{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T06:09:04Z","timestamp":1762409344987,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2017,9,29]],"date-time":"2017-09-29T00:00:00Z","timestamp":1506643200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U1509203,61503206,61333005"],"award-info":[{"award-number":["U1509203,61503206,61333005"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Zhejiang Provincial Natural Science Foundation of China","award":["LZ16F030002"],"award-info":[{"award-number":["LZ16F030002"]}]},{"name":"the Aerospace Science Foundation of China","award":["2015ZC76006"],"award-info":[{"award-number":["2015ZC76006"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, a novel infrared target co-detection model combining the self-correlation features of backgrounds and the commonality features of targets in the spatio-temporal domain is proposed to detect small targets in a sequence of infrared images with complex backgrounds. Firstly, a dense target extraction model based on nonlinear weights is proposed, which can better suppress background of images and enhance small targets than weights of singular values. Secondly, a sparse target extraction model based on entry-wise weighted robust principal component analysis is proposed. The entry-wise weight adaptively incorporates structural prior in terms of local weighted entropy, thus, it can extract real targets accurately and suppress background clutters efficiently. Finally, the commonality of targets in the spatio-temporal domain are used to construct target refinement model for false alarms suppression and target confirmation. Since real targets could appear in both of the dense and sparse reconstruction maps of a single frame, and form trajectories after tracklet association of consecutive frames, the location correlation of the dense and sparse reconstruction maps for a single frame and tracklet association of the location correlation maps for successive frames have strong ability to discriminate between small targets and background clutters. Experimental results demonstrate that the proposed small target co-detection method can not only suppress background clutters effectively, but also detect targets accurately even if with target-like interference.<\/jats:p>","DOI":"10.3390\/s17102242","type":"journal-article","created":{"date-parts":[[2017,9,29]],"date-time":"2017-09-29T12:24:04Z","timestamp":1506687844000},"page":"2242","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Robust Small Target Co-Detection from Airborne Infrared Image Sequences"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4272-8767","authenticated-orcid":false,"given":"Jingli","family":"Gao","sequence":"first","affiliation":[{"name":"College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China"},{"name":"College of Software Engineering, Pingdingshan University, Pingdingshan 467000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chenglin","family":"Wen","sequence":"additional","affiliation":[{"name":"School of Automation, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0693-6574","authenticated-orcid":false,"given":"Meiqin","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,9,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"9451","DOI":"10.3390\/s140609451","article-title":"Sparse Representation for Infrared Dim Target Detection via a Discriminative Over-Complete Dictionary Learned Online","volume":"14","author":"Li","year":"2014","journal-title":"Sensors"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"20297","DOI":"10.3390\/s141120297","article-title":"Advances in target detection and tracking in Forward-Looking InfraRed (FLIR) imagery","volume":"14","author":"Sanna","year":"2014","journal-title":"Sensors"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"7267","DOI":"10.3390\/s150407267","article-title":"High-speed incoming infrared target detection by fusion of spatial and temporal detectors","volume":"15","author":"Kim","year":"2015","journal-title":"Sensors"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zhao, H., Ji, Z., Li, N., Gu, J., and Li, Y. (2017). Target Detection over the Diurnal Cycle Using a Multispectral Infrared Sensor. Sensors, 17.","DOI":"10.3390\/s17010056"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.infrared.2015.09.003","article-title":"Moving target detection by nonlinear adaptive filtering on temporal profiles in infrared image sequences","volume":"73","author":"Liu","year":"2015","journal-title":"Infrared Phys. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/j.infrared.2011.06.006","article-title":"Small target detection using bilateral filter and temporal cross product in infrared images","volume":"54","author":"Bae","year":"2011","journal-title":"Infrared Phys. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.infrared.2013.12.007","article-title":"Spatial and temporal bilateral filter for infrared small target enhancement","volume":"63","author":"Bae","year":"2014","journal-title":"Infrared Phys. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4996","DOI":"10.1109\/TIP.2013.2281420","article-title":"Infrared Patch-Image Model for Small Target Detection in a Single Image","volume":"22","author":"Gao","year":"2013","journal-title":"IEEE Trans. Image Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1109\/TGRS.2013.2242477","article-title":"A local contrast method for small infrared target detection","volume":"52","author":"Chen","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4204","DOI":"10.1109\/TGRS.2016.2538295","article-title":"Small Infrared Target Detection Based on Weighted Local Difference Measure","volume":"54","author":"Deng","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.infrared.2015.09.010","article-title":"Infrared target tracking via weighted correlation filter","volume":"73","author":"He","year":"2015","journal-title":"Infrared Phys. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1109\/LGRS.2015.2506758","article-title":"Infrared Target Tracking Based on Robust Low-Rank Sparse Learning","volume":"13","author":"He","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1109\/TPAMI.2014.2359453","article-title":"Sparse and Dense Hybrid Representation via Dictionary Decomposition for Face Recognition","volume":"37","author":"Jiang","year":"2015","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1592","DOI":"10.1109\/TIP.2016.2524198","article-title":"Dense and Sparse Reconstruction Error Based Saliency Descriptor","volume":"25","author":"Lu","year":"2016","journal-title":"IEEE Trans. Image Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.jvcir.2015.08.003","article-title":"Saliency detection based on singular value decomposition","volume":"32","author":"Ma","year":"2015","journal-title":"J. Vis. Commun. Image Represent."