{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:10:39Z","timestamp":1760148639957,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,5,16]],"date-time":"2023-05-16T00:00:00Z","timestamp":1684195200000},"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","doi-asserted-by":"publisher","award":["12105177","61988102","21ZR1444300","HQ202204002"],"award-info":[{"award-number":["12105177","61988102","21ZR1444300","HQ202204002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Shanghai","award":["12105177","61988102","21ZR1444300","HQ202204002"],"award-info":[{"award-number":["12105177","61988102","21ZR1444300","HQ202204002"]}]},{"name":"Opened Foundation of Hongque Innovation Center","award":["12105177","61988102","21ZR1444300","HQ202204002"],"award-info":[{"award-number":["12105177","61988102","21ZR1444300","HQ202204002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Terahertz video synthetic aperture radar (THz-ViSAR) has tremendous research and application value due to its high resolution and high frame rate imaging benefits. However, it requires more efficient imaging algorithms. Thus, a novel multistage back projection fast imaging algorithm for the THz-ViSAR system is proposed in this paper to enable continuous playback of images like video. The radar echo data of the entire aperture is first divided into multiple sub-apertures, as with the fast-factorized back projection algorithm (FFBP). However, there are two improvements in sub-aperture imaging. On the one hand, the back projection algorithm (BPA) is replaced by the polar format algorithm (PFA) to improve the sub-aperture imaging efficiency. The imaging process, on the other hand, uses the global Cartesian coordinate system rather than the local polar coordinate system, and the wavenumber domain data of the full aperture are obtained step by step through simple splicing and fusion, avoiding the amount of two-dimensional (2D) interpolation operations required for local polar coordinate system transformation in FFBP. Finally, 2D interpolation for full-resolution images is carried out to image the ground object targets in the same coordinate system due to the geometric distortion caused by linear phase error (LPE) and the mismatch of coordinate systems in different imaging frames. The simulation experiments of point targets and surface targets both verify the effectiveness and superiority of the proposed algorithm. Under the same conditions, the running time of the proposed algorithm is only about 6% of FFBP, while the imaging quality is guaranteed.<\/jats:p>","DOI":"10.3390\/rs15102602","type":"journal-article","created":{"date-parts":[[2023,5,17]],"date-time":"2023-05-17T01:58:06Z","timestamp":1684288686000},"page":"2602","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Novel Multistage Back Projection Fast Imaging Algorithm for Terahertz Video Synthetic Aperture Radar"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6945-8293","authenticated-orcid":false,"given":"Qibin","family":"Zheng","sequence":"first","affiliation":[{"name":"School of Health Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China"},{"name":"Terahertz Technology Innovation Research Institute, University of Shanghai for Science and Technology, Shanghai 200093, China"}]},{"given":"Shuangli","family":"Shang","sequence":"additional","affiliation":[{"name":"School of Health Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0002-186X","authenticated-orcid":false,"given":"Yinwei","family":"Li","sequence":"additional","affiliation":[{"name":"Terahertz Technology Innovation Research Institute, University of Shanghai for Science and Technology, Shanghai 200093, China"}]},{"given":"Yiming","family":"Zhu","sequence":"additional","affiliation":[{"name":"Terahertz Technology Innovation Research Institute, University of Shanghai for Science and Technology, Shanghai 200093, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2838","DOI":"10.1109\/TAES.2016.150581","article-title":"Processing video-SAR data with the fast backprojection method","volume":"52","author":"Song","year":"2017","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1109\/MGRS.2022.3218801","article-title":"Sparse synthetic aperture radar imaging from compressed sensing and machine learning: Theories, applications, and trends","volume":"10","author":"Xu","year":"2022","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Zhang, B., Xu, G., Zhou, R., Zhang, H., and Hong, W. (2022). Multi-channel back-projection algorithm for mmwave automotive MIMO SAR imaging with Doppler-division multiplexing. IEEE J. Sel. Top. Signal Process., 1\u201313.","DOI":"10.1109\/JSTSP.2022.3207902"},{"key":"ref_4","first-page":"103295","article-title":"Joint autofocus and registration for video-SAR by using sub-aperture point cloud","volume":"118","author":"Shi","year":"2023","journal-title":"Int. J. Appl. Earth Obs. Geoinf."