{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:21:44Z","timestamp":1760235704061,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2021,9,24]],"date-time":"2021-09-24T00:00:00Z","timestamp":1632441600000},"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":["61771478"],"award-info":[{"award-number":["61771478"]}],"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>Distributed radar array brings several new forthcoming advantages in aerospace target detection and imaging. The two-dimensional distributed array avoids the imperfect motion compensation in coherent processing along slow time and can achieve single snapshot 3D imaging. Some difficulties exist in the 3D imaging processing. The first one is that the distributed array may be only in small amount. This means that the sampling does not meet the Nyquist sample theorem. The second one refers to echoes of objects in the same beam that will be mixed together, which makes sparse optimization dictionary too long for it to bring the huge computation burden in the imaging process. In this paper, we propose an innovative method on 3D imaging of the aerospace targets in the wide airspace with sparse radar array. Firstly, the case of multiple targets is not suitable to be processed uniformly in the imaging process. A 3D Hough transform is proposed based on the range profiles plane difference, which can detect and separate the echoes of different targets. Secondly, in the subsequent imaging process, considering the non-uniform sparse sampling of the distributed array in space, the migration through range cell (MTRC)-tolerated imaging method is proposed to process the signal of the two-dimensional sparse array. The uniformized method combining compressed sensing (CS) imaging in the azimuth direction and matched filtering in the range direction can realize the 3D imaging effectively. Before imaging in the azimuth direction, interpolation in the range direction is carried out. The main contributions of the proposed method are: (1) echo separation based on 3D transform avoids the huge amount of computation of direct sparse optimization imaging of three-dimensional data, and ensures the realizability of the algorithm; and (2) uniformized sparse solving imaging is proposed, which can remove the difficulty cause by MTRC. Simulation experiments verified the effectiveness and feasibility of the proposed method.<\/jats:p>","DOI":"10.3390\/rs13193817","type":"journal-article","created":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T22:16:38Z","timestamp":1632780998000},"page":"3817","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["MTRC-Tolerated Multi-Target Imaging Based on 3D Hough Transform and Non-Equal Sampling Sparse Solution"],"prefix":"10.3390","volume":"13","author":[{"given":"Yimeng","family":"Zou","sequence":"first","affiliation":[{"name":"College of Electronic Science and Technology, National University of Defense Technology, No. 109 Deya Road, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0255-3499","authenticated-orcid":false,"given":"Jiahao","family":"Tian","sequence":"additional","affiliation":[{"name":"College of Electronic Science and Technology, National University of Defense Technology, No. 109 Deya Road, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guanghu","family":"Jin","sequence":"additional","affiliation":[{"name":"College of Electronic Science and Technology, National University of Defense Technology, No. 109 Deya Road, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongsheng","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Electronic Science and Technology, National University of Defense Technology, No. 109 Deya Road, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1109\/IRET-MIL.1962.5008415","article-title":"Some Early Developments in Synthetic Aperture Radar Systems","volume":"MIL-6","author":"Sherwin","year":"1962","journal-title":"IRE Trans. Mil. Electron."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1109\/PROC.1985.13132","article-title":"Fifty years of radar","volume":"73","author":"Skolnik","year":"1985","journal-title":"IEEE Proc."},{"key":"ref_3","unstructured":"Soumekh, M. (1999). Synthetic Aperture Radar Signal Processing with Matlab Algorithms, Wiley."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1109\/62.879403","article-title":"Radar in the twentieth century","volume":"15","author":"Skolnik","year":"2000","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1146\/annurev.earth.28.1.169","article-title":"Synthetic Aperture Radar Interferometry to Measure Earth\u2019s Surface Topography and Its Deformation","volume":"28","author":"Burgmann","year":"2000","journal-title":"Annu. Rev. Earth Planet. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/74.511949","article-title":"The ALCOR C-band imaging radar","volume":"38","author":"Avent","year":"1996","journal-title":"IEEE Antennas Propag. Mag."},{"key":"ref_7","unstructured":"Delaney, W., and Ward, W. (2001). An Overview of the First Fifty Years, Radar Development at Lincoln Laboratory."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1109\/TAES.1980.308873","article-title":"Target-Motion-Induced Radar Imaging","volume":"AES\u201316","author":"Chen","year":"1980","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Jia, X., Song, H., and He, W. (2021). A Novel Method for Refocusing Moving Ships in SAR Images via ISAR Technique. Remote Sens., 13.","DOI":"10.3390\/rs13142738"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1983","DOI":"10.1109\/TAES.2010.5595608","article-title":"Estimation of Precession Parameters and Generation of ISAR Images of Ballistic Missile Targets","volume":"46","author":"Wang","year":"2010","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Karine, A., Toumi, A., Khenchaf, A., and El Hassouni, M. (2018). Radar Target Recognition Using Salient Keypoint Descriptors and Multitask Sparse Representation. Remote Sens., 10.","DOI":"10.20944\/preprints201804.0251.v1"},{"key":"ref_12","unstructured":"Zhang, Y., Liu, S., and Zhu, H. (2007, January 5\u20138). Interferometric ISAR 3D Imaging of Target Satellite in Low Earth Orbit. Proceedings of the International Symposium on Test and Measurement (ISTM), Beijing, China."