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arxiv: 2603.25132 · v2 · submitted 2026-03-26 · 💻 cs.CV · cs.LG

Recognition: no theorem link

Robust Principal Component Completion

Yinjian Wang , Wei Li , Yuanyuan Gui , James E. Fowler , Gemine Vivone
Authors on Pith no claims yet

Pith reviewed 2026-05-15 00:26 UTC · model grok-4.3

classification 💻 cs.CV cs.LG
keywords robust principal component analysisprincipal component completionvariational Bayesian inferencesparse tensor factorizationforeground extractionanomaly detectionsupport identification
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The pith

Robust principal component completion identifies the support of a sparse occluding component in low-rank data through variational Bayesian inference on sparse tensor factorization.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Standard robust principal component analysis assumes a sparse component adds to a low-rank background, but many applications involve the sparse part replacing or occluding background elements instead. The paper introduces robust principal component completion to model this replacement directly by recovering the exact support of the sparse component. It solves the resulting problem with variational Bayesian inference on a fully probabilistic Bayesian sparse tensor factorization model. The inference procedure is shown to converge to a hard binary classifier for the support locations, which removes the need for separate post-hoc thresholding steps required by most earlier approaches. On synthetic data the method recovers near-optimal estimates, while on real color video it separates foreground objects effectively and on hyperspectral data it detects anomalies as replacements.

Core claim

By reframing the separation task as one of completing the low-rank background after sparse replacements have occurred, and by applying variational Bayesian inference to a Bayesian sparse tensor factorization, the method converges to a hard classifier that directly labels which elements belong to the sparse support. This produces estimates of both the low-rank background and the sparse component without requiring manual thresholding afterward.

What carries the argument

Variational Bayesian inference on a Bayesian sparse tensor factorization model that identifies the support of the sparse occluding component.

If this is right

  • Near-optimal recovery of both low-rank and sparse parts on synthetic data where ground-truth support is known.
  • Robust foreground extraction from low-rank backgrounds in real color video sequences.
  • Effective anomaly detection in hyperspectral datasets by treating anomalies as sparse replacements.
  • Elimination of post-processing thresholding that most prior RPCA methods require for support decisions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The replacement modeling choice may improve results in physical settings where occlusion is the actual generative process rather than additive noise.
  • The tensor factorization structure could extend naturally to higher-order data such as multi-view video or spectral-time cubes.
  • The demonstrated convergence to a hard classifier might apply to other Bayesian sparse recovery problems that currently rely on soft probabilities.

Load-bearing premise

The observed data consists of a low-rank background whose elements are exactly replaced rather than added to by the sparse component, and the variational inference procedure converges to a reliable hard decision on which locations belong to that support.

What would settle it

Synthetic datasets constructed so the sparse component adds to rather than replaces the background values, on which the method would produce higher reconstruction error than standard robust principal component analysis.

Figures

Figures reproduced from arXiv: 2603.25132 by Gemine Vivone, James E. Fowler, Wei Li, Yinjian Wang, Yuanyuan Gui.

Figure 1
Figure 1. Figure 1: Visual comparison of various quantities of the RPCA [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: B-Unfolding: The reorganization of each tensor block [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Box plots of RRSE and IoU on synthetic data. RRSE [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Hyperparameter tuning for foreground extraction [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Foreground extraction for the Highway dataset. Row 1: Frame 10. Row 2: Frame 25. Row 3: Frame 50. [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Foreground extraction for the Turnpike dataset. Row 1: Frame 10. Row 2: Frame 25. Row 3: Frame 50. [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Foreground extraction for the Crossroad dataset. Row 1: Frame 10. Row 2: Frame 45. Row 3: Frame 50. [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Foreground extraction for the Busstation dataset. Row 1: Frame 1. Row 2: Frame 25. Row 3: Frame 50. [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: Hyperspectral datasets for anomaly detection; [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Hyperparameter tuning for hyperspectral anomaly [PITH_FULL_IMAGE:figures/full_fig_p012_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Anomaly detection on Belcher (row 1), Urban (row 2), Beach (row 3), and Salinas (row 4). [PITH_FULL_IMAGE:figures/full_fig_p013_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Anomaly-detection performance in terms of [PITH_FULL_IMAGE:figures/full_fig_p013_14.png] view at source ↗
read the original abstract

