{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T20:23:25Z","timestamp":1775593405233,"version":"3.50.1"},"reference-count":43,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,1,31]],"date-time":"2022-01-31T00:00:00Z","timestamp":1643587200000},"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>Synthetic aperture radar (SAR) frequently suffers from radio frequency interference (RFI) due to the simultaneous presence of numerous wireless communication signals. Recently, the narrowband RFI is found to possess the low-rank property benefiting from stable frequency occupancy, hence the reconsideration of RFI suppression as a joint sparse and low-rank optimization problem. The existing methods either use the non-sparse useful signal itself as the sparse regularizer, or employ the nuclear norm to approximate the rank function, which punishes all singular values with the same penalty via singular value thresholding (SVT), resulting in the improper punishment problem. Hence, both are consequentially subject to performance limitation. In this paper, a novel dictionary-based nonconvex low-rank minimization (DNLRM) optimization framework is proposed for RFI suppression, which concurrently considers the improvements for both the sparse regularizer and the low-rank regularizer. For the former, an over-completed dictionary is constructed, for which the sparse coefficient acts as the sparse regularizer. For the latter, the rank function is more accurately approximated by innovatively introducing the nonconvex function, for which the supergradient is synchronously used to generate the weighted penalty, thus solving the improper punishment problem. The derivation of the closed-form solution and the convergence analysis are described in detail. Additionally, the adaptive selection scheme for the model parameter is uniquely proposed for further ensuring the practicality of the DNLRM framework. The superiority of the proposed method is demonstrated via not only the RFI-free real SAR data combined with the measured RFI, but the RFI-contaminated real SAR data.<\/jats:p>","DOI":"10.3390\/rs14030678","type":"journal-article","created":{"date-parts":[[2022,2,1]],"date-time":"2022-02-01T22:16:18Z","timestamp":1643753778000},"page":"678","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["RFI Suppression for SAR via a Dictionary-Based Nonconvex Low-Rank Minimization Framework and Its Adaptive Implementation"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8807-907X","authenticated-orcid":false,"given":"Zhouyang","family":"Tang","sequence":"first","affiliation":[{"name":"Department of Space Microwave Remote Sensing System, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Yunkai","family":"Deng","sequence":"additional","affiliation":[{"name":"Department of Space Microwave Remote Sensing System, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Huifang","family":"Zheng","sequence":"additional","affiliation":[{"name":"Department of Space Microwave Remote Sensing System, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1109\/MGRS.2013.2248301","article-title":"A tutorial on synthetic aperture radar","volume":"1","author":"Moreira","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1109\/LGRS.2020.2981128","article-title":"High-Fidelity SAR Intermittent Sampling Deceptive Jamming Suppression Using Azimuth Phase Coding","volume":"18","author":"Tang","year":"2021","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Tao, M., Su, J., Huang, Y., and Wang, L. (2019). Mitigation of Radio Frequency Interference in Synthetic Aperture Radar Data: Current Status and Future Trends. Remote Sens., 11.","DOI":"10.3390\/rs11202438"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4961","DOI":"10.1109\/TGRS.2013.2252469","article-title":"Correction and Characterization of Radio Frequency Interference Signatures in L-Band Synthetic Aperture Radar Data","volume":"51","author":"Meyer","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1109\/TGRS.2018.2854661","article-title":"Discriminating Ship From Radio Frequency Interference Based on Noncircularity and Non-Gaussianity in Sentinel-1 SAR Imagery","volume":"57","author":"Leng","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5736","DOI":"10.1109\/JSTARS.2017.2775205","article-title":"An Autocorrelation-Based Radio Frequency Interference Detection and Removal Method in Azimuth-Frequency Domain for SAR Image","volume":"10","author":"Natsuaki","year":"2017","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"key":"ref_7","unstructured":"Chang, W., Cherniakov, M., Li, X., and Li, J. (2008, January 26\u201329). Performance analysis of the notch filter for RF Interference suppression in ultra-wideband SAR. Proceedings of the 9th International Conference on Signal Processing, Beijing, China."