{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:37:02Z","timestamp":1760236622212,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2021,12,8]],"date-time":"2021-12-08T00:00:00Z","timestamp":1638921600000},"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":["61601437"],"award-info":[{"award-number":["61601437"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Azimuth non-uniform signal-reconstruction is a critical step for azimuth multi-channel high-resolution wide-swath (HRWS) synthetic aperture radar (SAR) data processing. However, the received non-uniform signal has noise in the actual azimuth multi-channel SAR (MCSAR) operation, which leads to the serious reduction in the signal-to-noise ratio (SNR) of the results processed by a traditional reconstruction algorithm. Aiming to address the problem of reducing the SNR of the traditional reconstruction algorithm in the reconstruction of non-uniform signal with noise, a novel signal-reconstruction algorithm based on two-step projection technology (TSPT) for the MCSAR system is proposed in this paper. The key part of the TSPT algorithm consists of a two-step projection. The first projection is to project the given signal into the selected intermediate subspace, spanned by the integer conversion of the compact support kernel function. This process generates a set of sparse equations, which can be solved efficiently by using the sparse equation solver. The second key projection is to project the first projection result into the subspace of the known sampled signal. The secondary projection can be achieved with a digital linear translation invariant (LSI) filter and generate a uniformly spaced signal. As a result, compared with the traditional azimuth MCSAR signal-reconstruction algorithm, the proposed algorithm can improve SNR and reduce the azimuth ambiguity-signal-ratio (AASR). The processing results of simulated data and real raw data verify the effectiveness of the proposed algorithm.<\/jats:p>","DOI":"10.3390\/rs13244988","type":"journal-article","created":{"date-parts":[[2021,12,8]],"date-time":"2021-12-08T23:30:00Z","timestamp":1639006200000},"page":"4988","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["An Azimuth Signal-Reconstruction Method Based on Two-Step Projection Technology for Spaceborne Azimuth Multi-Channel High-Resolution and Wide-Swath SAR"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4358-6449","authenticated-orcid":false,"given":"Ning","family":"Li","sequence":"first","affiliation":[{"name":"College of Computer and Information Engineering, Henan University, Kaifeng 475004, China"},{"name":"Henan Engineering Research Center of Intelligent Technology and Application, Henan University, Kaifeng 475004, China"},{"name":"Henan Key Laboratory of Big Data Analysis and Processing, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hanqing","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Computer and Information Engineering, Henan University, Kaifeng 475004, China"},{"name":"Henan Engineering Research Center of Intelligent Technology and Application, Henan University, Kaifeng 475004, China"},{"name":"Henan Key Laboratory of Big Data Analysis and Processing, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3027-9837","authenticated-orcid":false,"given":"Jianhui","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Computer and Information Engineering, Henan University, Kaifeng 475004, China"},{"name":"Henan Engineering Research Center of Intelligent Technology and Application, Henan University, Kaifeng 475004, China"},{"name":"Henan Key Laboratory of Big Data Analysis and Processing, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2211-2965","authenticated-orcid":false,"given":"Lin","family":"Wu","sequence":"additional","affiliation":[{"name":"College of Computer and Information Engineering, Henan University, Kaifeng 475004, China"},{"name":"Henan Engineering Research Center of Intelligent Technology and Application, Henan University, Kaifeng 475004, China"},{"name":"Henan Key Laboratory of Big Data Analysis and Processing, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhengwei","family":"Guo","sequence":"additional","affiliation":[{"name":"College of Computer and Information Engineering, Henan University, Kaifeng 475004, China"},{"name":"Henan Engineering Research Center of Intelligent Technology and Application, Henan University, Kaifeng 475004, China"},{"name":"Henan Key Laboratory of Big Data Analysis and Processing, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,8]]},"reference":[{"key":"ref_1","unstructured":"Cumming, I.G., and Wong, F.H. (2005). Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation, Artech House."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4462","DOI":"10.1109\/TGRS.2013.2282192","article-title":"Staggered SAR: High-Resolution Wide-Swath Imaging by Continuous PRI Variation","volume":"52","author":"Villano","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1109\/TGRS.2012.2201947","article-title":"First Spaceborne Demonstration of Digital Beamforming for Azimuth Ambiguity Suppression","volume":"51","author":"Kim","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Yang, J., Qiu, X., Zhong, L., Shang, M., and Ding, C. (2019). A Simultaneous Imaging Scheme of Stationary Clutter and Moving Targets for Maritime Scenarios with the First Chinese Dual-Channel Spaceborne SAR Sensor. Remote Sens., 11.","DOI":"10.3390\/rs11192275"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Xu, W., Wei, Z., Huang, P., Tan, W., Liu, B., Gao, Z., and Dong, Y. (2020). Azimuth Multi-Channel Reconstruction for Moving Targets in Geosynchronous Spaceborne\u2013Airborne Bistatic SAR. Remote Sens., 12.","DOI":"10.3390\/rs12111703"},{"key":"ref_6","unstructured":"Curlander, J., and McDonough, R. (1991). Synthetic Aperture Radar: Systems and Signal Processing, Artech House."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1109\/LGRS.2011.2144563","article-title":"Airborne demonstration of multichannel SAR imaging","volume":"8","author":"Gebert","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1109\/36.823926","article-title":"The myth of the minimum SAR antenna area constraint","volume":"38","author":"Freeman","year":"2000","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1109\/LGRS.2004.832700","article-title":"Unambiguous SAR signal-reconstruction from nonuniform displaced phase center sampling","volume":"1","author":"Krieger","year":"2004","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Gebert, N., Krieger, G., and Moreira, A. (August, January 31). Digital Beam Forming for HRWS-SAR Imaging: System Design, Performance and Optimization Strategies. Proceedings of the 2006 IEEE International Symposium on Geoscience and Remote Sensing, Denver, CO, USA.","DOI":"10.1109\/IGARSS.2006.474"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Gebert, N., Krieger, G., Younis, M., Bordoni, F., and Moreira, A. (2008, January 6\u201311). Ultra Wide Swath Imaging with Multi-Channel ScanSAR. Proceedings of the IEEE International Geoscience and Remote Sensing Symposium, Boston, MA, USA.","DOI":"10.1109\/IGARSS.2008.4780017"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3881","DOI":"10.1109\/TGRS.2019.2959217","article-title":"Signal-reconstruction Algorithm for Azimuth Multichannel SAR System Based on a Multiobjective Optimization Model","volume":"58","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1109\/TGRS.2007.905974","article-title":"Multidimensional Waveform Encoding: A New Digital Beamforming Technique for Synthetic Aperture Radar Remote Sensing","volume":"46","author":"Krieger","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2994","DOI":"10.1109\/TGRS.2010.2041356","article-title":"Multi-channel Azimuth Processing in ScanSAR and TOPS Mode Operation","volume":"48","author":"Gebert","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4998","DOI":"10.1109\/JSTARS.2015.2421303","article-title":"Modifications on Multichannel Reconstruction Algorithm for SAR Processing Based on Periodic Nonuniform Sampling Theory and Nonuniform Fast Fourier Transform","volume":"8","author":"Zhao","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1109\/TGRS.2003.815662","article-title":"Digital beamforming in SAR systems","volume":"41","author":"Younis","year":"2003","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"782","DOI":"10.1109\/LGRS.2009.2025245","article-title":"Azimuth Phase Center Adaptation on Transmit for High-Resolution Wide-Swath SAR Imaging","volume":"6","author":"Gebert","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1049\/ip-f-2.1992.0016","article-title":"Wide-swath SAR","volume":"139","author":"Currie","year":"1992","journal-title":"IEE Proc. F Radar Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1109\/LGRS.2004.840610","article-title":"Generation of wide-swath and high-resolution SAR images