{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T21:22:52Z","timestamp":1767993772182,"version":"3.49.0"},"reference-count":34,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,5,9]],"date-time":"2022-05-09T00:00:00Z","timestamp":1652054400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China (NNSFC)","doi-asserted-by":"publisher","award":["61861136008"],"award-info":[{"award-number":["61861136008"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China (NNSFC)","doi-asserted-by":"publisher","award":["SAST2020\u2212038"],"award-info":[{"award-number":["SAST2020\u2212038"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shanghai Aerospace Science and Technology Innovation Fund","award":["61861136008"],"award-info":[{"award-number":["61861136008"]}]},{"name":"Shanghai Aerospace Science and Technology Innovation Fund","award":["SAST2020\u2212038"],"award-info":[{"award-number":["SAST2020\u2212038"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Ultra\u2212high spatial resolution, which can bring more detail to ground observation, is a constant pursuit of the modern space\u2212borne synthetic aperture radar. However, the exact imaging in this case has always been a complex technical problem due to its complicated imaging geometry and signal structure. To achieve those applications\u2019 strict requirements, a novel ultra\u2212high resolution imaging algorithm based on an accurate high\u2212order 2\u2212D spectrum is presented in this paper. The only first two Doppler parameters needed as range models in the defective spectrum are replaced by a polynomial range model, which can derive coefficients from the relative motion between the radar and the targets. Then, the new spectrum is calculated through the Lagrange inversion formula. Based on this, the novel imaging algorithm is elaborated in detail as follows: The range high\u2212order term of the spectrum is compensated completely, and the range chirp rate space variance is eliminated by the cubic phase term. Two steps of range cell migration correct are applied in this algorithm before and after the range compression; one is the traditional linear chirp scaling method, and another is the interpolation to correct the quadratic range cell migration introduced by the range chirp rate equalization. The simulation results illustrate that the proposed algorithm can handle the exact imaging processing with a 0.25 m resolution around the azimuth and range in 2 km \u00d7 6 km, which validates the feasibility of the proposed algorithm.<\/jats:p>","DOI":"10.3390\/rs14092284","type":"journal-article","created":{"date-parts":[[2022,5,10]],"date-time":"2022-05-10T00:30:28Z","timestamp":1652142628000},"page":"2284","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Novel Ultra\u2212High Resolution Imaging Algorithm Based on the Accurate High\u2212Order 2\u2212D Spectrum for Space\u2212Borne SAR"],"prefix":"10.3390","volume":"14","author":[{"given":"Tao","family":"He","sequence":"first","affiliation":[{"name":"School of Electronics and Information Engineering, Beihang University, Beijing 100191, China"}]},{"given":"Lei","family":"Cui","sequence":"additional","affiliation":[{"name":"Shanghai Institute of Satellite Engineering, Shanghai 201109, China"}]},{"given":"Pengbo","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Beihang University, Beijing 100191, China"}]},{"given":"Yanan","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Beihang University, Beijing 100191, China"}]},{"given":"Lei","family":"Zhuang","sequence":"additional","affiliation":[{"name":"Shanghai Institute of Satellite Engineering, Shanghai 201109, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"606","DOI":"10.1109\/TGRS.2009.2031062","article-title":"The TerraSAR\u2212X Mission and System Design","volume":"48","author":"Werninghaus","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1109\/TGRS.2009.2035497","article-title":"TerraSAR\u2212X SAR Processing and Products","volume":"48","author":"Breit","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1109\/TGRS.2009.2037432","article-title":"The TerraSAR\u2212X Satellite","volume":"48","author":"Pitz","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.jog.2010.01.001","article-title":"COSMO\u2212SkyMed an existing opportunity for observing the Earth","volume":"49","author":"Covello","year":"2010","journal-title":"J. Geodyn."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Mezzasoma, S., Gallon, A., Impagnatiello, F., Angino, G., Fagioli, S., Capuzi, A., Caltagirone, F., Leonardi, R., and Ziliotto, U. (2008, January 26\u201330). COSMO\u2212SkyMed system commissioning: End\u2212to\u2212end system performance verification. Proceedings of the 2008 IEEE Radar Conference, Rome, Italy.","DOI":"10.1109\/RADAR.2008.4720930"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Janoth, J., Gantert, S., Schrage, T., and Kaptein, A. (2013, January 21\u201326). Terrasar next generation\u2014Mission capabilities. Proceedings of the 2013 IEEE International Geoscience and Remote Sensing Symposium\u2014IGARSS, Melbourne, VIC, Australia.","DOI":"10.1109\/IGARSS.2013.6723277"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1080\/01431169108929650","article-title":"A new approach to range\u2212Doppler SAR processing","volume":"12","author":"Smith","year":"1991","journal-title":"Int. J. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"786","DOI":"10.1109\/36.298008","article-title":"Precision SAR processing using chirp scaling","volume":"32","author":"Raney","year":"1994","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1109\/7.78293","article-title":"SAR data focusing using seismic migration techniques","volume":"27","author":"Cafforio","year":"1991","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2668","DOI":"10.1109\/36.803414","article-title":"Time\u2212varying step\u2212transform algorithm for high squint SAR imaging","volume":"37","author":"Sun","year":"1999","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"706","DOI":"10.1109\/36.158864","article-title":"A comparison of range\u2212Doppler and wavenumber domain SAR focusing algorithms","volume":"30","author":"Bamler","year":"1992","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_12","unstructured":"Yegulalp, F.A. (1999, January 22). Fast backprojection algorithm for synthetic aperture radar. Proceedings of the 1999 IEEE Radar Conference. Radar into the Next Millennium (Cat. No.99CH36249), Waltham, MA, USA."