{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T17:41:39Z","timestamp":1757612499884,"version":"3.44.0"},"reference-count":56,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,9,28]],"date-time":"2021-09-28T00:00:00Z","timestamp":1632787200000},"content-version":"vor","delay-in-days":270,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007941","name":"Addis Ababa University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100007941","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011381","name":"State Key Laboratory of Robotics and System","doi-asserted-by":"publisher","award":["SKLRS-2019-KF-15"],"award-info":[{"award-number":["SKLRS-2019-KF-15"]}],"id":[{"id":"10.13039\/501100011381","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>In this paper, we propose a novel robust algorithm for image recovery via affine transformations, the weighted nuclear, <jats:italic>L<\/jats:italic><jats:sub>\u2217,<jats:italic>w<\/jats:italic><\/jats:sub>, and the <jats:italic>L<\/jats:italic><jats:sub>2,1<\/jats:sub> norms. The new method considers the spatial weight matrix to account the correlated samples in the data, the <jats:italic>L<\/jats:italic><jats:sub>2,1<\/jats:sub> norm to tackle the dilemma of extreme values in the high\u2010dimensional images, and the <jats:italic>L<\/jats:italic><jats:sub>\u2217,<jats:italic>w<\/jats:italic><\/jats:sub> norm newly added to alleviate the potential effects of outliers and heavy sparse noises, enabling the new approach to be more resilient to outliers and large variations in the high\u2010dimensional images in signal processing. The determination of the parameters is involved, and the affine transformations are cast as a convex optimization problem. To mitigate the computational complexity, alternating iteratively reweighted direction method of multipliers (ADMM) method is utilized to derive a new set of recursive equations to update the optimization variables and the affine transformations iteratively in a round\u2010robin manner. The new algorithm is superior to the state\u2010of\u2010the\u2010art works in terms of accuracy on various public databases.<\/jats:p>","DOI":"10.1155\/2021\/3047712","type":"journal-article","created":{"date-parts":[[2021,9,28]],"date-time":"2021-09-28T16:34:04Z","timestamp":1632846844000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["New Robust PCA for Outliers and Heavy Sparse Noises\u2019 Detection via Affine Transformation, the <i>L<\/i><sub>\u2217,<i>w<\/i><\/sub> and <i>L<\/i><sub>2,1<\/sub> Norms, and Spatial Weight Matrix in High\u2010Dimensional Images: From the Perspective of Signal Processing"],"prefix":"10.1155","volume":"2021","author":[{"given":"Peidong","family":"Liang","sequence":"first","affiliation":[]},{"given":"Habte Tadesse","family":"Likassa","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0978-9565","authenticated-orcid":false,"given":"Chentao","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Jielong","family":"Guo","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,9,28]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2008.79"},{"key":"e_1_2_9_2_2","doi-asserted-by":"crossref","unstructured":"YangJ. YuK. GongY. andHuangT. Linear spatial pyramid matching using sparse coding for image classification 2009 IEEE Conference on Computer Vision and Pattern Recognition June 2009 Miami FL USA IEEE 1794\u20131801 https:\/\/doi.org\/10.1109\/cvpr.2009.5206757.","DOI":"10.1109\/CVPR.2009.5206757"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.5194\/isprs-archives-xlii-2-w11-187-2019"},{"key":"e_1_2_9_4_2","unstructured":"YanY.andHuangL. Large-scale image processing research cloud Proceedings of the International Conference on Cloud Computing 2014 Prairie View TX 88\u201393."},{"key":"e_1_2_9_5_2","doi-asserted-by":"crossref","unstructured":"AgarwalS.andRothD. Learning a sparse representation for object detection Proceedings of the European Conference on Computer Vision 2002 Springer Nature Switzerland Springer 113\u2013127 https:\/\/doi.org\/10.1007\/3-540-47979-1_8.","DOI":"10.1007\/3-540-47979-1_8"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/tcsvt.2017.2771150"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.inffus.2018.11.019"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2018.2836802"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1109\/jproc.2018.2853141"},{"key":"e_1_2_9_10_2","doi-asserted-by":"crossref","unstructured":"HuangD. StorerM. De la TorreF. andBischofH. Supervised local subspace learning for