background-Free Ground Moving Target Imaging for Multi-PRF Airborne SAR","volume":"57","author":"Jin","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"7646","DOI":"10.1109\/JSEN.2016.2604046","article-title":"Parametric Sparse Representation Method for Motion Parameter Estimation of Ground Moving Target","volume":"16","author":"Gu","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_12","unstructured":"Pascazio, V., Schirinzi, G., and Farina, A. (2001, January 9\u201313). Moving Target Detection by Alongtrack Interferometry. Proceedings of the IEEE IGARSS, Sydney, NSW, Australia."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1325","DOI":"10.1109\/TGRS.2016.2622712","article-title":"Image-Based Target Detection and Radial Velocity Estimation Methods for Multichannel SAR-GMTI","volume":"55","author":"Suwa","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Chen, Y., Li, G., Zhang, Q., and Sun, J. (2017). Refocusing of Moving Targets in SAR Images via Parametric Sparse Representation. Remote Sens., 9.","DOI":"10.3390\/rs9080795"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1049\/iet-rsn.2011.0310","article-title":"ISAR based technique for refocusing non-cooperative targets in SAR images","volume":"6","author":"Martorella","year":"2012","journal-title":"IET Radar Sonar Navig."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1062","DOI":"10.1109\/TGRS.2015.2473705","article-title":"High-Resolution SAR-Based Ground Moving Target Imaging with Defocused ROI Data","volume":"54","author":"Zhang","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1049\/iet-rsn:20060040","article-title":"Approach for Single Channel SAR Ground Moving Target Imaging and Motion Parameter Estimation","volume":"1","author":"Zhou","year":"2007","journal-title":"IET Radar Sonar Navig."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1109\/LGRS.2008.2000621","article-title":"Doppler Keystone Transform-An Approach Suitable for Parallel Implementation of SAR Moving Target Imaging","volume":"5","author":"Li","year":"2008","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3283","DOI":"10.1109\/TGRS.2018.2883210","article-title":"SAR Ground Moving Target Imaging Based on a New Range Model Using a Modified Keystone Transform","volume":"57","author":"Jin","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Wan, J., Tan, X., Chen, Z., Li, D., Liu, Q., Zhou, Y., and Zhang, L. (2021). Refocusing of Ground Moving Targets with Doppler Ambiguity Using Keystone Transform and Modified Second-Order Keystone Transform for Synthetic Aperture Radar. Remote Sens., 13.","DOI":"10.3390\/rs13020177"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1049\/iet-spr:20070114","article-title":"SAR Imaging of Moving Targets Using Polynomial Fourier Transform","volume":"2","author":"Djurovic","year":"2008","journal-title":"IET Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1049\/iet-rsn.2019.0313","article-title":"Sparse Long-Time Coherent Integration-Based Detection Method for Radar Low-Observable Maneuvering Target","volume":"14","author":"Chen","year":"2020","journal-title":"IET Radar Sonar Navig."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"5476","DOI":"10.1109\/TGRS.2019.2899728","article-title":"Ground Moving Target Refocusing in SAR Imagery Based on RFRT-FrFT","volume":"57","author":"Huang","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1109\/TCI.2019.2956879","article-title":"Low Rank Plus Sparse Decomposition of Synthetic Aperture Radar Data for Target Imaging","volume":"6","author":"Matan","year":"2020","journal-title":"IEEE Trans. Comput. Imaging."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1238","DOI":"10.1109\/JSEN.2019.2947114","article-title":"Ground Moving Target Imaging Based on Compressive Sensing Framework with Single-Channel SAR","volume":"20","author":"Kang","year":"2020","journal-title":"IEEE Sens. J."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1279","DOI":"10.1049\/iet-rsn.2018.5558","article-title":"Iterative Minimum Entropy Algorithm for Refocusing of Moving Targets in SAR Images","volume":"13","author":"Chen","year":"2019","journal-title":"IET Radar Sonar Navig."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1109\/LGRS.2016.2533631","article-title":"An Improved Range Model and Omega-K-Based Imaging Algorithm for High-Squint SAR With Curved Trajectory and Constant Acceleration","volume":"13","author":"Li","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1443","DOI":"10.1109\/JSTARS.2016.2611005","article-title":"Sparsity-Driven SAR Imaging for Highly Maneuvering Ground Target by the Combination of Time-Frequency Analysis and Parametric Bayesian Learning","volume":"10","author":"Yang","year":"2017","journal-title":"IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/j.dsp.2016.10.001","article-title":"A fast ground moving target focusing method based on first-order discrete polynomial-phase transform","volume":"60","author":"Xin","year":"2017","journal-title":"Digit. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Tian, M., Liao, G., Zhu, S., He, X., Liu, Y., and Li, Y. (2021). An Efficient Method for Ground Maneuvering Target Refocusing and Motion Parameter Estimation Based on DPT\u2013KT\u2013MFP. Remote Sens., 13.","DOI":"10.3390\/rs13061092"},{"key":"ref_31","unstructured":"Cumming, I.G., and Wong, F.H. (2005). Digital Processing of Synthetic Aperture Radar Data: Algorithm and Implementation, Artech House."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1109\/LGRS.2013.2271691","article-title":"Imaging and parameter estimation of fast-moving targets with single-antenna SAR","volume":"11","author":"Yang","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Jing, K., Xu, J., Hang, Z., Yao, D., and Long, T. (2016). GMTI for Squint Looking XTI-SAR with Rotatable Forward-Looking Array. Sensors, 16.","DOI":"10.3390\/s16060873"},{"key":"ref_34","first-page":"458","article-title":"Multi-channel SAR-GMTI Clutter Suppression Method Based on Hypersonic Platform Forward Squint","volume":"42","author":"Wang","year":"2020","journal-title":"J. Electron. Inf. Technol."},{"key":"ref_35","unstructured":"Xiong, B., Xu, J., Peng, S., and Yang, J. (2013, January 14\u201316). Ground moving targets signal modeling for multi-channel squint-looking SAR. Proceedings of the International Radar Conference, Xi\u2019an, China."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Han, J., Cao, Y., Yeo, T.-S., and Wang, F. (2021). Robust Clutter Suppression and Ground Moving Target Imaging Method for a Multi-channel SAR with High-Squint Angle Mounted on Hypersonic Vehicle. Remote Sens., 13.","DOI":"10.3390\/rs13112051"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"6241","DOI":"10.1109\/TGRS.2015.2436371","article-title":"Signature morphology effects of squint angle for arbitrarily moving surface targets in spotlight synthetic aperture radar","volume":"53","author":"Garren","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Chen, Z., Zhou, Y., Zhang, L., Lin, C., Huang, Y., and Tang, S. (2018). Ground Moving Target Imaging and Analysis for Near-Space Hypersonic Vehicle-Borne Synthetic Aperture Radar System with Squint Angle. Remote Sens., 10.","DOI":"10.3390\/rs10121966"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2928","DOI":"10.1109\/TGRS.2019.2958067","article-title":"From Theory to Application: Real-Time Sparse SAR Imaging","volume":"58","author":"Bi","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/j.dsp.2018.05.004","article-title":"Fast Non-Searching Method for Ground Moving Target Refocusing and Motion Parameters Estimation","volume":"79","author":"He","year":"2018","journal-title":"Digit. Signal Process."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/21\/4373\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:23:25Z","timestamp":1760167405000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/21\/4373"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,30]]},"references-count":40,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["rs13214373"],"URL":"https:\/\/doi.org\/10.3390\/rs13214373","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,10,30]]}}}