},{"key":"ref_5","unstructured":"Defense Advanced Research Projects Agency (2022, March 02). Broad Agency Announcement: Video Synthetic Aperture Radar (Visar) System Design and Development, Available online: https:\/\/govtribe.com\/project\/videosynthetic-aperture-radarvisar-system-design-and-development."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1109\/TTHZ.2018.2872412","article-title":"Unified Coordinate System Algorithm for Terahertz Video-SAR Image Formation","volume":"8","author":"Zuo","year":"2018","journal-title":"IEEE Trans. Terahertz Sci. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1109\/LGRS.2020.2988165","article-title":"Robust shadow tracking for video SAR","volume":"18","author":"Zhao","year":"2021","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Shen, W., Xia, L., Lin, Y., Shang, S., and Hong, W. (2023). Video SAR Moving Target Shadow Detection Based on Intensity Information and Neighborhood Similarity. Remote Sens., 15.","DOI":"10.3390\/rs15071859"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Yang, C., Chen, Z., Deng, Y., Wang, W., Wang, P., and Zhao, F. (2023). Generation of Multiple Frames for High Resolution Video SAR Based on Time Frequency Sub-Aperture Technique. Remote Sens., 15.","DOI":"10.3390\/rs15010264"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Miller, J., Bishop, E., and Doerry, A. (2013, January 23). An application of backprojection for video SAR image formation exploiting a subaperature circular shift register. Proceedings of the Algorithms for Synthetic Aperture Radar Imagery XX, Baltimore, MD, USA.","DOI":"10.1117\/12.2016417"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wallace, H.B. (2015, January 21). Development of a video SAR for FMV through clouds. Proceedings of the Open Architecture\/Open Business Model Net-Centric Systems and Defense Transformation, Baltimore, MD, USA.","DOI":"10.1117\/12.2181420"},{"key":"ref_12","unstructured":"Langdon, R.M., Handerek, V., Harrison, P., Eisele, H., Stringer, M., Tae, C.F., and Dunn, M.H. (2004, January 20\u201321). Military applications of terahertz imaging. Proceedings of the 1st EMRS DTC Technical Conference, Edinburgh, UK."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Li, Y., Wu, Q., Jiang, J., Ding, X., Zheng, Q., and Zhu, Y. (2021). A High-Frequency Vibration Error Compensation Method for Terahertz SAR Imaging Based on Short-Time Fourier Transform. Appl. Sci., 11.","DOI":"10.3390\/app112210862"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1038\/nphoton.2007.3","article-title":"Cutting-edge terahertz technology","volume":"1","author":"Tonouchi","year":"2007","journal-title":"Nat. Photonics"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Li, Y., Ding, L., Zheng, Q., Zhu, Y., and Sheng, J. (2020). A Novel High-Frequency Vibration Error Estimation and Compensation Algorithm for THz-SAR Imaging Based on Local FrFT. Sensors, 20.","DOI":"10.3390\/s20092669"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1683","DOI":"10.1109\/JPROC.2007.898832","article-title":"Millimeter-Wave and Submillimeter-Wave Imaging for Security and Surveillance","volume":"95","author":"Appleby","year":"2007","journal-title":"Proc. IEEE"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"5485","DOI":"10.1109\/ACCESS.2020.3047856","article-title":"Estimation of High-Frequency Vibration Parameters for Terahertz SAR Imaging Based on FrFT with Combination of QML and RANSAC","volume":"9","author":"Li","year":"2021","journal-title":"IEEE Access"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Jiang, J., Li, Y., and Zheng, Q. (2021, January 15\u201319). A THz Video SAR Imaging Algorithm Based on Chirp Scaling. Proceedings of the 2021 CIE International Conference