{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,6]],"date-time":"2026-08-06T18:04:37Z","timestamp":1786039477763,"version":"3.56.0"},"reference-count":32,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,6,13]],"date-time":"2021-06-13T00:00:00Z","timestamp":1623542400000},"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":["61971332, 61801344, 61631019"],"award-info":[{"award-number":["61971332, 61801344, 61631019"]}],"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>A deep-learning architecture, dubbed as the 2D-ADMM-Net (2D-ADN), is proposed in this article. It provides effective high-resolution 2D inverse synthetic aperture radar (ISAR) imaging under scenarios of low SNRs and incomplete data, by combining model-based sparse reconstruction and data-driven deep learning. Firstly, mapping from ISAR images to their corresponding echoes in the wavenumber domain is derived. Then, a 2D alternating direction method of multipliers (ADMM) is unrolled and generalized to a deep network, where all adjustable parameters in the reconstruction layers, nonlinear transform layers, and multiplier update layers are learned by an end-to-end training through back-propagation. Since the optimal parameters of each layer are learned separately, 2D-ADN exhibits more representation flexibility and preferable reconstruction performance than model-driven methods. Simultaneously, it is able to better facilitate ISAR imaging with limited training samples than data-driven methods owing to its simple structure and small number of adjustable parameters. Additionally, benefiting from the good performance of 2D-ADN, a random phase error estimation method is proposed, through which well-focused imaging can be acquired. It is demonstrated by experiments that although trained by only a few simulated images, the 2D-ADN shows good adaptability to measured data and favorable imaging results with a clear background can be obtained in a short time.<\/jats:p>","DOI":"10.3390\/rs13122326","type":"journal-article","created":{"date-parts":[[2021,6,14]],"date-time":"2021-06-14T22:25:46Z","timestamp":1623709546000},"page":"2326","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["High-Resolution ISAR Imaging and Autofocusing via 2D-ADMM-Net"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6580-1648","authenticated-orcid":false,"given":"Xiaoyong","family":"Li","sequence":"first","affiliation":[{"name":"Key Laboratory of Electronic Information Countermeasure and Simulation Technology of Ministry of Education, Xidian University, Xi\u2019an 710071, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xueru","family":"Bai","sequence":"additional","affiliation":[{"name":"National Lab of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Feng","family":"Zhou","sequence":"additional","affiliation":[{"name":"Key Laboratory of Electronic Information Countermeasure and Simulation Technology of Ministry of Education, Xidian University, Xi\u2019an 710071, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,13]]},"reference":[{"key":"ref_1","unstructured":"Kang, L., Luo, Y., Zhang, Q., Liu, X.-W., and Liang, B.-S. (2020). 3-D Scattering Image Sparse Reconstruction via Radar Network. IEEE Trans. Geosci. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"9912","DOI":"10.1109\/TGRS.2019.2930112","article-title":"Robust pol-ISAR target recognition based on ST-MC-DCNN","volume":"57","author":"Bai","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_3","unstructured":"Carrara, W.G., Goodman, R.S., and Majewski, R.M. (1995). Spotlight Synthetic Aperture Radar: Signal Processing Algorithms, Artech House. Chapter 2."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1109\/MSP.2016.2573847","article-title":"The race to improve radar imagery: An overview of recent progress in statistical sparsity-based techniques","volume":"33","author":"Zhao","year":"2016","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"972","DOI":"10.1109\/TGRS.2018.2863743","article-title":"High-resolution radar imaging in complex environments based on Bayesian learning with mixture models","volume":"57","author":"Bai","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3437","DOI":"10.1109\/JSEN.2020.3025053","article-title":"Deep Learning Approach for Sparse Aperture ISAR Imaging and Autofocusing Based on Complex-Valued ADMM-Net","volume":"21","author":"Li","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"6791","DOI":"10.1109\/TGRS.2020.2974550","article-title":"High-Resolution ISAR Imaging and Motion Compensation With 2-D Joint Sparse Reconstruction","volume":"58","author":"Shao","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5043","DOI":"10.1109\/TIP.2017.2728182","article-title":"ISAR imaging of high-speed maneuvering target using gapped stepped-frequency waveform and compressive sensing","volume":"26","author":"Kang","year":"2017","journal-title":"IEEE Trans. Image Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"9315","DOI":"10.1109\/JSEN.2018.2869832","article-title":"Sparse subband ISAR imaging based on autoregressive model and smoothed l0 algorithm","volume":"18","author":"Hu","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1137\/080716542","article-title":"A fast iterative shrinkage-thresholding algorithm for linear inverse problems","volume":"2","author":"Beck","year":"2009","journal-title":"SIAM J. Imag. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1109\/LGRS.2019.2943937","article-title":"Radar imaging by sparse optimization incorporating MRF clustering prior","volume":"17","author":"Li","year":"2020","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2345","DOI":"10.1109\/TIP.2010.2047910","article-title":"Fast image recovery using variable splitting and constrained optimization","volume":"19","author":"Afonso","year":"2010","journal-title":"IEEE Trans. Image Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.1109\/TAES.2017.2667899","article-title":"Obtaining JTF-signature of space-debris from incomplete and phase-corrupted data","volume":"53","author":"Bai","year":"2017","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1275","DOI":"10.1109\/TGRS.2020.3004006","article-title":"High-Resolution Radar Imaging in Low SNR Environments Based on Expectation Propagation","volume":"59","author":"Bai","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"7088","DOI":"10.1109\/JSEN.2016.2599540","article-title":"ISAR imaging by two-dimensional convex optimization-based compressive sensing","volume":"16","author":"Li","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"13349","DOI":"10.1109\/JSEN.2020.3006105","article-title":"Sparsity-Driven ISAR Imaging Based on Two-Dimensional ADMM","volume":"20","author":"Hashempour","year":"2020","journal-title":"IEEE Sens. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2232","DOI":"10.1109\/TIP.2021.3051484","article-title":"Deep SAR Imaging and Motion Compensation","volume":"30","author":"Pu","year":"2021","journal-title":"IEEE Trans. Image Process."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Pu, W. (2021). Shuffle GAN with Autoencoder: A Deep Learning Approach to Separate Moving and Stationary Targets in SAR Imagery. IEEE Trans. Neural Netw. Learn. Syst.","DOI":"10.1109\/TNNLS.2021.3060747"},{"key":"ref_19","first-page":"7096","article-title":"Inverse synthetic aperture radar imaging using complex-value deep neural network","volume":"2019","author":"Hu","year":"2019","journal-title":"J. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Zhang, J., and Ghanem, B. (2018, January 19\u201321). ISTA-Net: Interpretable optimization-inspired deep network for image compressive sensing. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00196"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Ram\u00edrez, J.M., Torre, J.I.M., and Fuentes, H.A. (2021, June 10). LADMM-Net: An Unrolled Deep Network for Spectral Image Fusion from Compressive Data. Available online: https:\/\/arxiv.org\/abs\/2103.00940.","DOI":"10.1016\/j.sigpro.2021.108239"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1109\/MSP.2020.3016905","article-title":"Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing","volume":"38","author":"Monga","year":"2021","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Hu, C.Y., Li, Z., Wang, L., Guo, J., and Loffeld, O. (2019, January 26\u201328). Inverse synthetic aperture radar imaging using a Deep ADMM Network. Proceedings of the 20th International Radar Symposium (IRS), Ulm, Germany.","DOI":"10.23919\/IRS.2019.8768138"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"6119","DOI":"10.1109\/TGRS.2013.2295162","article-title":"High-resolution fully polarimetric ISAR imaging based on compressive sensing","volume":"52","author":"Qiu","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5146","DOI":"10.1109\/JSTARS.2015.2491307","article-title":"Adaptive translational motion compensation method for ISAR imaging under low SNR based on particle swarm optimization","volume":"8","author":"Liu","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1137\/080724265","article-title":"A new alternating minimization algorithm for total variation image reconstruction","volume":"1","author":"Wang","year":"2009","journal-title":"SIAM J. Imag. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1168","DOI":"10.1137\/050626090","article-title":"Signal recovery by proximal forward-backward splitting","volume":"4","author":"Combettes","year":"2005","journal-title":"Siam J. Multiscale Modeling Simul."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"6392","DOI":"10.1109\/TGRS.2013.2296497","article-title":"An autofocus technique for high-resolution inverse synthetic aperture radar imagery","volume":"52","author":"Zhao","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_29","unstructured":"Sun, J., Li, H.B., and Xu, Z.B. (2016, January 5\u201310). Deep ADMM-Net for compressive sensing MRI. Proceedings of the 30th International Conference on Neural Information Processing Systems, Barcelona, Spain."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1109\/TPAMI.2018.2883941","article-title":"ADMM-CSNet: A deep learning approach for image compressive sensing","volume":"42","author":"Yang","year":"2020","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_31","unstructured":"Petersen, K.B., and Pedersen, M.S. (2012). The Matrix Cookbook, Technical University of Denmark. Available online: http:\/\/www2.compute.dtu.dk\/pubdb\/pubs\/3274-full.html."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"9447","DOI":"10.1080\/01431161.2020.1799449","article-title":"ISAR imaging enhancement: Exploiting deep convolutional neural network for signal reconstruction","volume":"41","author":"Yang","year":"2020","journal-title":"Int. J. Remote Sens."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/12\/2326\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:13:59Z","timestamp":1760163239000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/12\/2326"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,13]]},"references-count":32,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["rs13122326"],"URL":"https:\/\/doi.org\/10.3390\/rs13122326","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,13]]}}}