from multi-channel small spaceborne SAR systems","volume":"2","author":"Li","year":"2005","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1109\/TAES.2006.1642562","article-title":"Performance improvement for constellation SAR using signal processing techniques","volume":"42","author":"Li","year":"2006","journal-title":"IEEE Trans. Aero. Elec. Sys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1209","DOI":"10.1109\/TGRS.2015.2476496","article-title":"Improved DBF Algorithm for Multi-channel High-Resolution Wide-Swath SAR","volume":"54","author":"Liu","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1109\/JSTARS.2016.2630048","article-title":"Modified Multi-Channel Reconstruction Method of SAR with Highly Nonuniform Spatial Sampling","volume":"10","author":"Liu","year":"2017","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1425","DOI":"10.1109\/JSTARS.2016.2618518","article-title":"Improved Signal-reconstruction Algorithm for Multi-channel SAR Based on the Doppler Spectrum Estimation","volume":"10","author":"Zuo","year":"2017","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4306","DOI":"10.1109\/TGRS.2013.2281329","article-title":"Multi-channel HRWS SAR Imaging Based on Range-Variant Channel Calibration and Multi-Doppler-Direction Restriction Ambiguity Suppression","volume":"52","author":"Zhang","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"564","DOI":"10.1109\/TAES.2009.5089542","article-title":"Digital Beamforming on Receive: Techniques and Optimization Strategies for High-Resolution Wide-Swath SAR Imaging","volume":"45","author":"Gebert","year":"2009","journal-title":"IEEE Trans. Aero. Electron. Sys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"628","DOI":"10.1109\/TMI.2016.2623711","article-title":"The SPURS Algorithm for Resampling an Irregularly Sampled Signal onto a Cartesian Grid","volume":"36","author":"Kiperwas","year":"2017","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Zhang, L., Gao, Y., Wang, K., and Liu, X. (2017, January 8\u201312). A Blind Reconstruction of Azimuth Signal for Multi-Channel HRWS SAR System. Proceedings of the Proceedings of the 2017 IEEE Radar Conference (RadarConf), Seattle, WA, USA.","DOI":"10.1109\/RADAR.2017.7944353"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Zhang, L., Gao, Y., Wang, K., and Liu, X. (2016, January 10\u201313). Azimuth Signal-Reconstruction for HRWS SAR from Recurrent Nonuniform Samples. Proceedings of the 2016 CIE International Conference on Radar (RADAR), Guangzhou, China.","DOI":"10.1109\/RADAR.2016.8059211"},{"key":"ref_29","unstructured":"Li, Z. (2006). Distributed Small Satellite SAR-InSAR-GMTI Signal Processing Algorithms. [Ph.D. Thesis, Xidian University]."},{"key":"ref_30","unstructured":"Zhang, S. (2014). High-Resolution and Wide-Swath Multi-Channel SAR and Moving Target Imaging Theory and Methods. [Ph.D. Thesis, Xidian University]."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Zhang, L. (2018). Azimuth Multi-Channel High-resolution and Wide-swath SAR Imaging Processing Technique. [Ph.D. Thesis, Shanghai Jiao Tong University].","DOI":"10.1109\/ACCESS.2018.2873739"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1145\/992200.992206","article-title":"An unsymmetric-pattern multifrontal method","volume":"30","author":"Davis","year":"2004","journal-title":"ACM Trans. Math. Softw."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Davis, T.A. (2006). Direct Methods for Sparse Linear Systems, Artech House.","DOI":"10.1137\/1.9780898718881"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Eldar, Y.C. (2015). Sampling Theory: Beyond Bandlimited Systems, Cambridge University Press.","DOI":"10.1017\/CBO9780511762321"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Zhao, P., Deng, Y., Wang, W., Zhang, Y., and Wang, R. (2021). Ambiguity Suppression Based on Joint Optimization for Multi-channel Hybrid and \u00b1\u03c0\/4 Quad-Pol SAR Systems. Remote Sens., 13.","DOI":"10.3390\/rs13101907"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/24\/4988\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:43:25Z","timestamp":1760168605000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/24\/4988"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,8]]},"references-count":35,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["rs13244988"],"URL":"https:\/\/doi.org\/10.3390\/rs13244988","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2021,12,8]]}}}