on Radar, Haikou, China.","DOI":"10.1109\/Radar53847.2021.10028231"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1109\/TNNLS.2020.2978017","article-title":"Video SAR Imaging Based on Low-Rank Tensor Recovery","volume":"32","author":"Pu","year":"2021","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_20","first-page":"5214913","article-title":"Joint Low-Rank and Sparse Tensors Recovery for Video Synthetic Aperture Radar Imaging","volume":"60","author":"An","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1109\/TCI.2021.3069762","article-title":"Video-SAR Imaging of Dynamic Scenes Using Low-Rank and Sparse Decomposition","volume":"7","author":"Moradikia","year":"2021","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Gorham, L., and Moore, R.J. (2010, January 8\u20139). SAR image formation toolbox for MATLAB. Proceedings of the Algorithms for Synthetic Aperture Radar Imagery XVII, Orlando, FL, USA.","DOI":"10.1117\/12.855375"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Musgrove, C. (2012). Polar Format Algorithm: Survey of Assumptions and Approximations.","DOI":"10.2172\/1059472"},{"key":"ref_24","unstructured":"Yegulalp, A.F. (1999, January 22\u201322). 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_25","doi-asserted-by":"crossref","first-page":"1760","DOI":"10.1109\/83.869187","article-title":"O(N2log2N) filtered backprojection reconstruction algorithm for tomography","volume":"9","author":"Basu","year":"2000","journal-title":"IEEE Trans. Image Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1109\/TAES.2003.1238734","article-title":"Synthetic-aperture radar processing using fast factorized back-projection","volume":"39","author":"Ulander","year":"2003","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_27","first-page":"8","article-title":"An implementation of a fast backprojection image formation algorithm for spotlight-mode SAR","volume":"6970","author":"Wahl","year":"2008","journal-title":"Proc. Spie"},{"key":"ref_28","unstructured":"Yang, Z.M., Sun, G.C., and Xing, M. (2013, January 23\u201327). A new fast Back-Projection Algorithm using Polar Format Algorithm. Proceedings of the Synthetic Aperture Radar (APSAR), Tsukuba, Japan."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1460","DOI":"10.1109\/LGRS.2013.2295326","article-title":"A Fast BP Algorithm With Wavenumber Spectrum Fusion for High-Resolution Spotlight SAR Imaging","volume":"11","author":"Lei","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_30","first-page":"11","article-title":"A coordinate-transform based FFBP algorithm for high-resolution spotlight SAR imaging","volume":"2","author":"Yang","year":"2015","journal-title":"Sci. China Inf. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Gorham, L., Majumder, U.K., Buxa, P., Backues, M.J., and Lindgren, A.C. (2006, January 17\u201321). Implementation and analysis of a fast backprojection algorithm. Proceedings of the Algorithms for Synthetic Aperture Radar Imagery XIII, Orlando, FL, USA.","DOI":"10.1117\/12.674024"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2949","DOI":"10.1109\/TAES.2011.6034676","article-title":"Efficient Time-Domain Image Formation with Precise Topography Accommodation for General Bistatic SAR Configurations","volume":"47","author":"Prats","year":"2011","journal-title":"Aerosp. Electron. Syst. IEEE Trans."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"724","DOI":"10.1109\/LGRS.2017.2676118","article-title":"Spectrum-Oriented FFBP Algorithm in Quasi-Polar Grid for SAR Imaging on Maneuvering Platform","volume":"14","author":"Yang","year":"2017","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1494","DOI":"10.1109\/JSTARS.2016.2639580","article-title":"Fast Factorized Backprojection Algorithm for One-Stationary 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_35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11432-015-0927-3","article-title":"Application of fast factorized back-projection algorithm for high-resolution highly squinted airborne SAR imaging","volume":"60","author":"Zhang","year":"2017","journal-title":"Sci. China Inf. Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1049\/ip-rsn:20045110","article-title":"Evaluation of angular interpolation kernels in fast back-projection SAR processing","volume":"153","author":"Ulander","year":"2006","journal-title":"IEE Proc.