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1016\/j.infrared.2016.06.021","article-title":"Infrared small target and background separation via column-wise weighted robust principal component analysis","volume":"77","author":"Dai","year":"2016","journal-title":"Infrared Phys. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1117\/12.157758","article-title":"Morphology-based algorithm for point target detection in infrared backgrounds","volume":"1954","author":"Tom","year":"1993","journal-title":"Proc. SPIE"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Deshpande, S.D., Meng, H.E., Venkateswarlu, R., and Chan, P. (1999, January 4). Max-mean and max-median filters for detection of small targets. Proceedings of the SPIE\u2019s International Symposium on Optical Science, Engineering, and Instrumentation, Denver, CO, USA.","DOI":"10.1117\/12.364049"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"838","DOI":"10.1109\/JSEE.2012.00102","article-title":"Novel detection method for infrared small targets using weighted information entropy","volume":"23","author":"Qu","year":"2012","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1016\/j.infrared.2014.07.029","article-title":"Multiscale facet model for infrared small target detection","volume":"67","author":"Yang","year":"2014","journal-title":"Infrared Phys. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1016\/j.infrared.2016.06.026","article-title":"A fast-saliency method for real-time infrared small target detection","volume":"77","author":"Qi","year":"2016","journal-title":"Infrared Phys. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1016\/j.patcog.2016.04.002","article-title":"Multiscale patch-based contrast measure for small infrared target detection","volume":"58","author":"Wei","year":"2016","journal-title":"Pattern Recognit."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1016\/S1350-4495(96)00003-5","article-title":"Temporal filters for tracking weak slow point targets in evolving cloud clutter","volume":"37","author":"Silverman","year":"1996","journal-title":"Infrared Phys. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.infrared.2015.01.017","article-title":"Adaptive detection method of infrared small target based on target-background separation via robust principal component analysis","volume":"69","author":"Wang","year":"2015","journal-title":"Infrared Phys. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Oh, T.H., Kim, H., Tai, Y.W., Bazin, J.C., and Kweon, I.S. (2013, January 1\u20138). Partial Sum Minimization of Singular Values in RPCA for Low-Level Vision. Proceedings of the IEEE International Conference on Computer Vision, Sydney, Australia.","DOI":"10.1109\/ICCV.2013.25"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"744","DOI":"10.1109\/TPAMI.2015.2465956","article-title":"Partial Sum Minimization of Singular Values in Robust PCA: Algorithm and Applications","volume":"38","author":"Oh","year":"2016","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_27","unstructured":"Wright, J., Peng, Y., Ma, Y., Ganesh, A., and Rao, S. (2009, January 7\u201310). Robust principal component analysis: exact recovery of corrupted low-rank matrices by convex optimization. Proceedings of the International Conference on Neural Information Processing Systems, Vancouver, BC, Canada."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Manning, C.D., Raghavan, P., and Sch\u00fctze, H. (2008). Introduction to Information Retrieval, Cambridge University Press.","DOI":"10.1017\/CBO9780511809071"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/s00170-003-1832-6","article-title":"Automatic defect inspection for LCDs using singular value decomposition","volume":"25","author":"Lu","year":"2005","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Beigi, H. (2011). Probability Theory and Statistics. Fundamentals of Speaker Recognition, Springer.","DOI":"10.1007\/978-0-387-77592-0"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Lin, Z., Ganesh, A., Wright, J., Wu, L., Chen, M., and Ma, Y. (2009, January 13\u201316). Fast convex optimization algorithms for exact recovery of a corrupted low-rank matrix. Proceedings of the Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), Aruba, Dutch Antilles, The Netherlands.","DOI":"10.1109\/CAMSAP.2009.5413299"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1561\/2400000003","article-title":"Proximal Algorithms","volume":"1","author":"Parikh","year":"2014","journal-title":"Found. Trends Optim."},{"key":"ref_33","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. Imaging Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1107","DOI":"10.1137\/070698920","article-title":"Fixed-point continuation for l1-minimization: Methodology and convergence","volume":"19","author":"Hale","year":"2008","journal-title":"SIAM J. Optim."},{"key":"ref_35","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_36","unstructured":"Miezianko, R. (2016, December 20). IEEE OTCBVS WS Series Bench, 2006. Available online: http:\/\/vcipl-okstate.org\/pbvs\/bench\/Data\/05\/download.html."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"6518","DOI":"10.1364\/AO.53.006518","article-title":"Real-time infrared target tracking based on \u21131 minimization and compressive features","volume":"53","author":"Li","year":"2014","journal-title":"Appl. Opt."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1109\/7.826309","article-title":"Optimization of point target tracking filters","volume":"36","author":"Caefer","year":"2000","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/j.patcog.2011.06.009","article-title":"Scale invariant small target detection by optimizing signal-to-clutter ratio in heterogeneous background for infrared search and track","volume":"45","author":"Kim","year":"2012","journal-title":"Pattern Recognit."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1109\/LGRS.2009.2039192","article-title":"A Kernel-Based Nonparametric Regression Method for Clutter Removal in Infrared Small-Target Detection Applications","volume":"7","author":"Gu","year":"2010","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"5706","DOI":"10.1109\/TIP.2015.2487833","article-title":"Salient Object Detection: A Benchmark","volume":"24","author":"Borij","year":"2015","journal-title":"IEEE Trans. Image Process."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1886","DOI":"10.1117\/1.600620","article-title":"Detection of dim targets in digital infrared imagery by morphological image processing","volume":"35","author":"Fortin","year":"1996","journal-title":"Opt. Eng."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/10\/2242\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:46:16Z","timestamp":1760208376000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/10\/2242"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,29]]},"references-count":42,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2017,10]]}},"alternative-id":["s17102242"],"URL":"https:\/\/doi.org\/10.3390\/s17102242","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2017,9,29]]}}}