{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,21]],"date-time":"2025-11-21T06:32:12Z","timestamp":1763706732435,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,2,13]],"date-time":"2024-02-13T00:00:00Z","timestamp":1707782400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>A novel compressive sensing (CS) synthetic-aperture radar (SAR) called AgileSAR has been proposed to increase swath width for sparse scenes while preserving azimuthal resolution. AgileSAR overcomes the limitation of the Nyquist sampling theorem so that it has a small amount of data and low system complexity. However, traditional CS optimization-based algorithms suffer from manual tuning and pre-definition of optimization parameters, and they generally involve high time and computational complexity for AgileSAR imaging. To address these issues, a pseudo-L0-norm fast iterative shrinkage algorithm network (pseudo-L0-norm FISTA-net) is proposed for AgileSAR imaging via the deep unfolding network in this paper. Firstly, a pseudo-L0-norm regularization model is built by taking an approximately fair penalization rule based on Bayesian estimation. Then, we unfold the operation process of FISTA into a data-driven deep network to solve the pseudo-L0-norm regularization model. The network\u2019s parameters are automatically learned, and the learned network significantly increases imaging speed, so that it can improve the accuracy and efficiency of AgileSAR imaging. In addition, the nonlinearly sparsifying transform can learn more target details than the traditional sparsifying transform. Finally, the simulated and data experiments demonstrate the superiority and efficiency of the pseudo-L0-norm FISTA-net for AgileSAR imaging.<\/jats:p>","DOI":"10.3390\/rs16040671","type":"journal-article","created":{"date-parts":[[2024,2,14]],"date-time":"2024-02-14T06:59:26Z","timestamp":1707893966000},"page":"671","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Pseudo-L0-Norm Fast Iterative Shrinkage Algorithm Network: Agile Synthetic Aperture Radar Imaging via Deep Unfolding Network"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9009-0657","authenticated-orcid":false,"given":"Wenjiao","family":"Chen","sequence":"first","affiliation":[{"name":"The Department of Space Control and Communication, Space Engineering University, Beijing 102249, China"}]},{"given":"Jiwen","family":"Geng","sequence":"additional","affiliation":[{"name":"The School of Information Science and Engineering, Southeast University, Nanjing 214135, China"}]},{"given":"Fanjie","family":"Meng","sequence":"additional","affiliation":[{"name":"The Department of Space Control and Communication, Space Engineering University, Beijing 102249, China"}]},{"given":"Li","family":"Zhang","sequence":"additional","affiliation":[{"name":"The 15th Research Institute of China Electronics Technology Corporation, Beijing 100083, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3317","DOI":"10.1109\/TGRS.2007.900693","article-title":"TanDEM-X: A satellite formation for high-resolution SAR interferometry","volume":"45","author":"Krieger","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_2","unstructured":"Krieger, G., Younis, M., Gebert, N., Huber, S., and Moreira, A. (2010, January 7\u201310). Advanced concepts for high-resolution wide-swath SAR imaging. Proceedings of the 8th European Conference on Synthetic Aperture Radar, Aachen, Germany."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6095","DOI":"10.1109\/TGRS.2013.2294940","article-title":"Optimum signal processing for multichannel SAR: With application to high-resolution wideswath imaging","volume":"52","author":"Sikaneta","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2628","DOI":"10.1109\/TGRS.2013.2263934","article-title":"MIMO-SAR: Opportunities and pitfalls","volume":"52","author":"Krieger","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4203","DOI":"10.1109\/TIT.2005.858979","article-title":"Decoding by linear programming","volume":"51","author":"Candes","year":"2005","journal-title":"IEEE Trans. Inf. Theory."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1109\/TIT.2005.860430","article-title":"Stable recovery of sparse overcomplete representations in the presence of noise","volume":"52","author":"Donoho","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1109\/MSP.2007.4286571","article-title":"Compressive sensing","volume":"24","author":"Baraniuk","year":"2007","journal-title":"IEEE Signal Process Mag."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1109\/ACCESS.2018.2885615","article-title":"AgileSAR: Achieving Wide-Swath Spaceborne SAR Based on Time-Space Sampling","volume":"7","author":"Yu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1248","DOI":"10.1109\/TIT.2013.2290112","article-title":"The computational complexity of the restricted isometry property, the nullspace property, and related concepts in compressed sensing","volume":"60","author":"Tilllmann","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4655","DOI":"10.1109\/TIT.2007.909108","article-title":"Signal recovery from partial information via orthogonal matching pursuit","volume":"53","author":"Tropp","year":"2007","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.cor.2017.03.016","article-title":"Carousel greedy: A generalized greedy algorithm with applications in optimization","volume":"85","author":"Cerrone","year":"2017","journal-title":"Comput. Oper. Res."},{"key":"ref_12","first-page":"2313","article-title":"The Dantzig selector: Statistical estimation when p is much larger than n","volume":"35","author":"Candes","year":"2007","journal-title":"Ann. Stat."