Robust principal component analysis (RPCA) seeks a low-rank component and a sparse component from their summation. Yet, in many applications of interest, the sparse foreground actually replaces, or occludes, elements from the low-rank background. To address this mismatch, a new framework is proposed in which the sparse component is identified indirectly through determining its support. This approach, called robust principal component completion (RPCC), is solved via variational Bayesian inference applied to a fully probabilistic Bayesian sparse tensor factorization. Convergence to a hard classifier for the support is shown, thereby eliminating the post-hoc thresholding required of most prior RPCA-driven approaches. Experimental results reveal that the proposed approach delivers near-optimal estimates on synthetic data as well as robust foreground-extraction and anomaly-detection performance on real color video and hyperspectral datasets, respectively. Source implementation and Appendices are available at https://github.com/WongYinJ/BCP-RPCC.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper introduces Robust Principal Component Completion (RPCC) to address cases where the sparse foreground occludes rather than adds to the low-rank background, unlike standard RPCA. It models the problem via a fully probabilistic Bayesian sparse tensor factorization solved by variational inference, with the central claim that this inference converges to a hard (0/1) classifier on the support, thereby removing any need for post-hoc thresholding. Experiments report near-optimal recovery on synthetic data and strong foreground-extraction/anomaly-detection results on real color video and hyperspectral datasets.

Significance. If the convergence-to-hard-classifier claim is placed on a rigorous footing, RPCC would offer a principled probabilistic alternative to RPCA that avoids thresholding artifacts, with potential impact on video processing and hyperspectral imaging. The reported experimental performance and the provision of open-source code are strengths that would support adoption if the modeling assumptions hold.

major comments (3)
  1. [Abstract] Abstract: the assertion that 'convergence to a hard classifier for the support is shown' is load-bearing for the novelty claim yet is presented without reference to a theorem, convergence analysis, or derivation establishing that the chosen variational family forces the support indicators to exact binary values rather than soft probabilities.
  2. [§3 and §4] §3 (model definition) and §4 (variational updates): the occlusion modeling assumption (sparse component replaces background elements) is central but the likelihood formulation is not shown to differ from additive RPCA in a way that is preserved under the mean-field variational approximation; without this, the method risks reducing to standard RPCA plus thresholding.
  3. [Experimental results] Experimental section (synthetic results): the claim of 'near-optimal estimates' is not accompanied by an explicit error metric, baseline comparison table, or analysis of how the hard-classifier property was verified (e.g., fraction of support variables with posterior mass >0.99), making it impossible to confirm that the advantage is not due to post-hoc decisions.
minor comments (2)
  1. [§2 and §3] Notation for the tensor factorization and variational parameters should be introduced with a single consistent table to avoid repeated re-definition across sections.
  2. [Experimental results] The GitHub repository link is welcome, but the manuscript should state the exact random seeds, hyperparameter settings, and data preprocessing steps used for the reported video and hyperspectral experiments to ensure reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment point by point below, providing clarifications and indicating where revisions will be made to improve the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that 'convergence to a hard classifier for the support is shown' is load-bearing for the novelty claim yet is presented without reference to a theorem, convergence analysis, or derivation establishing that the chosen variational family forces the support indicators to exact binary values rather than soft probabilities.

    Authors: We will revise the abstract to explicitly reference the convergence analysis in Section 4 and Appendix B. There we show via the fixed-point equations of the variational updates that the chosen mean-field family and spike-and-slab prior drive the support posterior probabilities to the boundaries (0 or 1) at convergence; the derivation follows from the fact that the expected complete-data log-likelihood term becomes strictly linear in the support variable once the other factors are fixed, forcing the variational optimum to a vertex of the probability simplex. revision: yes

  2. Referee: [§3 and §4] §3 (model definition) and §4 (variational updates): the occlusion modeling assumption (sparse component replaces background elements) is central but the likelihood formulation is not shown to differ from additive RPCA in a way that is preserved under the mean-field variational approximation; without this, the method risks reducing to standard RPCA plus thresholding.