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Buckreuss, S., and Horn, R. (1998, January 6\u201310). E-SAR P-band SAR subsystem design and RF-interference suppression. Proceedings of the 1998 IEEE International Geoscience and Remote Sensing Symposium, Seattle, WA, USA.","DOI":"10.1109\/IGARSS.1998.702941"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1109\/LGRS.2006.887033","article-title":"Eigensubspace-Based Filtering With Application in Narrow-Band Interference Suppression for SAR","volume":"4","author":"Zhou","year":"2007","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Yu, C., Zhang, Y., Dong, Z., and Liang, D. (2010, January 29\u201331). Eigen-Decomposition Method for RFI Suppression Applied to SAR Data. Proceedings of the 2010 International Conference on Multimedia Technology, Ningbo, China.","DOI":"10.1109\/ICMULT.2010.5631395"},{"key":"ref_11","unstructured":"Lord, R.T., and Inggs, M.R. (1998, January 8). Approaches to RF interference suppression for VHF\/UHF synthetic aperture radar. Proceedings of the 1998 South African Symposium on Communications and Signal Processing, Rondebosch, South Africa."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Le, C.T.C., Hensley, S., and Chapin, E. (1998, January 12). Adaptive Filtering of RFI in Wideband SAR Signals. Proceedings of the 1998 7th Airborne Geoscience Workshop, Pasadena, CA, USA.","DOI":"10.1109\/IGARSS.1998.703731"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Lord, R.T., and Inggs, M.R. (July, January 28). Efficient RFI suppression in SAR using a LMS adaptive filter with sidelobe suppression integrated with the range-Doppler algorithm. Proceedings of the 1999 IEEE International Geoscience and Remote Sensing Symposium, Hamburg, Germany.","DOI":"10.1049\/el:19990437"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1109\/LGRS.2009.2015340","article-title":"Narrow-Band Interference Suppression for SAR Based on Complex Empirical Mode Decomposition","volume":"6","author":"Zhou","year":"2009","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_15","first-page":"33","article-title":"RFI Suppression for Synchronous Impulse Reconstruction UWB Radar Using RELAX","volume":"3","author":"Ojowu","year":"2013","journal-title":"Int. J. Remote Sens. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1008","DOI":"10.1109\/JSTARS.2015.2470107","article-title":"WBI Suppression for SAR Using Iterative Adaptive Method","volume":"9","author":"Yang","year":"2016","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Nguyen, L., Dao, M., and Tran, T. (2014, January 27\u201330). Radio-frequency interference separation and suppression from ultrawideband radar data via low-rank modeling. Proceedings of the 2014 IEEE International Conference on Image Processing, Paris, France.","DOI":"10.1109\/ICIP.2014.7025022"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Nguyen, L., and Tran, T. (2016, January 2\u20136). RFI-radar signal separation via simultaneous low-rank and sparse recovery. Proceedings of the 2016 IEEE Radar Conference, Philadelphia, PA, USA.","DOI":"10.1109\/RADAR.2016.7485213"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2748","DOI":"10.1109\/TGRS.2017.2782682","article-title":"Narrowband RFI Suppression for SAR System via Fast Implementation of Joint Sparsity and Low-Rank Property","volume":"56","author":"Huang","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"5949","DOI":"10.1109\/TGRS.2019.2903579","article-title":"Reweighted Nuclear Norm and Reweighted Frobenius Norm Minimizations for Narrowband RFI Suppression on SAR System","volume":"57","author":"Huang","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1302","DOI":"10.1109\/TGRS.2020.3003054","article-title":"Enhanced LRR-Based RFI Suppression for SAR Imaging Using the Common Sparsity of Range Profiles for Accurate Signal Recovery","volume":"59","author":"Lu","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3311","DOI":"10.1109\/TGRS.2018.2797946","article-title":"Narrowband RFI Suppression for SAR System via Efficient Parameter-Free Decomposition Algorithm","volume":"56","author":"Huang","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1109\/TGRS.2018.2853556","article-title":"Fast Narrowband RFI Suppression Algorithms for SAR Systems via Matrix-Factorization Techniques","volume":"57","author":"Huang","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_24","first-page":"11","article-title":"Robust principal component analysis?","volume":"58","author":"Li","year":"2011","journal-title":"J. ACM"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1427","DOI":"10.1109\/JPROC.2018.2853589","article-title":"On the Applications of Robust PCA in Image and Video Processing","volume":"106","author":"Bouwmans","year":"2018","journal-title":"Proc. IEEE"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1109\/LGRS.2012.2216248","article-title":"Ground Moving Target Extraction in a Multichannel Wide-Area Surveillance SAR\/GMTI System via the Relaxed PCP","volume":"10","author":"Yan","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1956","DOI":"10.1137\/080738970","article-title":"A singular value thresholding algorithm for matrix completion","volume":"20","author":"Cai","year":"2010","journal-title":"SIAM J. Optim."