continuous head pose estimation CVPR 2011 June 2011 Colorado Springs CO USA IEEE 2921\u20132928 https:\/\/doi.org\/10.1109\/cvpr.2011.5995683 2-s2.0-80052890826.","DOI":"10.1109\/CVPR.2011.5995683"},{"key":"e_1_2_9_11_2","doi-asserted-by":"crossref","unstructured":"DrouardV. BaS. EvangelidisG. DeleforgeA. andHoraudR. Head pose estimation via probabilistic high-dimensional regression Proceedings of the 2015 IEEE International Conference on Image Processing (ICIP) September 2015 Quebec City QC Canada IEEE 4624\u20134628 https:\/\/doi.org\/10.1109\/icip.2015.7351683 2-s2.0-84956649013.","DOI":"10.1109\/ICIP.2015.7351683"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1109\/tci.2017.2744626"},{"key":"e_1_2_9_13_2","doi-asserted-by":"publisher","DOI":"10.1145\/1970392.1970395"},{"key":"e_1_2_9_14_2","doi-asserted-by":"crossref","unstructured":"EbadiS.andIzquierdoE. Approximated RPCA for fast and efficient recovery of corrupted and linearly correlated images and video frames Proceedings of the International Conference on Systems Signals and Image Processing (IWSSIP) September 2015 London UK IEEE 49\u201352 https:\/\/doi.org\/10.1109\/iwssip.2015.7314174 2-s2.0-84961730145.","DOI":"10.1109\/IWSSIP.2015.7314174"},{"key":"e_1_2_9_15_2","first-page":"2080","article-title":"Robust principal component analysis: exact recovery of corrupted low-rank matrices via convex optimization","volume":"58","author":"Wright J.","year":"2009","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_2_9_16_2","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2011.112"},{"key":"e_1_2_9_17_2","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2019.2921031"},{"key":"e_1_2_9_18_2","doi-asserted-by":"publisher","DOI":"10.1109\/tpami.2015.2465956"},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2019.2891760"},{"key":"e_1_2_9_20_2","doi-asserted-by":"publisher","DOI":"10.1109\/taes.2019.2909728"},{"key":"e_1_2_9_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2018.05.020"},{"key":"e_1_2_9_22_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11432-015-5419-2"},{"key":"e_1_2_9_23_2","doi-asserted-by":"publisher","DOI":"10.1109\/tfuzz.2020.3030498"},{"key":"e_1_2_9_24_2","article-title":"Robust tensor decomposition based background\/foreground separation in noisy videos and its applications in additive manufacturing","author":"Shen B.","year":"2021","journal-title":"TechRXiv"},{"key":"e_1_2_9_25_2","unstructured":"CaiH. HammK. HuangL. andNeedellD. Robust cur decomposition: theory and imaging applications 2021 https:\/\/arxiv.org\/2101.05231."},{"key":"e_1_2_9_26_2","doi-asserted-by":"publisher","DOI":"10.1109\/tci.2019.2891389"},{"key":"e_1_2_9_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/s1077-3142(03)00076-6"},{"volume-title":"Long-rank Approximation and Sparse Recovery for Visual Data Reconstruction","year":"2012","author":"Nguyen D. T.","key":"e_1_2_9_28_2"},{"key":"e_1_2_9_29_2","doi-asserted-by":"publisher","DOI":"10.1137\/100781894"},{"key":"e_1_2_9_30_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-87811-9"},{"key":"e_1_2_9_31_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-87811-9_3"},{"key":"e_1_2_9_32_2","doi-asserted-by":"crossref","unstructured":"BaghaieA. D\u2019souzaR. M. andYuZ. Sparse and low rank decomposition based batch image alignment for speckle reduction of retinal OCT images Proceedings of the 2015 IEEE 12th International Symposium on Biomedical Imaging (ISBI) April 2015 Brooklyn NY USA IEEE 226\u2013230 https:\/\/doi.org\/10.1109\/isbi.2015.7163855 2-s2.0-84944321901.","DOI":"10.1109\/ISBI.2015.7163855"},{"key":"e_1_2_9_33_2","doi-asserted-by":"crossref","unstructured":"LikassaH. T. FangW.-H. andChuangY.-A. Modified robust image alignment by sparse and low rank decomposition for highly linearly correlated data Proceedings of the 2018 3rd International Conference on Intelligent Green Building and Smart Grid (IGBSG) April 2018 Yilan Taiwan IEEE 1\u20134 https:\/\/doi.org\/10.1109\/igbsg.2018.8393549 2-s2.0-85050159791.","DOI":"10.1109\/IGBSG.2018.8393549"},{"key":"e_1_2_9_34_2","doi-asserted-by":"crossref","unstructured":"ZhengQ. WangY. andHengP.