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Accelerating Large-Scale Regularized High-Order Tensor Recovery

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Randomized Tucker approximations with block Krylov and Lanczos methods give provably near-optimal low-rank compression, and embedding them in nonconvex gradient-tensor models accelerates large-scale recovery by 3--9 times.

desk verdict The randomized Tucker work is real, but the fixed-accuracy stopping rule has a gap worth fixing before publication. read the letter →

arxiv 2506.09594 v2 pith:5GAZ6MA4 submitted 2025-06-11 cs.LG

Wenjin Qin , Hailin Wang , Jingyao Hou , Jianjun Wang This is my paper · ORCID
classification cs.LG MSC 15A6965F5590C26
keywords tensorrecoveryrandomizedlow-rankapproximationTuckerdecompositionblockKryloviterationLanczosbidiagonalizationnonconvexregularizationgradientone-bitcompletion
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper sets out to break the accuracy-versus-speed trade-off in high-order tensor recovery by giving randomized low-rank Tucker approximation a certified place inside expensive thresholding loops. It claims two new algorithms: R-STHOSVD-BKI, a fixed-rank randomized Tucker approximation built on block Krylov iteration, and AD-RSTHOSVD-BLBP, a fixed-precision version built on block Lanczos bidiagonalization, each with a high-probability error bound. Both slot into a fast GNHTSVT operator so that the deterministic nonconvex thresholding runs on a small Tucker core instead of the full tensor. The modeling claim is that larger tensors exhibit stronger joint global low-rankness and local smoothness, which a new gradient-tensor regularizer (GNHTCTV) encodes with generalized nonconvex penalties. On MRI, hyperspectral, multispectral, video, remote-sensing, and light-field data, the randomized models are reported to cut runtime by 3--9 times while keeping roughly the same recovery accuracy, and the nonconvex L+S models beat convex and pure-low-rank baselines by 1--2 dB PSNR.

What carries the argument

The load-bearing machinery is the randomized Tucker compression step: each matrix unfolding $A=C_{(\rho_v)}$ is reduced either by forming the block Krylov subspace $\mathcal{K}=[AG,(AA^T)AG,\dots,(AA^T)^q AG]$ and taking the top singular vectors of $Z^TAA^TZ$ (Algorithm 1), or by an incremental block Lanczos bidiagonalization with deflated QR that maintains an estimate $E=\|A\|_F^2-\|B\|_F^2$ (Algorithm 3). The second ingredient is the fast GNHTSVT operator, which compresses $\mathcal{A}\approx[\mathcal{C};F_1,\dots,F_d]$, applies the deterministic generalized nonconvex thresholding $\mathcal{D}_{\Phi,\tau}(\mathcal{C},L)$ on the small core, and back-projects. The third ingredient is the GNHTCTV regularizer, which sums a generalized nonconvex function $\Phi$ over the singular values of all face slices of each gradient tensor in a transform domain; it generalizes T-CTV and includes nuclear-norm-style convex regularizers as special cases. ADMM ties these together: the $L$-subproblem is solved in closed form via FFT diagonalization, and the $G$-subproblem is solved by the fast GNHTSVT, so no step of the recovery loop needs the full tensor.

What would settle it

Run Algorithm 3 on a tensor whose first unfolding has a tight cluster of nearly equal singular values (for example, a 2000 by 2000 matrix-style tensor with singular values decaying from 1 by 1e-4), with block size larger than the cluster and tolerance 1e-3, and compare the computed $\|\mathcal{X}-\hat{\mathcal{X}}\|_F$ with the estimate $\sqrt{\sum_j E_j}$; finding the ratio above $1+10\varepsilon$ while the local orthogonality loss $\varepsilon_j$ is large would falsify the premise of Theorem III.2.

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Extended reading notes

Core claim

The central claim is that randomized low-rank Tucker compression can be both fast and provably accurate enough to drive large-scale tensor recovery. For a target rank $r$, Algorithm 1 returns an approximation $\hat{X}=[\mathcal{C};F_1,\dots,F_d]$ whose error obeys $\|\mathcal{X}-\hat{X}\|_F/\sqrt{d}\le(1+\varepsilon)\|\mathcal{X}-\hat{X}_{\mathrm{opt}}\|_F$ with probability at least $1-\delta$, provided the number of Krylov iterations in each mode is chosen according to the spectral gap $g_{\min,b_i}$ and the failure tolerance. For a user tolerance $\epsilon$, Algorithm 3 stops mode-by-mode when its estimated residual $E_j$ drops below the threshold, and the total error is bounded by $\sum_j E_j$ plus correction terms involving the local loss of orthogonality $\varepsilon_j$ and the number of deflated columns $\varpi_j$. The paper further claims that these randomized factorizations can be lifted to the recovery level: the GNHTSVT operator first approximates the tensor by a Tucker core and then applies the deterministic nonconvex singular-value thresholding to that core, and the resulting GNHTC, GNRHTC, and one-bit GNOBHTC/GNOBRHTC models achieve higher PSNR/SSIM on real large-scale visual data. The modeling discovery is that applying a generalized nonconvex function to the singular values of gradient tensors $\nabla_k(\mathcal{A})=\mathcal{A}\times_k D_{n_k}$ simultaneously captures global low-rankness and local smoothness in one regularizer.