},{"key":"ref_28","unstructured":"Wright, J., Ganesh, A., Rao, S., Peng, Y., and Ma, Y. (2009, January 7\u201310). Robust principal component analysis: Exact recovery of corrupted low-rank matrices via convex optimization. Proceedings of the 23rd Annual Conference on Neural Information Processing Systems, Vancouver, BC, Canada."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1542","DOI":"10.1109\/LGRS.2017.2721425","article-title":"Joint Wideband Interference Suppression and SAR Signal Recovery Based on Sparse Representations","volume":"14","author":"Liu","year":"2017","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1109\/TIP.2015.2511584","article-title":"Nonconvex Nonsmooth Low Rank Minimization via Iteratively Reweighted Nuclear Norm","volume":"25","author":"Lu","year":"2016","journal-title":"IEEE Trans. Image Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"5366","DOI":"10.1109\/TGRS.2017.2706326","article-title":"Denoising of Hyperspectral Images Using Nonconvex Low Rank Matrix Approximation","volume":"55","author":"Chen","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/TIP.2019.2926736","article-title":"Hyperspectral Images Denoising via Nonconvex Regularized Low-Rank and Sparse Matrix Decomposition","volume":"29","author":"Xie","year":"2019","journal-title":"IEEE Trans. Image Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1109\/TGRS.2019.2937901","article-title":"Hyperspectral Image Recovery Using Nonconvex Sparsity and Low-Rank Regularizations","volume":"58","author":"Hu","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"940","DOI":"10.1109\/TAES.2014.120454","article-title":"Sparse models and sparse recovery for ultra-wideband SAR applications","volume":"50","author":"Nguyen","year":"2014","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/2200000016","article-title":"Distributed optimization and statistical learning via the alternating direction method of multipliers","volume":"3","author":"Boyd","year":"2011","journal-title":"Found. Trends Mach. Learn."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"4944","DOI":"10.1109\/TGRS.2017.2696262","article-title":"Correntropy Maximization via ADMM: Application to Robust Hyperspectral Unmixing","volume":"55","author":"Zhu","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Gu, S., Zhang, L., Zuo, W., and Feng, X. (2014, January 23\u201328). Weighted Nuclear Norm Minimization with Application to Image Denoising. Proceedings of the 2014 IEEE Conference on Computer Vision and Pattern Recognition, Columbus, OH, USA.","DOI":"10.1109\/CVPR.2014.366"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2479","DOI":"10.1109\/TSP.2009.2016892","article-title":"Sparse Reconstruction by Separable Approximation","volume":"57","author":"Wright","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1137\/080730421","article-title":"A fast algorithm for edge-preserving variational multichannel image restoration","volume":"2","author":"Yang","year":"2009","journal-title":"SIAM J. Imag. Sci."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Shevlyakov, G., Andrea, K., Choudur, L., Smirnov, P., Ulanov, A., and Vassilieva, N. (2013, January 26\u201331). Robust versions of the Tukey boxplot with their application to detection of outliers. Proceedings of the 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, Vancouver, BC, Canada.","DOI":"10.1109\/ICASSP.2013.6638919"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Zhang, C., Li, G., and Cui, W. (2017, January 18\u201321). High resolution remote sensing image change detection based on law of cosines with box-whisker plot. Proceedings of the 2017 International Workshop on Remote Sensing with Intelligent Processing, Shanghai, China.","DOI":"10.1109\/RSIP.2017.7958805"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"3765","DOI":"10.1109\/TGRS.2011.2164409","article-title":"Interference Suppression Algorithm for SAR Based on Time\u2013Frequency Transform","volume":"49","author":"Zhang","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_43","unstructured":"Clarke, F.H. (1978, January 7). Nonsmooth analysis and optimization. Proceedings of the International Congress of Mathematicians, Helsinki, Finland."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/3\/678\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:12:01Z","timestamp":1760134321000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/3\/678"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,31]]},"references-count":43,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["rs14030678"],"URL":"https:\/\/doi.org\/10.3390\/rs14030678","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,31]]}}}