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","article-title":"Regression shrinkage and selection via the Lasso","volume":"58","author":"Tibshirani","year":"1996","journal-title":"J. R. Stat. Soc. B"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2346","DOI":"10.1109\/TSP.2007.914345","article-title":"Bayesian Compressive Sensing","volume":"56","author":"Ji","year":"2008","journal-title":"IEEE Trans. Signal Process"},{"key":"ref_15","unstructured":"Tipping, M.E., and Faul, A.C. (2003, January 3\u20136). Fast marginal likelihood maximization for sparse Bayesian models. Proceedings of the Ninth International Workshop on Artificial Intelligence and Statistics, Key West, FL, USA."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1109\/TIP.2009.2032894","article-title":"Bayesian compressive sensing using laplace priors","volume":"19","author":"Babacan","year":"2010","journal-title":"IEEE Trans. Image Process."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Arjoune, Y., Kaabouch, N., Ghazi, H.E., and Tamtaoui, A. (2017, January 9\u201311). Compressive sensing: Performance comparison of sparse recovery algorithms. Proceedings of the Annual Computing and Communication Workshop and Conference (CCWC) 2017, Las Vegas, NV, USA.","DOI":"10.1109\/CCWC.2017.7868430"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Joshi, S., Siddamal, K.V., and Saroja, V.S. (2015, January 26\u201327). Performance analysis of compressive sensing reconstruction. Proceedings of the 2015 2nd International Conference on Electronics and Communication Systems (ICECS), Coimbatore, India.","DOI":"10.1109\/ECS.2015.7125006"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Celik, S., Basaran, M., Erkucuk, S., and Cirpan, H. (2016, January 16\u201319). Comparison of compressed sensing based algorithms for sparse signal reconstruction. Proceedings of the 2016 24th Signal Processing and Communication Application Conference (SIU), Zonguldak, Turkey.","DOI":"10.1109\/SIU.2016.7496021"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"9238","DOI":"10.1109\/TGRS.2020.3034102","article-title":"SPB-Net: A Deep Network for SAR Imaging and Despeckling with DownSampled Data","volume":"59","author":"Xiong","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","first-page":"5209721","article-title":"Lq-SPB-Net: A Real-Time Deep Network for SAR Imaging and Despeckling","volume":"60","author":"Xiong","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","first-page":"4501205","article-title":"SAR Imaging and Despeckling Based on Sparse, Low-Rank, and Deep CNN Priors","volume":"19","author":"Xiong","year":"2021","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_23","unstructured":"Hershey, J.R., Roux, J.L., and Weninger, F. (2014). Deep Unfolding: Model-Based Inspiration of Novel Deep Architectures. arXiv."},{"key":"ref_24","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 (CVPR), Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00196"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"You, D., Xie, J., and Zhang, J. (2021, January 5\u20139). ISTA-Net++: Flexible Deep Unfolding Network for Compressive Sensing. Proceedings of the 2021 IEEE International Conference on Multimedia and Expo (ICME), Shenzhen, China.","DOI":"10.1109\/ICME51207.2021.9428249"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhang, K., Gool, L.V., and Timofte, R. (2020, January 13\u201319). Deep Unfolding Network for Image Super-Resolution. Proceedings of the 2020 IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Seattle, WA, USA.","DOI":"10.1109\/CVPR42600.2020.00328"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1329","DOI":"10.1109\/TMI.2021.3054167","article-title":"FISTA-Net: Learning A Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging","volume":"40","author":"Xiang","year":"2021","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"8595","DOI":"10.1109\/JSTARS.2023.3295728","article-title":"HPHR-SAR-Net: Hyperpixel High-Resolution SAR Imaging Network Based on Nonlocal Total Variation","volume":"16","author":"Zhou","year":"2023","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_29","first-page":"4701918","article-title":"ATASI-Net: An Efficient Sparse Reconstruction Network for Tomographic SAR Imaging with Adaptive Threshold","volume":"61","author":"Wang","year":"2023","journal-title":"IEEE Trans. Geosci. Remote Sensing"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1418","DOI":"10.1198\/016214506000000735","article-title":"The adaptive lasso and its oracle properties","volume":"101","author":"Zou","year":"2006","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_31","first-page":"877","article-title":"Enhancing Sparsity by Reweighted L1 Minimization","volume":"14","author":"Wakin","year":"2007","journal-title":"J. Fourier Anal. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Seeger, M.W., and Nickisch, H. (2008, January 5\u20139). Compressed sensing and Bayesian experimental design. Proceedings of the 25th international conference on Machine Learning (ICML).","DOI":"10.1145\/1390156.1390271"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1109\/TCI.2016.2637079","article-title":"Adaptive basis scan by wavelet prediction for single-pixel imaging","volume":"3","author":"Rousset","year":"2017","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_34","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_35","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1109\/TIP.2003.819861","article-title":"Image quality assessment: From error visibility to structural similarity","volume":"13","author":"Wang","year":"2004","journal-title":"IEEE Trans. Image Process."},{"key":"ref_36","unstructured":"Golub, G., and Loan, C.F.V. (1996). Matrix Computations, Johns Hopkins University Press. [3rd ed.]."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/4\/671\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:59:29Z","timestamp":1760104769000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/4\/671"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,13]]},"references-count":36,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,2]]}},"alternative-id":["rs16040671"],"URL":"https:\/\/doi.org\/10.3390\/rs16040671","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2024,2,13]]}}}