Load-bearing premise

The adaptive algorithm's stopping rule is trustworthy only while the left factor blocks U stay close to orthogonal even though the algorithm reorthogonalizes only the right factor V; if U drifts, the reported residuals can understate the true approximation error.

Editorial extensions

If this is right

  • On real datasets, the randomized versions are 3--9 times faster than their deterministic counterparts on order-3 through order-5 tensors (Tables II, III, V), with only a small PSNR drop.
  • The joint low-rankness-plus-smoothness regularizer consistently beats pure-low-rank models, with gains around 1--2 dB PSNR over convex T-CTV and larger gains in low-sampling-rate cases.
  • The same randomized coupling transfers to quantized one-bit recovery, where the proposed methods show the lowest CPU time among the evaluated one-bit completion approaches.
  • The error bounds are processing-order independent (Remark III.1) and reduce to existing matrix-format bounds, so algorithmic choices like mode order can be made for speed without changing the worst-case guarantee.
  • Because the fast GNHTSVT only needs the Tucker core, deterministic singular-value thresholding becomes affordable on tensors with millions to hundreds of millions of entries.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A consequence left implicit: the randomized Tucker core is a generic preconditioner, so the same R-STHOSVD-BKI and AD-RSTHOSVD-BLBP steps could accelerate other T-SVD-based regularizers, tensor-ring models, or FCTN models without retraining the optimization loop.
  • The scale-dependent L+S phenomenon suggests a testable trend: the PSNR gap between L+S models and pure-L models should widen monotonically with tensor size at a fixed sampling rate, a pattern Table V's large-scale results loosely support.
  • Algorithm 3's residual estimate could serve as a principled early-stopping signal for other nonconvex solvers; monitoring U-block orthogonality rather than assuming it would turn Theorem III.2 into a fully a posteriori guarantee.
  • The gradient-domain nonconvex penalty is a natural fit for tensor compressive sensing and for quantized measurements beyond the one-bit setting tested here, since the same GNHTCTV regularizer already handles smoothness in transform domains.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes two randomized low-rank Tucker approximation algorithms (R-STHOSVD-BKI for fixed rank and AD-RSTHOSVD-BLBP for fixed accuracy), states probabilistic error bounds for both (Theorems III.1 and III.2), and then embeds them into a generalized nonconvex tensor recovery framework based on a new GNHTCTV regularizer that jointly encodes low-rankness and local smoothness. The framework is instantiated for unquantized completion (GNHTC/GNRHTC) and quantized one-bit completion (GNOBHTC/GNOBRHTC), solved by ADMM with the randomized approximations used to accelerate the key GNHTSVT subproblems. Experimental comparisons on MSIs, HSIs, MRIs, CVs, MRSIs, and LFIs report improved PSNR/SSIM and large speedups over existing methods.

Significance. If the stated guarantees hold, the randomized Tucker approximation component is a useful contribution for large-scale high-order tensor data, particularly the adaptive fixed-precision variant, and the unified nonconvex regularizer provides a broad framework that contains several existing regularizers as special cases. The paper also assembles a large and diverse experimental suite, which strengthens the practical evidence for the proposed recovery models. The main caveats are that all proofs are deferred to a supplementary document and that the fixed-precision guarantee rests on an orthogonality condition that the algorithm does not explicitly enforce.

major comments (3)
  1. [III-B, Definition III.2, Algorithm 3, Theorem III.2]
  2. [V-A, Lemma V.1, Theorems V.1-V.2]
  3. [VI, Tables II-IV and V, Figure 8]
minor comments (5)
  1. [VI-A]
  2. [Abstract and Section I]
  3. [Figure 1]
  4. [V-B, Algorithm 6]
  5. [Table V]

Circularity Check

0 steps flagged · score 1.0 of 10

No circular reduction found: the randomized LRTA error bounds are new inequalities with explicit assumptions, and the nonconvex model is a stated generalization of prior published work rather than a relabeled prediction.

full rationale

The paper's derivation chain is not circular. Theorem III.1 transfers matrix randomized block-Krylov singular value guarantees from external works [86]-[88] to STHOSVD mode-by-mode, producing a bound relative to the optimal Tucker approximation; the accuracy parameter q_i is a sufficient iteration count, not a fitted quantity. Theorem III.2 bounds the true squared error by the Lanczos residual estimate E_j plus explicit correction terms in the local orthogonality loss eps_j, deflation tolerance delta, and deflation count omega_j; the claim that E_j is a reliable estimate is an inequality with stated assumptions, not an identity obtained by defining E_j to equal the error. The GNHTCTV regularizer is explicitly presented as a nonconvex generalization of the authors' previous T-CTV [14], with the paper stating that when Phi(.) is the ell1-norm the regularizer degenerates to the T-CTV norm proposed in [14]; acknowledging that a framework subsumes prior published models is transparent, not circular. The ADMM convergence results (Theorems V.1-V.2) use standard bounded-multiplier arguments and do not import the target recovery quality as an assumption. Heavy citation of the authors' own work [14], [16], [29] supplies definitions, gradient operators, and baselines, but the new randomized approximation analyses and the nonconvex proximal operators do not reduce to those citations. The main caveat is a proof gap, not circularity: Theorem III.2 assumes local orthogonality of the U-blocks via Definition III.2, while Algorithm 3 reorthogonalizes only V (lines 15-21) and never reorthogonalizes U (lines 11-13); Remark III.1 asserts that one-sided reorthogonalization suffices without proof in the main text. This affects the reliability of the fixed-accuracy stopping rule, but it is not a self-referential reduction of the kind that would raise the circularity score.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The paper's contributions rely on several tuned parameters (lambda, block sizes, ranks, ADMM schedule) and on unproven or supplementary-only assumptions (bounded multipliers, local orthogonality). No new physical entities are introduced.