    Authors: The generative model in Eq. (3)–(5) is non-additive: each observed entry is drawn from either the low-rank background or the sparse foreground according to the binary support indicator, never their sum. This is encoded by a mixture likelihood whose mixing weights are the support variables themselves. Under the mean-field factorization the variational update for each support posterior is proportional to the difference in expected reconstruction errors under the two components; this difference is preserved exactly because the expectation is taken separately over the low-rank and sparse factors. We will add a short clarifying paragraph after Eq. (5) and a remark in Section 4 showing that the variational scheme does not collapse to the additive RPCA case. revision: yes

  3. Referee: [Experimental results] Experimental section (synthetic results): the claim of 'near-optimal estimates' is not accompanied by an explicit error metric, baseline comparison table, or analysis of how the hard-classifier property was verified (e.g., fraction of support variables with posterior mass >0.99), making it impossible to confirm that the advantage is not due to post-hoc decisions.

    Authors: We agree that additional quantitative detail is required. In the revised experimental section we will insert a table reporting relative Frobenius error on the recovered low-rank tensor, support recovery F1 score, and the empirical fraction of support variables whose variational posterior exceeds 0.99 (observed to be >0.97 across all synthetic trials). We will also include direct comparisons against RPCA with both fixed and oracle thresholding to demonstrate that the reported performance does not rely on post-hoc decisions. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The RPCC framework is motivated by an explicit modeling distinction (occlusion rather than additive corruption) and solved using standard variational Bayesian inference on a Bayesian sparse tensor factorization. The claim that inference converges to a hard support classifier is presented as a shown property of the chosen variational family rather than a redefinition of fitted parameters or a self-citation chain. No equations reduce the central result to its inputs by construction, and experimental claims are separated from the derivation. The approach therefore qualifies as non-circular under the stated criteria.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that sparse elements occlude rather than add to the low-rank background and on standard variational Bayesian approximations whose specific hyperparameters are not detailed in the abstract.

free parameters (1)
  • variational inference hyperparameters
    Typical free parameters in Bayesian sparse factorization models; exact values and fitting procedure not specified in abstract.
axioms (1)
  • domain assumption Sparse component replaces or occludes low-rank background elements
    Explicitly stated as the mismatch addressed by the new RPCC framework.

pith-pipeline@v0.9.0 · 5455 in / 1184 out tokens · 35635 ms · 2026-05-15T00:26:11.970484+00:00 · methodology

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Reference graph

Works this paper leans on

53 extracted references · 53 canonical work pages · 1 internal anchor

  1. [1]

    Robust principal component analysis: Exact recovery of corrupted low-rank matri- ces by convex optimization,

    J. Wright, A. Ganesh, S. Rao, Y . Peng, and Y . Ma, “Robust principal component analysis: Exact recovery of corrupted low-rank matri- ces by convex optimization,” in Advances in Neural Information Pro- cessing Systems, Y . Bengio, D. Schuurmans, J. Lafferty , C. Williams, and A. Culotta, Eds., vol. 22, Vancouver, Canada, 2009

    work page 2009

  2. [2]

    Linearized alternating direction method with adaptive penalty for low-rank representation,

    Z. Lin, R. Liu, and Z. Su, “Linearized alternating direction method with adaptive penalty for low-rank representation,” in Advances in Neural Information Processing Systems 24 , J. Shawe-Taylor, R. S. Zemel, P . L. Bartlett, F. Pereira, and K. Q. Weinberger, Eds., Granada, Spain, December 2011, pp. 612–620

    work page 2011

  3. [3]

    Robust principal compo- nent analysis?

    E. Candès, X. Li, Y . Ma, and J. Wright, “Robust principal compo- nent analysis?” Journal of the Association for Computing Machinery , vol. 58, no. 3, pp. 1–37, May 2011

    work page 2011

  4. [4]

    On the applications of robust PCA in image and video processing,

    T. Bouwmans, S. Javed, H. Zhang, Z. Lin, and R. Otazo, “On the applications of robust PCA in image and video processing,” Proceedings of the IEEE , vol. 106, no. 8, pp. 1427–1457, August 2018

    work page 2018

  5. [5]

    Moving object detection by de- tecting contiguous outliers in the low-rank representation,

    X. Zhou, C. Yang, and W. Yu, “Moving object detection by de- tecting contiguous outliers in the low-rank representation,” IEEE T ransactions on Pattern Analysis and Machine Intelligence , vol. 35, no. 3, pp. 597–610, 2013

    work page 2013

  6. [6]

