{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T16:00:41Z","timestamp":1762444841685,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,11,15]],"date-time":"2018-11-15T00:00:00Z","timestamp":1542240000000},"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":["61571388"],"award-info":[{"award-number":["61571388"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["F2016203251"],"award-info":[{"award-number":["F2016203251"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The imaging issue of a rotating maneuvering target with a large angle and a high translational speed has been a challenging problem in the area of inverse synthetic aperture radar (ISAR) autofocus imaging, in particular when the target has both radial and angular accelerations. In this paper, on the basis of the phase retrieval algorithm and the Gabor wavelet transform (GWT), we propose a new method for phase error correction. The approach first performs the range compression on ISAR raw data to obtain range profiles, and then carries out the GWT transform as the time-frequency analysis tool for the rotational motion compensation (RMC) requirement. The time-varying terms, caused by rotational motion in the Doppler frequency shift, are able to be eliminated at the selected time frame. Furthermore, the processed backscattered signal is transformed to the one in the frequency domain while applying the phase retrieval to run the translational motion compensation (TMC). Phase retrieval plays an important role in range tracking, because the ISAR echo module is not affected by both radial velocity and the acceleration of the target. Finally, after the removal of both the rotational and translational motion errors, the time-invariant Doppler shift is generated, and radar returned signals from the same scatterer are always kept in the same range cell. Therefore, the unwanted motion effects can be removed by applying this approach to have an autofocused ISAR image of the maneuvering target. Furthermore, the method does not need to estimate any motion parameters of the maneuvering target, which has proven to be very effective for an ideal range\u2013Doppler processing. Experimental and simulation results verify the feasibility of this approach.<\/jats:p>","DOI":"10.3390\/rs10111810","type":"journal-article","created":{"date-parts":[[2018,11,15]],"date-time":"2018-11-15T11:32:47Z","timestamp":1542281567000},"page":"1810","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["ISAR Autofocus Imaging Algorithm for Maneuvering Targets Based on Phase Retrieval and Gabor Wavelet Transform"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2919-9004","authenticated-orcid":false,"given":"Hongyin","family":"Shi","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering, Yanshan University, Qinhuangdao 066000, China"},{"name":"School of Mathematical &amp; Statistical Sciences, The University of Texas Rio Grande Valley, Edinburg, TX 78539, USA"}]},{"given":"Ting","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Yanshan University, Qinhuangdao 066000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5578-6181","authenticated-orcid":false,"given":"Zhijun","family":"Qiao","sequence":"additional","affiliation":[{"name":"School of Mathematical &amp; Statistical Sciences, The University of Texas Rio Grande Valley, Edinburg, TX 78539, USA"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2971","DOI":"10.1109\/JSTARS.2014.2301158","article-title":"ISAR Imaging of Maneuvering Target Based on the Local Polynomial Wigner Distribution and Integrated High-Order Ambiguity Function for Cubic Phase Signal Model","volume":"7","author":"Wang","year":"2017","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3954","DOI":"10.1109\/JSTARS.2015.2440911","article-title":"ISAR Imaging for Fluctuating Ships Based on a Fast Bilinear Parameter Estimation Algorithm","volume":"8","author":"Zheng","year":"2017","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"030502","DOI":"10.1117\/1.JRS.10.030502","article-title":"Kurtosis-based estimation of cross-range scaling factor for high-resolution inverse synthetic aperture radar imaging","volume":"10","author":"An","year":"2016","journal-title":"J. Appl. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1049\/iet-rsn.2009.0112","article-title":"Automatic algorithm for inverse synthetic aperture radar images recognition and classification","volume":"4","author":"Li","year":"2010","journal-title":"IET Radar Sonar Navig."},{"key":"ref_5","first-page":"909009","article-title":"New experiments in inverse synthetic aperture radar image exploitation for maritime surveillance","volume":"9090","author":"Sadjadi","year":"2014","journal-title":"Autom. Target Recognit. XXIV"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"43","DOI":"10.2528\/PIERB14070801","article-title":"Automatic recognition of ISAR images of multiple targets and ATR results","volume":"61","author":"Park","year":"2014","journal-title":"Prog. Electromagn. Res. B"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Zhou, Z.H., Zhou, B., and Yeh, C.M. (2009, January 26\u201330). Methods for the rotation of ISAR images. Synthetic Aperture Radar. Proceedings of the 2009 2nd Asian-Pacific Conference on Synthetic Aperture Radar, Xi\u2019an, China.","DOI":"10.1109\/APSAR.2009.5374164"},{"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-16","author":"Chen","year":"1980","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1240","DOI":"10.1109\/7.805442","article-title":"Autofocusing of ISAR images based on entropy minimization","volume":"35","author":"Li","year":"2002","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1109\/7.303752","article-title":"Phase Gradient Autofocus\u2014A Robust Tool for High Resolution SAR Phase Correction","volume":"30","author":"Wahl","year":"1994","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Xue, J., and Huang, L. (2015, January 19\u201324). An improved cross-correlation approach to parameter estimation based on fractional Fourier transform for ISAR motion compensation. Proceedings of the 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brisbane, Australia.","DOI":"10.1109\/ICASSP.2015.7178228"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1038\/nphys265","article-title":"Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources","volume":"2","author":"Pfeiffer","year":"2006","journal-title":"Nat. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1007\/s12532-016-0103-0","article-title":"Phase retrieval for imaging problems","volume":"8","author":"Fogel","year":"2016","journal-title":"Math. Program. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1334","DOI":"10.1364\/JOSAA.19.001334","article-title":"Phase retrieval, error reduction algorithm, and Fienup variants: A view from convex optimization","volume":"19","author":"Luke","year":"2002","journal-title":"J. Opt. Soc. Am. A Opt. Image Sci. Vis."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1107\/S0021889813002471","article-title":"Oversampling smoothness: An effective algorithm for phase retrieval of noisy diffraction intensities","volume":"46","author":"Rodriguez","year":"2013","journal-title":"J. Appl. Crystallogr."},{"key":"ref_16","unstructured":"Shi, H., and Xia, S. (2016, January 6\u201310). ISAR imaging based on oversampling smoothness of prior knowledge. Proceedings of the 2016 IEEE 13th International Conference on Signal Processing (ICSP), Chengdu, China."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"278","DOI":"10.21629\/JSEE.2018.02.08","article-title":"ISAR imaging based on improved phase retrieval algorithm","volume":"29","author":"Shi","year":"2018","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4814","DOI":"10.1109\/TSP.2015.2448516","article-title":"Phase retrieval using alternating minimization","volume":"63","author":"Netrapalli","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1109\/7.670330","article-title":"Joint time-frequency transform for radar range-Doppler imaging","volume":"34","author":"Chen","year":"1998","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3397","DOI":"10.1109\/78.258082","article-title":"Matching pursuits with time-frequency dictionaries","volume":"41","author":"Mallat","year":"1993","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"670","DOI":"10.1109\/7.670350","article-title":"ISAR motion compensation via adaptive joint time-frequency technique","volume":"34","author":"Wang","year":"1998","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Wang, Z., Yang, W., Chen, Z., Zhao, Z., Hu, H., and Qi, C. (2018). A Novel Adaptive Joint Time Frequency Algorithm by the Neural Network for the ISAR Rotational Compensation. Remote Sens., 10.","DOI":"10.3390\/rs10020334"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1109\/7.532282","article-title":"Autofocusing of Inverse Synthetic Aperture Radar Images Using Contrast Optimization","volume":"32","author":"Berizzi","year":"1996","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"6899","DOI":"10.3390\/rs5126899","article-title":"Ship discrimination using polarimetric SAR data and coherent time-frequency analysis","volume":"5","author":"Hu","year":"2013","journal-title":"Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2836","DOI":"10.1109\/78.324750","article-title":"Decomposition of the Wigner-Ville distribution and time-frequency distribution series","volume":"42","author":"Qian","year":"1994","journal-title":"IEEE Trans. Signal Process"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Thomas, G., Flores, B.C., and Martinez, A. (1997). ISAR imaging of moving targets via the Gabor wavelet transform. Proc. SPIE\u2013Int. Soc. Opt. Eng., 3161.","DOI":"10.1117\/12.283948"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1813","DOI":"10.3724\/SP.J.1146.2012.01500","article-title":"ISAR Image Recognition with Fusion of Gabor Magnitude and Phase Feature","volume":"35","author":"Wang","year":"2013","journal-title":"J. Electron. Inf. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"227","DOI":"10.2528\/PIER13022004","article-title":"Enhanced and Efficient ISAR Image Focusing Using the Discrete Gabor Representation in an Oversampling Scheme","volume":"138","author":"Park","year":"2013","journal-title":"Prog. Electomang. Res."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Chen, V.C., and Martorella, M. (2014). Inverse Synthetic Aperture Radar Imaging: Principles, Algorithms and Applications, SciTech Publishing.","DOI":"10.1049\/SBRA504E"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2758","DOI":"10.1364\/AO.21.002758","article-title":"Phase retrieval algorithms: A comparison","volume":"21","author":"Fienup","year":"1982","journal-title":"Appl. Opt."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/11\/1810\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:29:53Z","timestamp":1760196593000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/11\/1810"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,15]]},"references-count":30,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2018,11]]}},"alternative-id":["rs10111810"],"URL":"https:\/\/doi.org\/10.3390\/rs10111810","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2018,11,15]]}}}