{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:36:05Z","timestamp":1760150165865,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T00:00:00Z","timestamp":1698364800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2021YFC3001903","CSTB2022NSCQ-BHX0713","62101036"],"award-info":[{"award-number":["2021YFC3001903","CSTB2022NSCQ-BHX0713","62101036"]}]},{"name":"Natural Science Foundation of Chongqing, China","award":["2021YFC3001903","CSTB2022NSCQ-BHX0713","62101036"],"award-info":[{"award-number":["2021YFC3001903","CSTB2022NSCQ-BHX0713","62101036"]}]},{"name":"National Natural Science Foundation of China","award":["2021YFC3001903","CSTB2022NSCQ-BHX0713","62101036"],"award-info":[{"award-number":["2021YFC3001903","CSTB2022NSCQ-BHX0713","62101036"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The miniaturized and lightweight unmanned aerial vehicle synthetic aperture radar (UAV SAR) is gradually becoming a research hotspot. The motion errors of UAVs lead to a deviation from a straight flight path couple with an unknown elevation of the target area, which leads to a degradation in SAR image quality. To achieve high-precision SAR imaging results, external terrain elevation information should be utilized. However, such data are challenging to obtain and limited in accuracy. In response to this problem, a modified high-precision imaging algorithm based on imaging plane optimization with minimum entropy is proposed. The proposed algorithm makes good use of the nonlinear trajectory of the UAV, which is unfriendly to imaging. Then, the image entropy is taken into account as the evaluation metric to acquire an approximated optimization imaging plane. Finally, the BP imaging is performed on the optimization imaging plane. The proposed method does not rely on external terrain information. Instead, it makes full use of the non-linear trajectory of the UAV and autonomously generates the optimal imaging plane for different terrain areas. By doing so, it achieves high-precision imaging results. Simulations and actual measurements have validated the effectiveness and enhancement of the proposed method.<\/jats:p>","DOI":"10.3390\/rs15215147","type":"journal-article","created":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T09:56:36Z","timestamp":1698400596000},"page":"5147","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Modified High-Precision Imaging Algorithm Based on Imaging Plane Optimization with Minimum Entropy Applied to UAV SAR"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-5859-2083","authenticated-orcid":false,"given":"Xingwang","family":"Du","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering, Chongqing Three Gorges University, Chongqing 404020, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9618-6019","authenticated-orcid":false,"given":"Xin","family":"Xie","sequence":"additional","affiliation":[{"name":"Radar Research Lab, School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhijun","family":"Yang","sequence":"additional","affiliation":[{"name":"Chongqing Innovation Center Beijing, Institute of Technology, Chongqing 401147, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weiming","family":"Tian","sequence":"additional","affiliation":[{"name":"Radar Research Lab, School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China"},{"name":"Chongqing Innovation Center Beijing, Institute of Technology, Chongqing 401147, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,27]]},"reference":[{"key":"ref_1","unstructured":"Cumming, I.G., and Wong, F.H. (2005). Digital Processing of Synthetic Aperture Radar Data: Algorithm and Implementation, Artech House."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2013","DOI":"10.1109\/LGRS.2017.2747602","article-title":"Recent Advances in Synthetic Aperture Radar Remote Sensing\u2014Systems, Data Processing, and Applications","volume":"14","author":"Sun","year":"2017","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"910","DOI":"10.1109\/JSTARS.2019.2895467","article-title":"Dot and Segment Feature Analysis and Parameter Inversion of a Curved and Graded Bay Bridge from UAVSAR Imagery","volume":"12","author":"Gan","year":"2019","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_4","first-page":"511","article-title":"Optimizing the Minimum Cost Flow Algorithm for the Phase Unwrapping Process in SAR Radar","volume":"62","author":"Dudczyk","year":"2014","journal-title":"Bull. Pol. Acad. Sci. Tech. