{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T21:58:23Z","timestamp":1768514303937,"version":"3.49.0"},"reference-count":31,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2021,11,3]],"date-time":"2021-11-03T00:00:00Z","timestamp":1635897600000},"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":["62131020"],"award-info":[{"award-number":["62131020"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62001058"],"award-info":[{"award-number":["62001058"]}],"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>Synthetic aperture radar (SAR) imaging has developed rapidly in recent years. Although the traditional sparse optimization imaging algorithm has achieved effective results, its shortcomings are slow imaging speed, large number of parameters, and high computational complexity. To solve the above problems, an end-to-end SAR deep learning imaging algorithm is proposed. Based on the existing SAR sparse imaging algorithm, the SAR imaging model is first rewritten to the SAR complex signal form based on the real-value model. Second, instead of arranging the two-dimensional echo data into a vector to continuously construct an observation matrix, the algorithm only derives the neural network imaging model based on the iteration soft threshold algorithm (ISTA) sparse algorithm in the two-dimensional data domain, and then reconstructs the observation scene through the superposition and expansion of the multi-layer network. Finally, through the experiment of simulation data and measured data of the three targets, it is verified that our algorithm is superior to the traditional sparse algorithm in terms of imaging quality, imaging time, and the number of parameters.<\/jats:p>","DOI":"10.3390\/rs13214429","type":"journal-article","created":{"date-parts":[[2021,11,3]],"date-time":"2021-11-03T21:57:49Z","timestamp":1635976669000},"page":"4429","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["End-to-End SAR Deep Learning Imaging Method Based on Sparse Optimization"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8923-7877","authenticated-orcid":false,"given":"Siyuan","family":"Zhao","sequence":"first","affiliation":[{"name":"Institute of Information and Navigation, Air Force Engineering University, Xi\u2019an 710077, China"},{"name":"Collaborative Innovation Center of Information Sensing and Understanding, Xi\u2019an 710077, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4189-9206","authenticated-orcid":false,"given":"Jiacheng","family":"Ni","sequence":"additional","affiliation":[{"name":"Institute of Information and Navigation, Air Force Engineering University, Xi\u2019an 710077, China"},{"name":"Collaborative Innovation Center of Information Sensing and Understanding, Xi\u2019an 710077, China"}]},{"given":"Jia","family":"Liang","sequence":"additional","affiliation":[{"name":"Institute of Information and Navigation, Air Force Engineering University, Xi\u2019an 710077, China"},{"name":"Collaborative Innovation Center of Information Sensing and Understanding, Xi\u2019an 710077, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2710-4630","authenticated-orcid":false,"given":"Shichao","family":"Xiong","sequence":"additional","affiliation":[{"name":"Institute of Information and Navigation, Air Force Engineering University, Xi\u2019an 710077, China"},{"name":"Collaborative Innovation Center of Information Sensing and Understanding, Xi\u2019an 710077, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1460-4289","authenticated-orcid":false,"given":"Ying","family":"Luo","sequence":"additional","affiliation":[{"name":"Institute of Information and Navigation, Air Force Engineering University, Xi\u2019an 710077, China"},{"name":"Collaborative Innovation Center of Information Sensing and Understanding, Xi\u2019an 710077, China"},{"name":"Key Laboratory for Information Science of Electromagnetic Waves, Ministry of Education, Fudan University, Shanghai 200433, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4486","DOI":"10.1109\/TGRS.2013.2259178","article-title":"A large scene deceptive jamming method for space-borne SAR","volume":"51","author":"Zhou","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Xu, Z., Zhang, B., Zhou, G., Zhong, L., and Wu, Y. (2021). Sparse SAR Imaging and Quantitative Evaluation Based on Nonconvex and TV Regularization. Remote Sens., 13.","DOI":"10.3390\/rs13091643"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6910","DOI":"10.1109\/TGRS.2017.2735993","article-title":"A Modified Three-Step Algorithm for TOPS and Sliding Spotlight SAR Data Processing","volume":"55","author":"Yang","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4920","DOI":"10.1109\/JSEN.2018.2831921","article-title":"Compressed sensing SAR imaging based on centralized sparse representation","volume":"18","author":"Ni","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"219301:1","DOI":"10.1007\/s11432-020-2994-4","article-title":"An improved iterative thresholding algorithm for L1-norm regularization based sparse SAR imaging","volume":"63","author":"Bi","year":"2020","journal-title":"Sci. China Inf. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1109\/JSTARS.2013.2263309","article-title":"Fast Compressed Sensing SAR Imaging Based on Approximated Observation","volume":"7","author":"Fang","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Shi, W., Jiang, F., Zhang, S., and Zhao, D. (2017, January 10\u201314). Deep networks for compressed image sensing. Proceedings of the 2017 IEEE International Conference on Multimedia and Expo (ICME), Hong Kong, China.","DOI":"10.1109\/ICME.2017.8019428"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Zhang, J., and Ghanem, B. (2018, January 18\u201323). ISTA-Net: Interpretable Optimization-Inspired Deep Network for Image Compressive Sensing. Proceedings of the 2018 IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00196"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1717","DOI":"10.1049\/iet-rsn.2020.0160","article-title":"SAR imaging of multiple maritime moving targets based on sparsity Bayesian learning","volume":"14","author":"Zhang","year":"2020","journal-title":"IET Radar Sonar Navig."