    Variational message passing,

    J. Winn and C. M. Bishop, “Variational message passing,” Journal of Machine Learning Research , vol. 6, no. 23, pp. 661–694, 2005

    work page 2005

  7. [7]

    A generalized tensor formulation for hyperspectral image super-resolution un- der general spatial blurring,

    Y . Wang, W. Li, Y . Gui, Q. Du, and J. E. Fowler, “A generalized tensor formulation for hyperspectral image super-resolution un- der general spatial blurring,” IEEE T ransactions on Pattern Analysis and Machine Intelligence , vol. 47, no. 6, pp. 4684–4698, June 2025

    work page 2025

  8. [8]

    Robust estimates, resid- uals, and outlier detection with multiresponse data,

    R. Gnanadesikan and J. R. Kettenring, “Robust estimates, resid- uals, and outlier detection with multiresponse data,” Biometrics, vol. 28, no. 1, pp. 81–124, March 1972

    work page 1972

  9. [9]

    P . J. Huber,Robust Statistics. New York: John Wiley & Sons, Inc., 1981

    work page 1981

  10. [10]

    Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography ,

    M. A. Fischler and R. C. Bolles, “Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography ,” Communications of the ACM , vol. 24, no. 6, pp. 381–395, June 1981

    work page 1981

  11. [11]

    Bayesian robust principal compo- nent analysis,

    X. Ding, L. He, and L. Carin, “Bayesian robust principal compo- nent analysis,” IEEE T ransactions on Image Processing, vol. 20, no. 12, pp. 3419–3430, December 2011

    work page 2011

  12. [12]

    A pseudo- Bayesian algorithm for robust PCA,

    T.-H. Oh, Y . Matsushita, I. Kweon, and D. Wipf, “A pseudo- Bayesian algorithm for robust PCA,” in Advances in Neural In- formation Processing Systems , D. Lee, M. Sugiyama, U. Luxburg, I. Guyon, and R. Garnett, Eds., Barcelona, Spain, December 2016

    work page 2016

  13. [13]

    Fast algorithms for ro- bust PCA via gradient descent,

    X. Yi, D. Park, Y . Chen, and C. Caramanis, “Fast algorithms for ro- bust PCA via gradient descent,” in Advances in Neural Information Processing Systems , D. Lee, M. Sugiyama, U. Luxburg, I. Guyon, and R. Garnett, Eds., Barcelona, Spain, December 2016, pp. 4159– 4167

    work page 2016

  14. [14]

    Bilinear fac- tor matrix norm minimization for robust PCA: Algorithms and applications,

    F. Shang, J. Cheng, Y . Liu, Z.-Q. Luo, and Z. Lin, “Bilinear fac- tor matrix norm minimization for robust PCA: Algorithms and applications,” IEEE T ransactions on Pattern Analysis and Machine Intelligence, vol. 40, no. 9, pp. 2066–2080, December 2018

    work page 2066

  15. [15]

    Non-convex robust PCA,

    P . Netrapalli, U. N. Niranjan, S. Sanghavi, A. Anandkumar, and P . Jain, “Non-convex robust PCA,” in Advances in Neural Infor- mation Processing Systems , Z. Ghahramani, M. Welling, C. Cortes, N. Lawrence, and K. Weinberger, Eds., Montreal, Canada, Decem- ber 2014

    work page 2014

  16. [16]

    Learned robust PCA: A scalable deep unfolding approach for high-dimensional outlier detection,

    H. Cai, J. Liu, and W. Yin, “Learned robust PCA: A scalable deep unfolding approach for high-dimensional outlier detection,” in Advances in Neural Information Processing Systems , M. Ranzato, A. Beygelzimer, Y . Dauphin, P . S. Liang, and J. W. Vaughan, Eds., December 2021

    work page 2021

  17. [17]

    RPCANet++: Deep interpretable robust PCA for sparse object segmentation,

    F. Wu, Y . Dai, T. Zhang, Y . Ding, J. Yang, M.-M. Cheng, and Z. Peng, “RPCANet++: Deep interpretable robust PCA for sparse object segmentation,” arXiv:2508.04190

    work page arXiv

  18. [18]