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"McFadden, F.E. (2002). Three-dimensional reconstruction from ISAR sequences. Radar Sensor Technology and Data Visualization, SPIE Press. SPIE 4744.","DOI":"10.1117\/12.488289"},{"key":"ref_14","first-page":"320","article-title":"Investigation of 3-D RCS Image formation of ships using ISAR","volume":"5","author":"Lord","year":"2006","journal-title":"Physics"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2361","DOI":"10.1109\/TGRS.2010.2095423","article-title":"Three-Dimensional Target Geometry and Target Motion Estimation Method Using Multistatic ISAR Movies and Its Performance","volume":"49","author":"Suwa","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Suwa, K., Wakayama, T., and Iwamoto, M. (2008, January 6\u201311). Estimation of target motion and 3D target geometry using multistatic ISAR movies. Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Boston, MA, USA.","DOI":"10.1109\/IGARSS.2009.5417640"},{"key":"ref_17","unstructured":"Skolnik, M.I. (1990). Introduction to RADAR Systems, McGraw-Hill."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1109\/83.908519","article-title":"Three-dimensional ISAR imaging of maneuvering targets using three receivers","volume":"10","author":"Wang","year":"2001","journal-title":"IEEE Trans. Image Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1094","DOI":"10.1109\/83.931103","article-title":"Three-dimensional interferometric ISAR imaging for target scattering diagnosis and modeling","volume":"10","author":"Xu","year":"2001","journal-title":"IEEE Trans. Image Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3859","DOI":"10.1109\/TGRS.2012.2186304","article-title":"Bistatic ISAR Imaging Incorporating Interferometric 3-D Imaging Technique","volume":"50","author":"Ma","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Stagliano, D., Martorella, M., and Casalini, E. (2014, January 8\u201310). Interferometric bistatic ISAR processing for 3D target reconstruction. Proceedings of the 2014 11th European Radar Conference, Rome, Italy.","DOI":"10.1109\/EuRAD.2014.6991232"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Jiao, Z., Ding, C., Liang, X., Chen, L., and Zhang, F. (2018). Sparse Bayesian Learning Based Three-Dimensional Imaging Algorithm for Off-Grid Air Targets in MIMO Radar Array. Remote Sens., 10.","DOI":"10.3390\/rs10030369"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Del-Rey-Maestre, N., Mata-Moya, D., Jarabo-Amores, M.-P., G\u00f3mez-Del-Hoyo, P.-J., B\u00e1rcena-Humanes, J.-L., and Rosado-Sanz, J. (2017). Passive Radar Array Processing with Non-Uniform Linear Arrays for Ground Target\u2019s Detection and Localization. Remote Sens., 9.","DOI":"10.3390\/rs9070756"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Monteith, A.R., Ulander, L.M.H., and Tebaldini, S. (2019). Calibration of a Ground-Based Array Radar for Tomographic Imaging of Natural Media. Remote Sens., 11.","DOI":"10.3390\/rs11242924"},{"key":"ref_25","unstructured":"Rabideau, D.J., and Parker, P. (2003, January 9\u201312). Ubiquitous MIMO multifunction digital array radar. Proceedings of the 37th Asilomar Conference on Signals, Systems & Computers, Pacific Grove, CA, USA."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Baraniuk, R., and Steeghs, P. (2007, January 17\u201320). Compressive Radar Imaging. Proceedings of the 2007 IEEE Radar Conference, Boston, MA, USA.","DOI":"10.1109\/RADAR.2007.374203"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1016\/j.dsp.2012.07.011","article-title":"SAR image reconstruction and autofocus by compressed sensing","volume":"22","year":"2012","journal-title":"Digit. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"5106","DOI":"10.1007\/s00034-021-01712-x","article-title":"Compressed Sensing-Speech Coding Scheme for Mobile Communications","volume":"40","author":"Haneche","year":"2021","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1402","DOI":"10.1016\/j.sigpro.2009.11.009","article-title":"On compressive sensing applied to radar","volume":"90","author":"Ender","year":"2010","journal-title":"Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1109\/LGRS.2009.2038728","article-title":"Three-Dimensional Imaging via Wideband MIMO Radar System","volume":"7","author":"Duan","year":"2010","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2147","DOI":"10.1007\/s11432-011-4400-y","article-title":"A type of M 2-transmitter N 2-receiver MIMO radar array and 3D imaging theory","volume":"54","author":"Zhu","year":"2011","journal-title":"Sci. China Inf. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Gu, F., Chi, L., Zhang, Q., Zhu, F., and Liang, Y. (2011, January 14\u201316). An imaging method for MIMO radar with sparse array based on Compressed Sensing. Proceedings of the 2011 IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC), Xi\u2019an, China.","DOI":"10.1109\/ICSPCC.2011.6061784"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1137\/S0097539792240406","article-title":"Sparse approximate solutions to linear systems","volume":"24","author":"Natarajan","year":"1995","journal-title":"Siam J. Comput."},{"key":"ref_34","first-page":"129","article-title":"Atomic Decomposition by Basis Pursuit","volume":"43","author":"Chen","year":"2001","journal-title":"Siam J. Comput."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2197","DOI":"10.1073\/pnas.0437847100","article-title":"Optimally sparse representation in general (nonorthogonal) dictionaries via l~1 minimization","volume":"100","author":"Donoho","year":"2003","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"4655","DOI":"10.1109\/TIT.2007.909108","article-title":"Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit","volume":"53","author":"Tropp","year":"2007","journal-title":"IEEE Trans. Inf. 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