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Matuszewski, J. (2016, January 23\u201326). The Analysis of Modern Radar Signals Parameters in Electronic Intelligence System. Proceedings of the 13th International Conference on Modern Problems of Radio Engineering, Telecommunications and Computer Science (TCSET), Lviv, Ukraine.","DOI":"10.1109\/TCSET.2016.7452040"},{"key":"ref_6","first-page":"100","article-title":"An Improved Phase Filtering Method for Ground-based Differential Interferometer Radar Based on Non-Local Means","volume":"38","author":"Feng","year":"2022","journal-title":"J. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1858","DOI":"10.1109\/TMTT.2019.2961911","article-title":"Range-Doppler Map Improvement in FMCW Radar for Small Moving Drone Detection Using the Stationary Point Concentration Technique","volume":"68","author":"Park","year":"2020","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"706","DOI":"10.1109\/36.158864","article-title":"A comparison of range-Doppler and wavenumber domain SAR focusing algorithms","volume":"30","author":"Bamler","year":"1992","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","unstructured":"Frey, O., Magnard, C., R\u00fcegg, M., and Meier, E. (2008, January 2\u20135). Non-Linear SAR Data Processing by Time-Domain Back-Projection. Proceedings of the 7th European Conference on Synthetic Aperture Radar, Friedrichshafen, Germany."},{"key":"ref_10","unstructured":"Tian, W., Liu, F., Xie, X., Wang, C., Wang, J., and Deng, Y. (2023). Research on Parallel Acceleration Processing Technology of SAR Back Projection Algorithm Based on Two Granularities and Mixing Precision of GPU. J. Signal Process., (In Chinese)."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1109\/LGRS.2007.895712","article-title":"Comparison of Topography and Aperture Dependent Motion Compensation Algorithms for Airborne SAR","volume":"4","author":"Prats","year":"2007","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1109\/LGRS.2004.842465","article-title":"Precise topography- and aperture-dependent motion compensation for airborne SAR","volume":"2","author":"Scheiber","year":"2005","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2870","DOI":"10.1109\/TGRS.2009.2015657","article-title":"Motion compensation for UAV SAR based on raw radar data","volume":"47","author":"Xing","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Wang, W., An, D., Luo, Y., Zhou, Z., and Huang, X. (2018, January 6\u20139). A Modified Map-Drift Algorithm for SAR Autofocusing. Proceedings of the 2018 Asia-Pacific Microwave Conference (APMC), Kyoto, Japan.","DOI":"10.23919\/APMC.2018.8617613"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Huang, Y., Liu, F., Chen, Z., Li, J., and Hong, W. (IEEE Geosci. Remote Sensing. Lett., 2020). An improved map-drift algorithm for unmanned aerial vehicle SAR imaging, IEEE Geosci. Remote Sensing. Lett., early access.","DOI":"10.1109\/LGRS.2020.3011973"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1158","DOI":"10.1109\/LGRS.2016.2574752","article-title":"Range-dependent map-drift algorithm for focusing UAV SAR imagery","volume":"13","author":"Zhang","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Zhu, D. (2009, January 26\u201330). SAR signal based motion compensation through combining PGA and 2-D map drift. Proceedings of the 2009 2nd Asian-Pacific Conference on Synthetic Aperture Radar, Xi\u2019an, China.","DOI":"10.1109\/APSAR.2009.5374289"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1109\/LGRS.2020.2984909","article-title":"Azimuth migration-corrected phase gradient autofocus for bistatic SAR polar format imaging","volume":"18","author":"Miao","year":"2021","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2086","DOI":"10.1109\/TGRS.2014.2353515","article-title":"Semiparametric Statistical Stripmap Synthetic Aperture Autofocusing","volume":"53","author":"Marston","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4017805","DOI":"10.1109\/LGRS.2021.3106636","article-title":"Accelerating Minimum Entropy Autofocus with Stochastic Gradient for UAV SAR Imagery","volume":"19","author":"Meng","year":"2022","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3425","DOI":"10.1109\/TSP.2015.2422686","article-title":"Fast entropy minimization based autofocusing