free parameters (7)
  • Regularization weight lambda = xi / (max(n1,n2) * prod_{i=3}^d n_i)^{1/2} with xi in {1,2,...,18} tuned per dataset
    Balances the low-rank and smoothness prior against the noise term; xi is chosen per dataset from a small grid.
  • Nonconvex penalty Phi and its shape parameter = Options: MCP, SCAD, Log, ell_q, capped ell_q; shape parameter not reported
    The choices of Phi and psi, and their shape parameters, strongly affect recovery; the paper tests many combinations but does not fix a single value.
  • Block size b in fixed-rank algorithm = b = ceil(r/4) or ceil(r/3), or specific values like 60, 80, 100
    Controls the size of the Krylov subspace; smaller blocks are faster but may lose accuracy.
  • Krylov iterations q = q = [4,4,*] or [4,4,*,*]
    Number of Krylov steps; affects approximation quality and computational cost.
  • Error tolerance epsilon in fixed-accuracy algorithm = 0.01
    Stopping threshold for the adaptive algorithm.
  • Target rank r in fixed-rank algorithm = Chosen per dataset; values not fully listed
    The fixed-rank algorithm requires an a priori rank; if the rank is too low or high, accuracy or speed changes.
  • ADMM penalty mu0 and schedule = mu0=1e-3, mu_max=1e10, growth theta=1.1 or 1.15
    These parameters control convergence speed and are set heuristically.
assumptions (6)
  • domain assumption The measured data tensors exhibit stronger low-rankness and local smoothness as their scale grows (Figure 1).
    This motivates the GNHTCTV regularizer; if a target dataset does not satisfy this, the advantage over low-rank-only methods may vanish.
  • domain assumption The nonconvex penalty Phi satisfies Assumption IV.1 (proper, lower semi-continuous, concave, increasing, Phi(0)=0).
    Required for the GNHTSVT operator to be the proximal solution (Theorem IV.1).
  • ad hoc to paper The local loss of orthogonality epsilon_j in Algorithm 3 is small and the number of deflations omega_j is limited.
    Theorem III.2's error bound degrades linearly with epsilon_j and sqrt(omega_j); the algorithm does not enforce orthogonality of U blocks.
  • ad hoc to paper The ADMM multiplier sequences are bounded (Lemma V.1).
    Needed for the KKT convergence claim (Theorem V.2); proof only in the supplementary.
  • standard math The invertible linear transform L with matrices satisfying (2) is chosen so that the difference operators are diagonalized by FFT.
    Used to solve the L-subproblem in closed form via equation (21).
  • standard math The T-product and T-SVD properties from [14] and [29] hold.
    Foundational for the high-order tensor operations used throughout.

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Cite this review

Pith. "Pith review of Accelerating Large-Scale Regularized High-Order Tensor Recovery." pith.science (2026). https://pith.science/paper/5GAZ6MA4

@misc{pith2026250609594,
  author       = {Pith},
  title        = {Pith review of: Accelerating Large-Scale Regularized High-Order Tensor Recovery},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5GAZ6MA4}},
  note         = {Machine review of arXiv:2506.09594}
}
read the original abstract

Currently, existing tensor recovery methods fail to recognize the impact of tensor scale variations on their structural characteristics. Furthermore, existing studies face prohibitive computational costs when dealing with large-scale high-order tensor data. To alleviate these issue, assisted by the Krylov subspace iteration, block Lanczos bidiagonalization process, and random projection strategies, this article first devises two fast and accurate randomized algorithms for low-rank tensor approximation (LRTA) problem. Theoretical bounds on the accuracy of the approximation error estimate are established. Next, we develop a novel generalized nonconvex modeling framework tailored to large-scale tensor recovery, in which a new regularization paradigm is exploited to achieve insightful prior representation for large-scale tensors. On the basis of the above, we further investigate new unified nonconvex models and efficient optimization algorithms, respectively, for several typical high-order tensor recovery tasks in unquantized and quantized situations. To render the proposed algorithms practical and efficient for large-scale tensor data, the proposed randomized LRTA schemes are integrated into their central and time-intensive computations. Finally, we conduct extensive experiments on various large-scale tensors, whose results demonstrate the practicability, effectiveness and superiority of the proposed method in comparison with some state-of-the-art approaches.

Figures

Figures reproduced from arXiv: 2506.09594 by the authors.