-A. Online robust image alignment via subspace learning from gradient orientations Proceedings of the IEEE International Conference on Computer Vision (ICCV) October 2017 Venice Italy 1753\u20131762 https:\/\/doi.org\/10.1109\/iccv.2017.195 2-s2.0-85041896299.","DOI":"10.1109\/ICCV.2017.195"},{"key":"e_1_2_9_35_2","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2015.2472284"},{"key":"e_1_2_9_36_2","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2012.88"},{"key":"e_1_2_9_37_2","first-page":"1217","article-title":"High-dimensional support union recovery in multivariate regression","volume":"21","author":"Obozinski G. R.","year":"2009","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_2_9_38_2","doi-asserted-by":"publisher","DOI":"10.1109\/tip.2017.2691549"},{"key":"e_1_2_9_39_2","doi-asserted-by":"publisher","DOI":"10.1155\/2020\/8136384"},{"key":"e_1_2_9_40_2","doi-asserted-by":"publisher","DOI":"10.1109\/access.2019.2932470"},{"key":"e_1_2_9_41_2","unstructured":"LinZ. ChenM. andMaY. TThe augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices 2010 https:\/\/arxiv.org\/1009.5055."},{"key":"e_1_2_9_42_2","unstructured":"LiuG. LinZ. andYuY. Robust subspace segmentation by low-rank representation Proceedings of the 27th International Conference on Machine Learning (ICML-10) 2010 Haifa Israel."},{"key":"e_1_2_9_43_2","doi-asserted-by":"publisher","DOI":"10.1109\/tpami.2011.282"},{"key":"e_1_2_9_44_2","doi-asserted-by":"publisher","DOI":"10.1155\/2020\/1286909"},{"key":"e_1_2_9_45_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2017.01.013"},{"key":"e_1_2_9_46_2","doi-asserted-by":"crossref","unstructured":"LikassaH. T.andFangW.-H. Robust regression for image alignment via subspace recovery techniques Proceedings of the 2018 VII International Conference on Network Communication and Computing 2018 288\u2013293 https:\/\/doi.org\/10.1145\/3301326.3301385 2-s2.0-85063489154.","DOI":"10.1145\/3301326.3301385"},{"key":"e_1_2_9_47_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cosrev.2016.11.001"},{"key":"e_1_2_9_48_2","doi-asserted-by":"crossref","unstructured":"DingC. ZhouD. HeX. andZhaH. R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization Proceedings of the 23rd International Conference on Machine Learning (ICML) 2006 Berkeley CA 281\u2013288.","DOI":"10.1145\/1143844.1143880"},{"key":"e_1_2_9_49_2","doi-asserted-by":"crossref","unstructured":"GuS. ZhangL. ZuoW. andFengX. Weighted nuclear norm minimization with application to image denoising Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition June 2014 Columbus OH USA 2862\u20132869 https:\/\/doi.org\/10.1109\/cvpr.2014.366 2-s2.0-84911360659.","DOI":"10.1109\/CVPR.2014.366"},{"key":"e_1_2_9_50_2","doi-asserted-by":"crossref","unstructured":"SubbaraoR.andMeerP. Beyond RANSAC: user independent robust regression 2006 Conference on Computer Vision and Pattern Recognition Workshop (CVPRW\u201906) June 2006 New York NY USA IEEE https:\/\/doi.org\/10.1109\/cvprw.2006.43 2-s2.0-33845529122.","DOI":"10.1109\/CVPRW.2006.43"},{"key":"e_1_2_9_51_2","doi-asserted-by":"publisher","DOI":"10.1561\/2200000016"},{"key":"e_1_2_9_52_2","unstructured":"YangJ.andZhangY. Alternating algorithms for 1-problems in compressive sensing 2010 Rice University CAAM Houston TX Tech. Rep. TR09-37."},{"key":"e_1_2_9_53_2","unstructured":"CourrieuP. Fast computation of moore-penrose inverse matrices 2008 https:\/\/arxiv.org\/0804.4809."},{"key":"e_1_2_9_54_2","doi-asserted-by":"publisher","DOI":"10.1109\/5.726791"},{"volume-title":"Labeled Faces in the Wild: A Database for Studying Face Recognition in Unconstrained Environments","year":"2007","author":"Huang G. B.","key":"e_1_2_9_55_2"},{"key":"e_1_2_9_56_2","doi-asserted-by":"crossref","unstructured":"HoreA.andZiouD. Image quality metrics: PSNR vs SSIM 2010 20th International Conference on Pattern Recognition August 2010 Istanbul Turkey IEEE 2366\u20132369 https:\/\/doi.org\/10.1109\/icpr.2010.579 2-s2.0-78149476646.","DOI":"10.1109\/ICPR.2010.579"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2021\/3047712.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2021\/3047712.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2021\/3047712","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,4]],"date-time":"2025-09-04T12:46:18Z","timestamp":1756989978000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2021\/3047712"}},"subtitle":[],"editor":[{"given":"Niansheng","family":"Tang","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":56,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1155\/2021\/3047712"],"URL":"https:\/\/doi.org\/10.1155\/2021\/3047712","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2021,1]]},"assertion":[{"value":"2021-07-03","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-09-09","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-09-28","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"3047712"}}