technique for ISAR imaging","volume":"63","author":"Zhang","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_22","first-page":"5102113","article-title":"An Efficient ISAR Imaging Approach for Highly Maneuvering Targets Based on Subarray Averaging and Image Entropy","volume":"60","author":"Yang","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1109\/TGRS.2019.2936432","article-title":"Full-Aperture Azimuth Spatial-Variant Autofocus Based on Contrast Maximization for Highly Squinted Synthetic Aperture Radar","volume":"58","author":"Huang","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3408","DOI":"10.1109\/TGRS.2017.2670785","article-title":"An Autofocus Algorithm for Estimating Residual Trajectory Deviations in Synthetic Aperture Radar","volume":"55","author":"Ran","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1086","DOI":"10.1109\/LGRS.2013.2286410","article-title":"Sharpness-based autofocusing for strip map SAR using an adaptive-order polynomial model","volume":"11","author":"Gao","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"4545","DOI":"10.1109\/TGRS.2017.2693396","article-title":"A New Analytical Model to Study the Ionospheric Effects on VHF\/UHF Wideband SAR Imaging","volume":"55","author":"Wang","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1109\/MGRS.2015.2437353","article-title":"Tandem-L: A highly innovative bistatic SAR mission for global observation of dynamic processes on the Earth\u2019s surface","volume":"3","author":"Moreira","year":"2015","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Lin, C., Tang, S., Zhang, L., and Guo, P. (2018). Focusing High-Resolution Airborne SAR with Topography Variations Using an Extended BPA Based on a Time\/Frequency Rotation Principle. Remote Sens., 10.","DOI":"10.3390\/rs10081275"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Wang, Y., Song, Y., Lin, Y., Li, Y., Zhang, Q., and Liu, Y. (2019, January 26\u201329). The high precision imaging method for ArcSAR based on DEM-assist. Proceedings of the 2019 6th Asia-Pacific Conference on Synthetic Aperture Radar (APSAR), Xiamen, China.","DOI":"10.1109\/APSAR46974.2019.9048306"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Jones, C., Hensley, S., and Michel, T. (2009, January 4\u20138). Topography-dependent motion compensation: Application to UAVSAR data. Proceedings of the 2009 IEEE Radar Conference, Pasadena, CA, USA.","DOI":"10.1109\/RADAR.2009.4977084"},{"key":"ref_31","first-page":"466","article-title":"Evaluating the global elevation data from multiple sources for digital Earth applications","volume":"10","author":"Zhang","year":"2021","journal-title":"ISPRS Int. J. Geo-Inf."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1109\/83.199920","article-title":"Convolution back-projection image reconstruction for spotlight mode synthetic aperture radar","volume":"1","author":"Desai","year":"1992","journal-title":"IEEE Trans. Image Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"334","DOI":"10.3724\/SP.J.1300.2013.13013","article-title":"Performance Analysis of Flat Surface Assumption and Residual Motion Errors on Airborne Repeat-pass InSAR","volume":"2","author":"Xue","year":"2013","journal-title":"J. Radars"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1109\/LGRS.2011.2161456","article-title":"An autofocus method for back projection imagery in synthetic aperture radar","volume":"9","author":"Ash","year":"2012","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Yang, Z., Li, D., Tan, X., Liu, H., and Liao, G. (2020). A Fast Bistatic ISAR Imaging Approach for Rapidly Spinning Targets via Exploiting SAR Technique. Remote Sens., 12.","DOI":"10.3390\/rs12132077"},{"key":"ref_36","first-page":"1147","article-title":"Monotonic iterative algorithm for minimum-entropy autofocus","volume":"40","author":"Kragh","year":"2006","journal-title":"Adapt. Sens. Array Process. (ASAP) Workshop"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/21\/5147\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:13:05Z","timestamp":1760130785000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/21\/5147"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,27]]},"references-count":36,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["rs15215147"],"URL":"https:\/\/doi.org\/10.3390\/rs15215147","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2023,10,27]]}}}