{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:30:04Z","timestamp":1760232604787,"version":"build-2065373602"},"reference-count":54,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2022,11,16]],"date-time":"2022-11-16T00:00:00Z","timestamp":1668556800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Startup Foundation for Introducing Talent of Nanjing University of Information Science &amp; Technology","award":["2022R118","2020R053","MJY22018","MESTA-2020-B011"],"award-info":[{"award-number":["2022R118","2020R053","MJY22018","MESTA-2020-B011"]}]},{"name":"the Startup Foundation for Introducing Talent of Minjiang University","award":["2022R118","2020R053","MJY22018","MESTA-2020-B011"],"award-info":[{"award-number":["2022R118","2020R053","MJY22018","MESTA-2020-B011"]}]},{"name":"Open Fund of Key Laboratory of Marine Environmental Survey Technology and Application, Ministry of Natural Resources","award":["2022R118","2020R053","MJY22018","MESTA-2020-B011"],"award-info":[{"award-number":["2022R118","2020R053","MJY22018","MESTA-2020-B011"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The sparsity regularization based on the L1 norm can significantly stabilize the solution of the ill-posed sparsity inversion problem, e.g., azimuth super-resolution of radar forward-looking imaging, which can effectively suppress the noise and reduce the blurry effect of the convolution kernel. In practice, the total variation (TV) and TV-sparsity (TVS) regularizations based on the L1 norm are widely adopted in solving the ill-posed problem. Generally, however, the existence of bias is ignored, which is incomplete in theory. This paper places emphasis on analyzing the partially biased property of the L1 norm. On this basis, we derive the partially bias-corrected solution of TVS and TV, which improves the rigor of the theory. Lastly, two groups of experimental results reflect that the proposed methods with partial bias correction can preserve higher quality than those without bias correction. The proposed methods not only distinguish the adjacent targets, suppress the noise, and preserve the shape and size of targets in visual terms. Its improvement of Peak Signal-to-Noise Ratio, Structure-Similarity, and Sum-Squared-Errors assessment indexes are overall 2.15%, 1.88%, and 4.14%, respectively. As such, we confirm the theoretical rigor and practical feasibility of the partially bias-corrected solution with sparsity regularization based on the L1 norm.<\/jats:p>","DOI":"10.3390\/rs14225792","type":"journal-article","created":{"date-parts":[[2022,11,17]],"date-time":"2022-11-17T03:27:44Z","timestamp":1668655664000},"page":"5792","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Bias Analysis and Correction for Ill-Posed Inversion Problem with Sparsity Regularization Based on L1 Norm for Azimuth Super-Resolution of Radar Forward-Looking Imaging"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3376-3592","authenticated-orcid":false,"given":"Jie","family":"Han","sequence":"first","affiliation":[{"name":"School of Remote Sensing & Geomatics, Nanjing University of Information Science & Technology, Nanjing 210044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Songlin","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Surveying and Geoinformatics, Tongji University, Shanghai 200092, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shouzhu","family":"Zheng","sequence":"additional","affiliation":[{"name":"College of Geography and Oceanography, Minjiang University, Fuzhou 350108, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3758-775X","authenticated-orcid":false,"given":"Minghua","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Remote Sensing & Geomatics, Nanjing University of Information Science & Technology, Nanjing 210044, China"},{"name":"Key Laboratory of Marine Environmental Survey Technology and Application, Ministry of Natural Resources, Guangzhou 510300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haiyong","family":"Ding","sequence":"additional","affiliation":[{"name":"School of Remote Sensing & Geomatics, Nanjing University of Information Science & Technology, Nanjing 210044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6693-957X","authenticated-orcid":false,"given":"Qingyun","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Remote Sensing & Geomatics, Nanjing University of Information Science & Technology, Nanjing 210044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,16]]},"reference":[{"key":"ref_1","first-page":"L06604","article-title":"Geometry-specified troposphere decorrelation for subcentimeter real-time kinematic solutions over long baselines","volume":"115","author":"Li","year":"2010","journal-title":"J. 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