    Tensor robust principal component analysis with a new tensor nuclear norm,

    C. Lu, J. Feng, Y . Chen, W. Liu, Z. Lin, and S. Yan, “Tensor robust principal component analysis with a new tensor nuclear norm,” IEEE T ransactions on Pattern Analysis and Machine Intelli- gence, vol. 42, no. 4, pp. 925–938, April 2020

    work page 2020

  19. [19]

    Enhanced tensor RPCA and its application,

    Q. Gao, P . Zhang, W. Xia, D. Xie, X. Gao, and D. Tao, “Enhanced tensor RPCA and its application,” IEEE T ransactions on Pattern Analysis and Machine Intelligence , vol. 43, no. 6, pp. 2133–2140, June 2021

    work page 2021

  20. [20]

    Kronecker-basis- representation based tensor sparsity and its applications to tensor recovery ,

    Q. Xie, Q. Zhao, D. Meng, and Z. Xu, “Kronecker-basis- representation based tensor sparsity and its applications to tensor recovery ,”IEEE T ransactions on Pattern Analysis and Machine Intel- ligence, vol. 40, no. 8, pp. 1888–1902, August 2017

    work page 1902

  21. [21]

    Analysis of individual differ- ences in multidimensional scaling via an n-way generalization of “Eckart-Young

    J. D. Carroll and J.-J. Chang, “Analysis of individual differ- ences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition,” Psychometrika, vol. 35, pp. 283– 319, September 1970

    work page 1970

  22. [22]

    Foundations of the PARAFAC procedure: Mod- els and conditions for an “explanatory

    R. A. Harshman, “Foundations of the PARAFAC procedure: Mod- els and conditions for an “explanatory” multimodal factor analy- sis,” UCLA Working Papers in Phonetics , vol. 16, 1970

    work page 1970

  23. [23]

    Tensor low-rank representation for data recovery and clustering,

    P . Zhou, C. Lu, J. Feng, Z. Lin, and S. Yan, “Tensor low-rank representation for data recovery and clustering,” IEEE T ransactions on Pattern Analysis and Machine Intelligence , vol. 43, no. 5, pp. 1718– 1732, May 2021

    work page 2021

  24. [24]

    Guaranteed tensor recovery fused low-rankness and smoothness,

    H. Wang, J. Peng, W. Qin, J. Wang, and D. Meng, “Guaranteed tensor recovery fused low-rankness and smoothness,” IEEE T rans- actions on Pattern Analysis and Machine Intelligence , vol. 45, no. 9, pp. 10 990–11 007, September 2023

    work page 2023

  25. [25]

    Multiplex transformed tensor decomposition for multidimensional image recovery ,

    L. Feng, C. Zhu, Z. Long, J. Liu, and Y . Liu, “Multiplex transformed tensor decomposition for multidimensional image recovery ,”IEEE T ransactions on Image Processing, vol. 32, pp. 3397–3412, 2023

    work page 2023

  26. [26]

    Online nonconvex robust tensor principal component analysis,

    L. Feng, Y . Liu, Z. Liu, and C. Zhu, “Online nonconvex robust tensor principal component analysis,” IEEE T ransactions on Neural Networks and Learning Systems , vol. 36, no. 8, pp. 14 384–14 398, August 2025

    work page 2025

  27. [27]

    Deep unfolded tensor robust PCA with self-supervised learning,

    H. Dong, M. Shah, S. Donegan, and Y . Chi, “Deep unfolded tensor robust PCA with self-supervised learning,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Rhodes Island, Greece, June 2023

    work page 2023

  28. [28]

    HLRTF: Hierarchi- cal low-rank tensor factorization for inverse problems in multi- dimensional imaging,

    Y . Luo, X. Zhao, D. Meng, and T. Jiang, “HLRTF: Hierarchi- cal low-rank tensor factorization for inverse problems in multi- dimensional imaging,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition , New Orleans, LA, June 2022, pp. 19 281–19 290

    work page 2022

  29. [29]

    Low-rank tensor function representation for multi-dimensional data recov- ery ,

    Y . Luo, X. Zhao, Z. Li, M. K. Ng, and D. Meng, “Low-rank tensor function representation for multi-dimensional data recov- ery ,”IEEE T ransactions on Pattern Analysis and Machine Intelligence , vol. 46, no. 5, pp. 3351–3369, May 2024

    work page 2024

  30. [30]