-Radar Sonar Navig."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1109\/36.739168","article-title":"Evaluation of Interpolation Kernels for SAR Interferometry","volume":"37","author":"Hanssen","year":"1999","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1109\/LGRS.2007.895961","article-title":"Efficient Interpolation of SAR Images for Coregistration in SAR Interferometry","volume":"4","author":"Selva","year":"2007","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Garber, W.L., and Hawley, R.W. (2011, January 25\u201329). Extensions to polar formatting with spatially variant post-filtering. Proceedings of the Algorithms for Synthetic Aperture Radar Imagery XVIII, Orlando, FL, USA.","DOI":"10.1117\/12.888947"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Mao, D., and Rigling, B.D. (2017, January 8\u201312). Distortion correction and scene size limits for SAR bistatic polar format algorithm. Proceedings of the 2017 IEEE Radar Conference (RadarConf), Seattle, WA, USA.","DOI":"10.1109\/RADAR.2017.7944369"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1109\/TAES.2005.1413746","article-title":"Taylor expansion of the differential range for monostatic SAR","volume":"41","author":"Rigling","year":"2008","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Jakowatz, C.V., Wahl, D.E., Thompson, P.A., and Doren, N.E. (1997, January 21\u201325). Space-variant filtering for correction of wavefront curvature effects in spotlight-mode SAR imagery formed via polar formatting. Proceedings of the Algorithms for Synthetic Aperture Radar Imagery IV, Orlando, FL, USA.","DOI":"10.1117\/12.281576"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Doerry, A.W. (2007). Wavefront Curvature Limitations and Compensation to Polar Format Processing for Synthetic Aperture Radar Images.","DOI":"10.2172\/902879"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1011","DOI":"10.1109\/TSP.2006.887144","article-title":"Range resampling in the polar format algorithm for spotlight SAR image formation using the chirp z-transform","volume":"55","author":"Zhu","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1109\/LGRS.2008.2000971","article-title":"The Polar Format Imaging Algorithm Based on Double Chirp-Z Transforms","volume":"5","author":"Yu","year":"2008","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_46","unstructured":"Zuo, F., and Li, J. (2018, January 14\u201316). A ViSAR Imaging Method for Terahertz Band Using Chirp Z-Transform. Proceedings of the Communications, Signal Processing, and Systems: Proceedings of the 2018 CSPS Volume II: Signal Processing 7th, Dalian, China."},{"key":"ref_47","first-page":"108","article-title":"Digital processing of synthetic aperture radar data","volume":"1","author":"Cumming","year":"2005","journal-title":"Artech House"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"60","DOI":"10.3724\/SP.J.1300.2013.20107","article-title":"Joint Three-dimensional Location Algorithm for Airborne Interferometric SAR System","volume":"2","author":"Mao","year":"2013","journal-title":"J. Radars"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1109\/36.124221","article-title":"SARAS: A synthetic aperture radar(SAR) raw signal simulator","volume":"30","author":"Franceschetti","year":"1992","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_50","unstructured":"Shoalehvar, A. (2012). Synthetic Aperture Radar (SAR) Raw Signal Simulation. [Master\u2019s Thesis, California Polytechnic State University]."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Zhang, S.-S., Zeng, T., Long, T., and Chen, J. (2006, January 16\u201319). Research on echo simulation of space-borne bistatic SAR. Proceedings of the 2006 CIE International Conference on Radar, Shanghai, China.","DOI":"10.1109\/ICR.2006.343302"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/10\/2602\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:36:26Z","timestamp":1760124986000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/10\/2602"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,16]]},"references-count":51,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["rs15102602"],"URL":"https:\/\/doi.org\/10.3390\/rs15102602","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2023,5,16]]}}}