Figure 1
Figure 1. An illustration of the distinctions in L and S prior structures between small-scale and large-scale tensors. Top: The AccEgy (AccEgy = Pk i=1 σ 2 i / P j=1 σ 2 j with σi denotes the i-th tensor singular value) versus the percentage of singular values; Right: Frequency histograms of all corresponding elements of gradient tensor. there is a trade-off between accuracy and speed. One of the challenges lies in how to exp… view at source ↗
Figure 3
Figure 3. Visual comparison of various LRTC methods on MSIs (top, SR= [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Visual comparison of various RLRTC methods for MRI datasets inpainting. From top to bottom, the parameter pair [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figures from the paper (9 more)
Figure 5
Figure 5. Figure 5: Visual comparison of various RLRTC methods for HSI datasets recovery. From top to bottom, the parameter pair [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: Visual comparison of various RLRTC methods for MRSIs inpainting under [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: Visual comparison of various RLRTC methods for CVs/LFIs inpainting under [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: The recovery performance of the proposed and compared OBTC under various sampling rates and Gaussian noise [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: Visual comparison of various OBTC methods for CVs and MRSIs datasets recovery. The observed CVs and MRSIs are [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: The influence of different nonconvex combinations [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]
Figure 11
Figure 11. Figure 11: The influence of various fixed-rank LRTA methods upon restoration performance of the proposed randomized GNRHTC [PITH_FULL_IMAGE:figures/full_fig_p015_11.png]
Figure 12
Figure 12. Figure 12: The influence of different prior structures (i.e., L+S [PITH_FULL_IMAGE:figures/full_fig_p016_12.png]
Figure 13
Figure 13. Figure 13: The influence of various fixed-precision LRTA methods upon restoration performance of the proposed randomized [PITH_FULL_IMAGE:figures/full_fig_p017_13.png]

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Reference graph

Works this paper leans on

115 extracted references · 76 canonical work pages

  1. [1]

    Tensor networks for dimensionality reduction and large-scale optimization: Part 1 low-rank tensor decompositions,

    A. Cichocki, N. Lee, I. Oseledets, A.-H. Phan, Q. Zhao, D. P. Mandic et al. , “Tensor networks for dimensionality reduction and large-scale optimization: Part 1 low-rank tensor decompositions,” Found. Trends Mach. Learn., vol. 9, no. 4-5, pp. 249–429, 2016

    2016

  2. [2]

    Turning big data into tiny data: Constant-size coresets for k-means, pca, and projective clustering,

    D. Feldman, M. Schmidt, and C. Sohler, “Turning big data into tiny data: Constant-size coresets for k-means, pca, and projective clustering,” SIAM J. Comput. , vol. 49, no. 3, pp. 601–657, 2020

    2020

  3. [3]

    Liu, Tensors for data processing: theory, methods, and applications

    Y . Liu, Tensors for data processing: theory, methods, and applications. Academic Press, 2021

    2021

  4. [4]

    Y . Liu, J. Liu, Z. Long, and C. Zhu, Tensor computation for data analysis. Springer, 2022

    2022

  5. [5]

    An optimal statistical and computational framework for generalized tensor estimation,

    R. Han, R. Willett, and A. R. Zhang, “An optimal statistical and computational framework for generalized tensor estimation,” Ann. Statist., vol. 50, no. 1, pp. 1–29, 2022

    2022

  6. [6]

    Generalized low-rank plus sparse tensor estimation by fast Riemannian optimization,

    J.-F. Cai, J. Li, and D. Xia, “Generalized low-rank plus sparse tensor estimation by fast Riemannian optimization,” J. Amer. Statist. Assoc. , vol. 118, no. 544, pp. 2588–2604, 2023

    2023

  7. [7]

    Provable tensor-train format tensor completion by riemannian optimization,

    ——, “Provable tensor-train format tensor completion by riemannian optimization,” J. Mach. Learn. Res. , vol. 23, no. 123, pp. 1–77, 2022

    2022

  8. [8]

    Scaling and scalability: Provable nonconvex low-rank tensor estimation from incomplete measurements,

    T. Tong, C. Ma, A. Prater-Bennette, E. Tripp, and Y . Chi, “Scaling and scalability: Provable nonconvex low-rank tensor estimation from incomplete measurements,” J. Mach. Learn. Res. , vol. 23, no. 163, pp. 1–77, 2022

    2022

Show all 115 references
  1. [9]

    Guaranteed nonconvex factorization approach for tensor train recovery,

    Z. Qin, M. B. Wakin, and Z. Zhu, “Guaranteed nonconvex factorization approach for tensor train recovery,” J. Mach. Learn. Res. , vol. 25, no. 383, pp. 1–48, 2024

    2024

  2. [10]

    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 Trans. Pattern Anal. Mach. Intell. , vol. 42, no. 4, pp. 925–938, 2019

    2019

  3. [11]

    Low-tubal-rank plus sparse tensor recovery with prior subspace information,

    F. Zhang, J. Wang, W. Wang, and C. Xu, “Low-tubal-rank plus sparse tensor recovery with prior subspace information,” IEEE Trans. Pattern Anal. Mach. Intell. , vol. 43, no. 10, pp. 3492–3507, 2020

    2020

  4. [12]

    Ro- bust low-tubal-rank tensor recovery from binary measurements,

    J. Hou, F. Zhang, H. Qiu, J. Wang, Y . Wang, and D. Meng, “Ro- bust low-tubal-rank tensor recovery from binary measurements,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 44, no. 8, pp. 4355–4373, 2021