    Probabilistic matrix factoriza- tion,

    A. Mnih and R. Salakhutdinov , “Probabilistic matrix factoriza- tion,” in Advances in Neural Information Processing Systems , J. Platt, D. Koller, Y . Singer, and S. Roweis, Eds., Vancouver, Canada, December 2007

    work page 2007

  31. [31]

    Sparse Bayesian methods for low-rank matrix estimation,

    S. D. Babacan, M. Luessi, R. Molina, and A. K. Katsaggelos, “Sparse Bayesian methods for low-rank matrix estimation,” IEEE T ransactions on Signal Processing , vol. 60, no. 8, pp. 3964–3977, August 2012

    work page 2012

  32. [32]

    Bayesian CP factorization of incomplete tensors with automatic rank determination,

    Q. Zhao, L. Zhang, and A. Cichocki, “Bayesian CP factorization of incomplete tensors with automatic rank determination,” IEEE T ransactions on Pattern Analysis and Machine Intelligence , vol. 37, no. 9, pp. 1751–1763, September 2015. 15

    work page 2015

  33. [33]

    Bayesian robust tensor factorization for incomplete multiway data,

    Q. Zhao, G. Zhou, L. Zhang, A. Cichocki, and S.-I. Amari, “Bayesian robust tensor factorization for incomplete multiway data,” IEEE T ransactions on Neural Networks and Learning Systems , no. 4, pp. 736–748, April 2016

    work page 2016

  34. [34]

    Bayesian non- negative tensor completion with automatic rank determination,

    Z. Yang, L. T. Yang, H. Wang, H. Zhao, and D. Liu, “Bayesian non- negative tensor completion with automatic rank determination,” IEEE T ransactions on Image Processing, vol. 34, pp. 2036–2051, 2025

    work page 2036

  35. [35]

    Bayesian low-tubal-rank robust ten- sor factorization with multi-rank determination,

    Y . Zhou and Y .-M. Cheung, “Bayesian low-tubal-rank robust ten- sor factorization with multi-rank determination,” IEEE T ransac- tions on Pattern Analysis and Machine Intelligence , vol. 43, no. 1, pp. 62–76, January 2021

    work page 2021

  36. [36]

    Bayesian tensor tucker comple- tion with a flexible core,

    X. Tong, L. Cheng, and Y .-C. Wu, “Bayesian tensor tucker comple- tion with a flexible core,” IEEE T ransactions on Signal Processing , vol. 71, pp. 4077–4091, 2023

    work page 2023

  37. [37]

    Block- term tensor decomposition model selection and computation: The Bayesian way ,

    P . V . Giampouras, A. A. Rontogiannis, and E. Kofidis, “Block- term tensor decomposition model selection and computation: The Bayesian way ,”IEEE T ransactions on Signal Processing , vol. 70, pp. 1704–1717, 2022

    work page 2022

  38. [38]

    Tensor train factor- ization under noisy and incomplete data with automatic rank estimation,

    L. Xu, L. Cheng, N. Wong, and Y .-C. Wu, “Tensor train factor- ization under noisy and incomplete data with automatic rank estimation,” Pattern Recognition, vol. 141, 2023

    work page 2023

  39. [39]

    Bayesian low rank tensor ring for image recovery ,

    Z. Long, C. Zhu, J. Liu, and Y . Liu, “Bayesian low rank tensor ring for image recovery ,”IEEE T ransactions on Image Processing, vol. 30, pp. 3568–3580, 2021

    work page 2021

  40. [40]

    ReduNet: A white-box deep network from the principle of maximizing rate reduction,

    K. H. R. Chan, Y . Yu, C. You, H. Qi, J. Wright, and Y . Ma, “ReduNet: A white-box deep network from the principle of maximizing rate reduction,” Journal of Machine Learning Research , vol. 23, pp. 1–103, 2022

    work page 2022

  41. [41]

    Structured sparsity optimization with non-convex surrogates of ℓ2,0-norm: A unified algorithmic framework,

    X. Zhang, J. Zheng, D. Wang, G. Tang, Z. Zhou, and Z. Lin, “Structured sparsity optimization with non-convex surrogates of ℓ2,0-norm: A unified algorithmic framework,” IEEE T ransactions on Pattern Analysis and Machine Intelligence , vol. 45, no. 5, pp. 6386– 6402, May 2023

    work page 2023

  42. [42]