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.jneumeth.2016.11.002","article-title":"The extraction of motion-onset VEP BCI features based on deep learning and compressed sensing","volume":"275","author":"Ma","year":"2017","journal-title":"J. Neurosci. Methods"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"9217","DOI":"10.1109\/TVT.2020.3004842","article-title":"Deep Learning and Compressive Sensing-Based CSI Feedback in FDD Massive MIMO Systems","volume":"69","author":"Liang","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2838","DOI":"10.1109\/TCOMM.2020.2974457","article-title":"Sparse Channel Estimation and Hybrid Precoding Using Deep Learning for Millimeter Wave Massive MIMO","volume":"68","author":"Ma","year":"2020","journal-title":"IEEE Trans. Commun."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1509","DOI":"10.1049\/iet-ipr.2018.5172","article-title":"SAR image change detection based on deep denoising and CNN","volume":"13","author":"Cao","year":"2019","journal-title":"IET Images Process."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Zhou, Y.Y., Shi, J., Wang, C., Hu, Y., Zhou, Z.N., Yang, X.Q., Zhang, X.L., and Wei, S.J. (2020). SAR Ground Moving Target Refocusing by Combining mRe3 Network and TV\u03b2-LSTM. IEEE Trans. Geosci. Remote Sens., 1\u201314.","DOI":"10.1109\/TGRS.2020.3033656"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1178","DOI":"10.23919\/JSEE.2020.000090","article-title":"ISAR autofocus imaging algorithm for maneuvering targets based on deep learning and keystone transform","volume":"31","author":"Shi","year":"2020","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1109\/TIP.2019.2928136","article-title":"Image Compressed Sensing Using Convolutional Neural Network","volume":"29","author":"Shi","year":"2020","journal-title":"IEEE Trans. Image Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"7889","DOI":"10.1080\/01431161.2020.1766149","article-title":"A semi-greedy neural network CAE-HL-CNN for SAR target recognition with limited training data","volume":"41","author":"Qin","year":"2020","journal-title":"Int. J. Remote Sens."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1638","DOI":"10.1109\/TNN.2011.2164810","article-title":"Embedding Prior Knowledge Within Compressed Sensing by Neural Networks","volume":"22","author":"Merhej","year":"2011","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1003","DOI":"10.1109\/LGRS.2014.2372319","article-title":"A Novel SAR Imaging Algorithm Based on Compressed Sensing","volume":"12","author":"Bu","year":"2015","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1238","DOI":"10.1109\/JSEN.2019.2947114","article-title":"Ground Moving Target Imaging Based on Compressive Sensing Framework with Single-Channel SAR","volume":"20","author":"Kang","year":"2020","journal-title":"IEEE Sens. J."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"9400504","DOI":"10.1109\/TMAG.2017.2764949","article-title":"High-Resolution Millimeter-Wave Ground-Based SAR Imaging via Compressed Sensing","volume":"54","author":"Jung","year":"2018","journal-title":"IEEE Trans. Magn."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5529","DOI":"10.1109\/JSEN.2019.2904611","article-title":"Compressive Sensing Based SAR Imaging and Autofocus Using Improved Tikhonov Regularization","volume":"19","author":"Kang","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2848","DOI":"10.1109\/TIM.2011.2122190","article-title":"Applications of Compressed Sensing for SAR Moving-Target Velocity Estimation and Image Compression","volume":"60","author":"Khwaja","year":"2011","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3297","DOI":"10.1109\/JSTARS.2014.2328344","article-title":"Unsupervised Change Detection in SAR Image Based on Gauss-Log Ratio Image Fusion and Compressed Projection","volume":"7","author":"Hou","year":"2014","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1207","DOI":"10.1002\/cpa.20124","article-title":"Stable signal recovery from incomplete and inaccurate measurements","volume":"59","author":"Romberg","year":"2006","journal-title":"Commun. Pure Appl. Math."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"5006","DOI":"10.1109\/TGRS.2018.2803802","article-title":"Complex-Image-Based Sparse SAR Imaging and Its Equivalence","volume":"56","author":"Bi","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_27","first-page":"107","article-title":"Synthetic aperture radar learning-imaging method based on data-driven technique and artificial intelligence","volume":"9","author":"Luo","year":"2020","journal-title":"J. Radars"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4293","DOI":"10.1109\/TSP.2017.2708040","article-title":"AMP inspired deep networks for sparse linear inverse problems","volume":"65","author":"Borgerding","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"11484","DOI":"10.1109\/JSEN.2020.2996656","article-title":"GAN-Based Focusing-Enhancement Method for Monochromatic Synthetic Aperture Imaging","volume":"20","author":"Ye","year":"2020","journal-title":"IEEE Sens. J."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"102832","DOI":"10.1016\/j.dsp.2020.102832","article-title":"SAR moving target imaging based on convolutional neural network","volume":"106","author":"Lu","year":"2020","journal-title":"Digit. Signal Process."},{"key":"ref_31","unstructured":"Zhang, J., and Pei, Z. (2013, January 14\u201316). Ground-based SAR imaging based on improved Range-Doppler algorithm. Proceedings of the International Radar Conference IET, Xi\u2019an, China."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/21\/4429\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:25:27Z","timestamp":1760167527000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/21\/4429"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,3]]},"references-count":31,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["rs13214429"],"URL":"https:\/\/doi.org\/10.3390\/rs13214429","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,3]]}}}