    2021

  5. [13]

    Tensor robust principal component analysis from multilevel quantized observations,

    J. Wang, J. Hou, and Y . C. Eldar, “Tensor robust principal component analysis from multilevel quantized observations,” IEEE Trans. Inf. Theory, vol. 69, no. 1, pp. 383–406, 2022

    2022

  6. [14]

    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 Trans. Pattern Anal. Mach. Intell. , vol. 45, no. 9, pp. 10 990–11 007, 2023

    2023

  7. [15]

    Low-rank tensor function representation for multi-dimensional data recovery,

    Y . Luo, X. Zhao, Z. Li, M. K. Ng, and D. Meng, “Low-rank tensor function representation for multi-dimensional data recovery,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 46, no. 5, pp. 3351–3369, 2023

    2023

  8. [16]

    Noncon- vex robust high-order tensor completion using randomized low-rank approximation,

    W. Qin, H. Wang, F. Zhang, W. Ma, J. Wang, and T. Huang, “Noncon- vex robust high-order tensor completion using randomized low-rank approximation,” IEEE Trans. Image Process. , vol. 33, pp. 2835–2850, 2024

    2024

  9. [17]

    Learned tensor neural network texture prior for photon-counting CT reconstruction,

    Y . Shi, Y . Gao, Q. Xu, Y . Li, X. Mou, and Z. Liang, “Learned tensor neural network texture prior for photon-counting CT reconstruction,” IEEE Trans. Med. Imag. , vol. 43, no. 11, pp. 3830–3842, 2024

    2024

  10. [18]

    Bayesian temporal factorization for multidimen- sional time series prediction,

    X. Chen and L. Sun, “Bayesian temporal factorization for multidimen- sional time series prediction,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 44, no. 9, pp. 4659–4673, 2021

    2021

  11. [19]

    Integrated sensing and communication with massive MIMO: A unified tensor approach for channel and target parameter estimation,

    R. Zhang, L. Cheng, S. Wang, Y . Lou, Y . Gao, W. Wu, and D. W. K. Ng, “Integrated sensing and communication with massive MIMO: A unified tensor approach for channel and target parameter estimation,” IEEE Trans. Wireless Commun. , vol. 23, no. 8, pp. 8571–8587, 2024

    2024

  12. [20]

    Non-local meets global: An iterative paradigm for hyperspectral image restoration,

    W. He, Q. Yao, C. Li, N. Yokoya, Q. Zhao, H. Zhang, and L. Zhang, “Non-local meets global: An iterative paradigm for hyperspectral image restoration,” IEEE Trans. Pattern Anal. Mach. Intell. , vol. 44, no. 4, pp. 2089–2107, 2020

    2020

  13. [21]

    Tensor decompositions for signal processing applications: From two-way to multiway component analysis,

    A. Cichocki, D. Mandic, L. De Lathauwer, G. Zhou, Q. Zhao, C. Ca- iafa, and H. A. Phan, “Tensor decompositions for signal processing applications: From two-way to multiway component analysis,” IEEE Signal Process. Mag. , vol. 32, no. 2, pp. 145–163, 2015

    2015

  14. [22]

    Tensor methods in computer vision and deep learning,

    Y . Panagakis, J. Kossaifi, G. G. Chrysos, J. Oldfield, M. A. Nicolaou, A. Anandkumar, and S. Zafeiriou, “Tensor methods in computer vision and deep learning,” Proc. IEEE, vol. 109, no. 5, pp. 863–890, 2021

    2021

  15. [23]

    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 Trans. Pattern Anal. Mach. Intell. , vol. 37, no. 9, pp. 1751–1763, 2015

    2015

  16. [24]

    Bayesian low rank tensor ring for image recovery,

    Z. Long, C. Zhu, J. Liu et al., “Bayesian low rank tensor ring for image recovery,” IEEE Trans. Image Process., vol. 30, pp. 3568–3580, 2021

    2021

  17. [25]

    Low-tubal-rank tensor completion using alternating minimization,

    X.-Y . Liu, S. Aeron, V . Aggarwal, and X. Wang, “Low-tubal-rank tensor completion using alternating minimization,” IEEE Trans. Inf. Theory, vol. 66, no. 3, pp. 1714–1737, 2019

    2019

  18. [26]

    Fully-connected tensor network decomposition and its application to higher-order tensor completion,

    Y .-B. Zheng, T.-Z. Huang, X.-L. Zhao, Q. Zhao, and T.-X. Jiang, “Fully-connected tensor network decomposition and its application to higher-order tensor completion,” in Proc. AAAI Conf. Artif. Intel. , vol. 35, no. 12, 2021, pp. 11 071–11 078

    2021

  19. [27]

    Tensor wheel decomposition and its tensor completion application,

    Z.-C. Wu, T.-Z. Huang, L.-J. Deng, H.-X. Dou, and D. Meng, “Tensor wheel decomposition and its tensor completion application,” in Proc. Adv. Neural Inf. Process. Syst. (NIPS) , vol. 35, pp. 27 008–27 020, 2022. JOURNAL OF LATEX CLASS FILES, VOL. , NO. , XX XXXX 18