    C. M. Bishop, Pattern Recognition and Machine Learning . Springer, 2006

    work page 2006

  43. [43]

    Robust PCA via principal component pursuit: A review for a comparative evaluation in video surveillance,

    T. Bouwmans and E. H. Zahzah, “Robust PCA via principal component pursuit: A review for a comparative evaluation in video surveillance,” Computer Vision and Image Understanding , vol. 122, pp. 22–34, May 2014

    work page 2014

  44. [44]

    Total variation regularized tensor RPCA for background subtraction from compressive measurements,

    W. Cao, Y . Wang, J. Sun, D. Meng, C. Yang, A. Cichocki, and Z. Xu, “Total variation regularized tensor RPCA for background subtraction from compressive measurements,” IEEE T ransactions on Image Processing , vol. 25, no. 9, pp. 4075–4090, September 2016

    work page 2016

  45. [45]

    Learning spatial-temporal regularized tensor sparse RPCA for background subtraction,

    B. Alawode and S. Javed, “Learning spatial-temporal regularized tensor sparse RPCA for background subtraction,” IEEE T ransac- tions on Neural Networks and Learning Systems , vol. 36, no. 6, pp. 11 034–11 048, June 2025

    work page 2025

  46. [46]

    Hy- perspectral anomaly detection with attribute and edge-preserving filters,

    X. Kang, X. Zhang, S. Li, K. Li, J. Li, and J. A. Benediktsson, “Hy- perspectral anomaly detection with attribute and edge-preserving filters,” IEEE T ransactions on Geoscience and Remote Sensing , vol. 55, no. 10, pp. 5600–5611, October 2017

    work page 2017

  47. [47]

    Low-rank and sparse decom- position with mixture of Gaussian for hyperspectral anomaly detection,

    L. Li, W. Li, Q. Du, and R. Tao, “Low-rank and sparse decom- position with mixture of Gaussian for hyperspectral anomaly detection,” IEEE T ransactions on Cybernetics, vol. 51, no. 9, pp. 4363– 4372, September 2021

    work page 2021

  48. [48]

    Prior-based tensor approximation for anomaly detection in hyperspectral imagery ,

    L. Li, W. Li, Y . Qu, C. Zhao, R. Tao, and Q. Du, “Prior-based tensor approximation for anomaly detection in hyperspectral imagery ,” IEEE T ransactions on Neural Networks and Learning Systems , vol. 33, no. 3, pp. 1037–1050, March 2022

    work page 2022

  49. [49]

    Learn- ing tensor low-rank representation for hyperspectral anomaly detection,

    M. Wang, Q. Wang, D. Hong, S. K. Roy , and J. Chanussot, “Learn- ing tensor low-rank representation for hyperspectral anomaly detection,” IEEE T ransactions on Cybernetics, vol. 53, no. 1, pp. 679– 691, January 2023

    work page 2023

  50. [50]

    CDnet 2014: An expanded change detection benchmark dataset,

    Y . Wang, P .-M. Jodoin, F. Porikli, J. Konrad, Y . Benezeth, and P . Ishwar, “CDnet 2014: An expanded change detection benchmark dataset,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition , Columbus, OH, June 2014, pp. 393–400

    work page 2014

  51. [51]

    A generalized non- convex surrogated framework for anomaly detection on blurred hyperspectral images,

    Y . Wang, W. Li, Y . Gui, H. Xie, and L. Zhang, “A generalized non- convex surrogated framework for anomaly detection on blurred hyperspectral images,” IEEE T ransactions on Image Processing , vol. 34, pp. 3108–3122, 2025

    work page 2025

  52. [52]

    Implications of factor analysis of three-way matrices for measurement of change,

    L. R. Tucker, “Implications of factor analysis of three-way matrices for measurement of change,” Problems in Measuring Change, vol. 15, no. 122-137, p. 3, 1963

    work page 1963

  53. [53]

    Tensor Ring Decomposition

    Q. Zhao, G. Zhou, S. Xie, L. Zhang, and A. Cichocki, “Tensor ring decomposition,” arXiv preprint arXiv:1606.05535 , 2016

    work page internal anchor Pith review Pith/arXiv arXiv 2016