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1109\/TAES.2003.1238734","article-title":"Synthetic\u2212aperture radar processing using fast factorized back\u2212projection","volume":"39","author":"Ulander","year":"2003","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_14","first-page":"1","article-title":"Efficient Fast Time\u2212Domain Processing Framework for Airborne Bistatic SAR Continuous Imaging Integrated With Data\u2212Driven Motion Compensation","volume":"60","author":"Xu","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1494","DOI":"10.1109\/JSTARS.2016.2639580","article-title":"Fast Factorized Backprojection Algorithm for One\u2212Stationary Bistatic Spotlight Circular SAR Image Formation","volume":"10","author":"Xie","year":"2017","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"824","DOI":"10.1109\/7.705890","article-title":"A new fourth\u2212order processing algorithm for spaceborne SAR","volume":"34","author":"Eldhuset","year":"1998","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1109\/LGRS.2008.2010781","article-title":"Spaceborne Bistatic SAR Processing Using the EETF4 Algorithm","volume":"6","author":"Eldhuset","year":"2009","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1109\/TAES.2004.1292176","article-title":"Ultra high resolution spaceborne SAR processing","volume":"40","author":"Eldhuset","year":"2004","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Wang, P., Han, Y., Chen, J., Cui, Z., Yang, W., and Li, S. (2013, January 21\u201326). A refined chirp scaling algorithm for high\u2212resolution spaceborne SAR based on the fourth\u2212order model. Proceedings of the 2013 IEEE International Geoscience and Remote Sensing Symposium\u2014IGARSS, Melbourne, VIC, Australia.","DOI":"10.1109\/IGARSS.2013.6723214"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3473","DOI":"10.1109\/TGRS.2013.2273086","article-title":"A Novel High\u2212Order Range Model and Imaging Approach for High\u2212Resolution LEO SAR","volume":"52","author":"Luo","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1225","DOI":"10.1109\/TGRS.2014.2336241","article-title":"A High\u2212Order Imaging Algorithm for High\u2212Resolution Spaceborne SAR Based on a Modified Equivalent Squint Range Model","volume":"53","author":"Wang","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Vizitiu, I., Anton, L., Popescu, F., and Iubu, G. (2012, January 15\u201316). The synthesis of some NLFM laws using the stationary phase principle. Proceedings of the 2012 10th International Symposium on Electronics and Telecommunications, Timisoara, Romania.","DOI":"10.1109\/ISETC.2012.6408053"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Li, C., Zhang, H., and Deng, Y. (2021). Focus Improvement of Airborne High\u2212Squint Bistatic SAR Data Using Modified Azimuth NLCS Algorithm Based on Lagrange Inversion Theorem. Remote Sens., 13.","DOI":"10.3390\/rs13101916"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Chen, X., Yi, T., He, F., He, Z., and Dong, Z. (2019). An Improved Generalized Chirp Scaling Algorithm Based on Lagrange Inversion Theorem for High\u2212Resolution Low Frequency Synthetic Aperture Radar Imaging. Remote Sens., 11.","DOI":"10.3390\/rs11161874"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1109\/7.481254","article-title":"A chirp scaling approach for processing squint mode SAR data","volume":"32","author":"Davidson","year":"1996","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2493","DOI":"10.1109\/TGRS.2008.917599","article-title":"Focusing Bistatic SAR Data Using the Nonlinear Chirp Scaling Algorithm","volume":"46","author":"Wong","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Jeffrey, D.J., Kalugin, G.A., and Murdoch, N. (2015, January 21\u201324). Lagrange Inversion and Lambert W. Proceedings of the 2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), Timisoara, Romania.","DOI":"10.1109\/SYNASC.2015.16"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2889","DOI":"10.1109\/TGRS.2011.2174460","article-title":"Extended Two\u2212Step Focusing Approach for Squinted Spotlight SAR Imaging","volume":"50","author":"An","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1993","DOI":"10.1109\/36.951090","article-title":"Spotlight SAR data focusing based on a two\u2212step processing approach","volume":"39","author":"Lanari","year":"2001","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Pengbo, W., Zhou, Y., Chen, J., Li, C., Yu, Z., and Min, H. (August, January 31). A Deramp Frequency Scaling Algorithm for Processing Space\u2212Borne Spotlight SAR Data. Proceedings of the 2006 IEEE International Symposium on Geoscience and Remote Sensing, Denver, CO, USA.","DOI":"10.1109\/IGARSS.2006.808"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Deng, R., Tian, X., Kang, Z.\u2212M., Hong, B., and Wang, W.\u2212Q. (2021, January 11\u201316). Linear Programming Based Sidelobe Suppression for SAR Image Optimization. Proceedings of the 2021 IEEE International Geoscience and Remote Sensing Symposium IGARSS, Brussels, Belgium.","DOI":"10.1109\/IGARSS47720.2021.9554791"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1056","DOI":"10.1109\/7.953256","article-title":"Robust autofocus algorithm for ISAR imaging of moving targets","volume":"37","author":"Li","year":"2001","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"5220714","DOI":"10.1109\/TGRS.2021.3139914","article-title":"SAE\u2212Net: A Deep Neural Network for SAR Autofocus","volume":"60","author":"Pu","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Liu, Z., Yang, S., Feng, Z., Gao, Q., and Wang, M. (2021). Fast SAR Autofocus Based on Ensemble Convolutional Extreme Learning Machine. Remote Sens., 13.","DOI":"10.3390\/rs13142683"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/9\/2284\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:08:18Z","timestamp":1760137698000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/9\/2284"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,9]]},"references-count":34,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["rs14092284"],"URL":"https:\/\/doi.org\/10.3390\/rs14092284","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,9]]}}}