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Sci. Comput."],"published-print":{"date-parts":[[2026,8,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Tensor robust principal component analysis (TRPCA) holds a crucial position in machine learning and computer vision. It aims to recover underlying low-rank structures and to characterize the sparse structures of noise. Current approaches often encounter difficulties in accurately capturing the low-rank properties of tensors and balancing the trade-off between low-rank and sparse components, especially in a mixed-noise scenario. To address these challenges, we introduce a Bayesian framework for TRPCA, which integrates a low-rank tensor nuclear norm prior and a generalized sparsity-inducing prior. By embedding the priors within the Bayesian framework, our method can automatically determine the optimal tensor nuclear norm and achieve a balance between the nuclear norm and sparse components. Furthermore, our method can be efficiently extended to the weighted tensor nuclear norm model. Experiments conducted on synthetic and real-world datasets demonstrate the effectiveness and superiority of our method compared to state-of-the-art approaches.<\/jats:p>","DOI":"10.1137\/24m1700752","type":"journal-article","created":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T07:00:52Z","timestamp":1783580452000},"page":"C684-C707","source":"Crossref","is-referenced-by-count":0,"title":["Variational Bayesian Inference for Tensor Robust Principal Component Analysis"],"prefix":"10.1137","volume":"48","author":[{"given":"Chao","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen 518005, Guangdong Province, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huiwen","family":"Zheng","sequence":"additional","affiliation":[{"name":"Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen 518005, Guangdong Province, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0910-4685","authenticated-orcid":true,"given":"Raymond","family":"Chan","sequence":"additional","affiliation":[{"name":"Lingnan University, Hong Kong SAR, China, Hong Kong Centre for Cerebro-cardiovascular Health Engineering."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9892-3668","authenticated-orcid":true,"given":"Youwei","family":"Wen","sequence":"additional","affiliation":[{"name":"Corresponding author. Key Laboratory of Computing and Stochastic Mathematics (LCSM), School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,7,9]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2013.2257810"},{"key":"ref2","volume":"2012","author":"Amizic B.","year":"2012","journal-title":"J. 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