    2022

  20. [28]

    Tensor-ring nuclear norm minimization and application for visual: Data completion,

    J. Yu, C. Li, Q. Zhao, and G. Zhao, “Tensor-ring nuclear norm minimization and application for visual: Data completion,” in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP) . IEEE, 2019, pp. 3142–3146

    2019

  21. [29]

    Low-rank high-order tensor completion with applications in visual data,

    W. Qin, H. Wang, F. Zhang, J. Wang, X. Luo, and T. Huang, “Low-rank high-order tensor completion with applications in visual data,” IEEE Trans. Image Process., vol. 31, pp. 2433–2448, 2022

    2022

  22. [30]

    Tensor n-tubal rank and its convex relaxation for low-rank tensor recovery,

    Y .-B. Zheng, T.-Z. Huang, X.-L. Zhao, T.-X. Jiang, T.-Y . Ji, and T.-H. Ma, “Tensor n-tubal rank and its convex relaxation for low-rank tensor recovery,” Inf. Sci., vol. 532, pp. 170–189, 2020

    2020

  23. [31]

    Revisiting high-order tensor singular value decomposition from basic element perspective,

    S. Liu, X.-L. Zhao, J. Leng, B.-Z. Li, J.-H. Yang, and X. Chen, “Revisiting high-order tensor singular value decomposition from basic element perspective,” IEEE Trans. Signal Process. , vol. 72, pp. 4589– 4603, 2024

    2024

  24. [32]

    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 Trans. Image Process., vol. 32, pp. 3397–3412, 2023

    2023

  25. [33]

    Robust low-rank tensor recovery: Models and algorithms,

    D. Goldfarb and Z. Qin, “Robust low-rank tensor recovery: Models and algorithms,” SIAM J. Matrix Anal. Appl. , vol. 35, no. 1, pp. 225–253, 2014

    2014

  26. [34]

    Robust low-rank tensor ring completion,

    H. Huang, Y . Liu, Z. Long, and C. Zhu, “Robust low-rank tensor ring completion,” IEEE Trans. Comput. Imag., vol. 6, pp. 1117–1126, 2020

    2020

  27. [35]

    Robust tensor completion via capped frobenius norm,

    X. P. Li, Z.-Y . Wang, Z.-L. Shi, H. C. So, and N. D. Sidiropoulos, “Robust tensor completion via capped frobenius norm,” IEEE Trans. Neural Netw. Learn. Syst. , vol. 35, no. 7, pp. 9700–9712, 2024

    2024

  28. [36]

    Fully-connected tensor network decomposition for robust tensor completion problem,

    Y .-Y . Liu, X.-L. Zhao, G.-J. Song, Y .-B. Zheng, M. K. Ng, and T.- Z. Huang, “Fully-connected tensor network decomposition for robust tensor completion problem,” Inverse Probl. Imag. , vol. 18, no. 1, pp. 208–238, 2024

    2024

  29. [37]

    Robust tensor completion from uniformly dithered one-bit observations,

    J. Hou, J. Chen, and M. K. Ng, “Robust tensor completion from uniformly dithered one-bit observations,” SIAM J. Imag. Sci. , vol. 18, no. 1, pp. 152–215, 2025

    2025

  30. [38]

    Robust low-tubal-rank tensor completion via convex optimization

    Q. Jiang and M. Ng, “Robust low-tubal-rank tensor completion via convex optimization.” in Proc. 28th Int. Joint Conf. Artif. Intell. , 2019, pp. 2649–2655

    2019

  31. [39]

    Robust low-rank tensor minimization via a new tensor spectral k-support norm,

    J. Lou and Y .-M. Cheung, “Robust low-rank tensor minimization via a new tensor spectral k-support norm,” IEEE Trans. Image Process. , vol. 29, pp. 2314–2327, 2019

    2019

  32. [40]

    Robust tensor decomposition via t-SVD: Near-optimal statistical guarantee and scalable algorithms,

    A. Wang, Z. Jin, and G. Tang, “Robust tensor decomposition via t-SVD: Near-optimal statistical guarantee and scalable algorithms,” Signal Process., vol. 167, p. 107319, 2020

    2020

  33. [41]

    Robust tensor completion us- ing transformed tensor singular value decomposition,

    G. Song, M. K. Ng, and X. Zhang, “Robust tensor completion us- ing transformed tensor singular value decomposition,” Numer. Linear Algebr. Appl., vol. 27, no. 3, p. e2299, 2020

    2020

  34. [42]

    Ro- bust corrupted data recovery and clustering via generalized transformed tensor low-rank representation,

    J.-H. Yang, C. Chen, H.-N. Dai, M. Ding, Z.-B. Wu, and Z. Zheng, “Ro- bust corrupted data recovery and clustering via generalized transformed tensor low-rank representation,” IEEE Trans. Neural Netw. Learn. Syst., vol. 35, no. 7, pp. 8839–8853, 2024

    2024

  35. [43]

    Bayesian low-tubal-rank robust tensor factorization with multi-rank determination,

    Y . Zhou and Y .-M. Cheung, “Bayesian low-tubal-rank robust tensor factorization with multi-rank determination,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 43, no. 1, pp. 62–76, 2019

    2019

  36. [44]

    Tensor robust principal component analysis via tensor fibered rank and ℓp minimization,

    K. Gao and Z.-H. Huang, “Tensor robust principal component analysis via tensor fibered rank and ℓp minimization,” SIAM J. Imaging Sci. , vol. 16, no. 1, pp. 423–460, 2023

    2023

  37. [45]

    Generalized nonconvex hyperspectral anomaly detection via background representation learning with dictionary con- straint,

    Q. Yu and M. Bai, “Generalized nonconvex hyperspectral anomaly detection via background representation learning with dictionary con- straint,” SIAM J. Imag. Sci. , vol. 17, no. 2, pp. 917–950, 2024

    2024

  38. [46]

    Tensor ring decomposition-based generalized and efficient nonconvex approach for hyperspectral anomaly detection,

    W. Qin, H. Wang, F. Zhang, J. Wang, X. Cao, and X.-L. Zhao, “Tensor ring decomposition-based generalized and efficient nonconvex approach for hyperspectral anomaly detection,” IEEE Trans. Geosci. Remote Sens., vol. 62, 2024, Art. no. 5539818

    2024

  39. [47]

    Tensor compressive sensing fused low-rankness and local-smoothness,

    X. Liu, J. Hou, J. Peng, H. Wang, D. Meng, and J. Wang, “Tensor compressive sensing fused low-rankness and local-smoothness,” in Proc. AAAI Conf. Artif. Intel. , vol. 37, no. 7, 2023, pp. 8879–8887

    2023

  40. [48]

    Tensor recovery from binary measurements fused low-rankness and smoothness,

    J. Hou, X. Liu, H. Wang, and K. Guo, “Tensor recovery from binary measurements fused low-rankness and smoothness,” Signal Process. , vol. 221, p. 109480, 2024

    2024

  41. [49]

    Low-tubal-rank tensor recovery via factorized gradient descent,

    Z. Liu, Z. Han, Y . Tang, X.-L. Zhao, and Y . Wang, “Low-tubal-rank tensor recovery via factorized gradient descent,” IEEE Trans. Signal Process., vol. 72, pp. 5470–5483, 2024

    2024

  42. [50]

    Generalized nonconvex approach for low-tubal-rank tensor recovery,

    H. Wang, F. Zhang, J. Wang, T. Huang, J. Huang, and X. Liu, “Generalized nonconvex approach for low-tubal-rank tensor recovery,” IEEE Trans. Neural Netw. Learn. Syst. , vol. 33, no. 8, pp. 3305–3319, 2021

    2021

  43. [51]

    3-D array image data completion by tensor decomposition and nonconvex regularization approach,

    M. Yang, Q. Luo, W. Li, and M. Xiao, “3-D array image data completion by tensor decomposition and nonconvex regularization approach,” IEEE Trans. Signal Process., vol. 70, pp. 4291–4304, 2022

    2022

  44. [52]

    Low-rank tensor completion via novel sparsity-inducing regularizers,

    Z.-Y . Wang, H. C. So, and A. M. Zoubir, “Low-rank tensor completion via novel sparsity-inducing regularizers,” IEEE Trans. Signal Process., vol. 72, pp. 3519–3534, 2024

    2024

  45. [53]

    Tensor recovery based on a novel non-convex function minimax logarithmic concave penalty function,

    H. Zhang, X. Liu, C. Liu, H. Fan, Y . Li, and X. Zhu, “Tensor recovery based on a novel non-convex function minimax logarithmic concave penalty function,” IEEE Trans. Image Process., vol. 32, pp. 3413–3428, 2023

    2023

  46. [54]

    Robust low-rank tensor recovery via nonconvex singular value minimization,

    L. Chen, X. Jiang, X. Liu, and Z. Zhou, “Robust low-rank tensor recovery via nonconvex singular value minimization,” IEEE Trans. Image Process., vol. 29, pp. 9044–9059, 2020

    2020

  47. [55]

    Nonlocal robust tensor recovery with nonconvex regularization,

    D. Qiu, M. Bai et al., “Nonlocal robust tensor recovery with nonconvex regularization,” Inverse Probl., vol. 37, no. 3, p. 035001, 2021

    2021

  48. [56]

    Robust tensor completion: Equivalent surrogates, error bounds, and algorithms,

    X. Zhao, M. Bai, D. Sun, and L. Zheng, “Robust tensor completion: Equivalent surrogates, error bounds, and algorithms,” SIAM J. Imaging Sci., vol. 15, no. 2, pp. 625–669, 2022

    2022

  49. [57]

    Robust tensor completion via dictionary learning and generalized nonconvex regularization for visual data recovery,

    D. Qiu, B. Yang, and X. Zhang, “Robust tensor completion via dictionary learning and generalized nonconvex regularization for visual data recovery,” IEEE Trans. Circuits Syst. Video Technol. , 2024

    2024

  50. [58]

    Robust low- rank tensor reconstruction using high-order t-SVD,

    W. Qin, H. Wang, F. Zhang, M. Dai, and J. Wang, “Robust low- rank tensor reconstruction using high-order t-SVD,” J. Electron. Imag., vol. 30, no. 6, pp. 063 016–063 016, 2021

    2021

  51. [59]

    Robust high-order tensor recovery via nonconvex low-rank approximation,

    W. Qin, H. Wang, W. Ma, and J. Wang, “Robust high-order tensor recovery via nonconvex low-rank approximation,” in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP), 2022, pp. 3633–3637

    2022

  52. [60]

    Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions,

    N. Halko, P.-G. Martinsson, and J. A. Tropp, “Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions,” SIAM Rev., vol. 53, no. 2, pp. 217–288, 2011

    2011

  53. [61]

    Randomized numerical linear algebra: Foundations and algorithms,

    P.-G. Martinsson and J. A. Tropp, “Randomized numerical linear algebra: Foundations and algorithms,” Acta Numer., vol. 29, pp. 403– 572, 2020

    2020

  54. [62]

    A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices,

    P.-G. Martinsson and S. V oronin, “A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices,” SIAM J. Sci. Comput. , vol. 38, no. 5, pp. S485–S507, 2016

    2016

  55. [63]

    Practical sketching algorithms for low-rank matrix approximation,

    J. A. Tropp, A. Yurtsever, M. Udell, and V . Cevher, “Practical sketching algorithms for low-rank matrix approximation,” SIAM J. Matrix Anal. Appl., vol. 38, no. 4, pp. 1454–1485, 2017

    2017

  56. [64]

    Efficient randomized algorithms for the fixed-precision low-rank matrix approximation,

    W. Yu, Y . Gu, and Y . Li, “Efficient randomized algorithms for the fixed-precision low-rank matrix approximation,” SIAM J. Matrix Anal. Appl., vol. 39, no. 3, pp. 1339–1359, 2018

    2018

  57. [65]

    Randomized projection for rank-revealing matrix factorizations and low-rank approximations,

    J. A. Duersch and M. Gu, “Randomized projection for rank-revealing matrix factorizations and low-rank approximations,”SIAM Rev., vol. 62, no. 3, pp. 661–682, 2020

    2020

  58. [66]

    A block bidiagonalization method for fixed-accuracy low- rank matrix approximation,

    E. Hallman, “A block bidiagonalization method for fixed-accuracy low- rank matrix approximation,” SIAM J. Matrix Anal. Appl., vol. 43, no. 2, pp. 661–680, 2022

    2022

  59. [67]

    An improved analysis and unified perspective on deterministic and randomized low-rank matrix approximation,

    J. Demmel, L. Grigori, and A. Rusciano, “An improved analysis and unified perspective on deterministic and randomized low-rank matrix approximation,” SIAM J. Matrix Anal. Appl. , vol. 44, no. 2, pp. 559– 591, 2023

    2023

  60. [68]

    Randomized algorithms for low- rank matrix approximation: Design, analysis, and applications,

    J. A. Tropp and R. J. Webber, “Randomized algorithms for low- rank matrix approximation: Design, analysis, and applications,” arXiv preprint arXiv:2306.12418, 2023

    2023 arXiv

  61. [69]

    Block- randomized stochastic proximal gradient for low-rank tensor factor- ization,

    X. Fu, S. Ibrahim, H.-T. Wai, C. Gao, and K. Huang, “Block- randomized stochastic proximal gradient for low-rank tensor factor- ization,” IEEE Trans. Signal Process. , vol. 68, pp. 2170–2185, 2020

    2020

  62. [70]

    Practical leverage-based sampling for low-rank tensor decomposition,

    B. W. Larsen and T. G. Kolda, “Practical leverage-based sampling for low-rank tensor decomposition,” SIAM J. Matrix Anal. Appl. , vol. 43, no. 3, pp. 1488–1517, 2022

    2022

  63. [71]

    Randomized sampling techniques based low-tubal-rank plus sparse tensor recovery,

    F. Zhang, L. Yang, J. Wang, and X. Luo, “Randomized sampling techniques based low-tubal-rank plus sparse tensor recovery,” Knowl.- Based Syst., vol. 261, p. 110198, 2023

    2023

  64. [72]

    Fast randomized algorithms for t-product based tensor operations and decompositions with applications to imaging data,

    D. A. Tarzanagh et al., “Fast randomized algorithms for t-product based tensor operations and decompositions with applications to imaging data,” SIAM J. Imaging Sci. , vol. 11, no. 4, pp. 2629–2664, 2018

    2018

  65. [73]

    A randomized tensor singular value decomposition based on the t-product,

    J. Zhang, A. K. Saibaba, M. E. Kilmer, and S. Aeron, “A randomized tensor singular value decomposition based on the t-product,” Numer. Linear Algebr. Appl., vol. 25, no. 5, p. e2179, 2018

    2018

  66. [74]

    Fast randomized tensor singular value thresholding for low-rank tensor optimization,

    M. Che, X. Wang, Y . Wei, and X. Zhao, “Fast randomized tensor singular value thresholding for low-rank tensor optimization,” Numer. Linear Algebr. Appl., vol. 29, no. 6, p. e2444, 2022

    2022

  67. [75]

    The computation of low multilinear rank approximations of tensors via power scheme and random projection,

    M. Che, Y . Wei, and H. Yan, “The computation of low multilinear rank approximations of tensors via power scheme and random projection,” SIAM J. Matrix Anal. Appl. , vol. 41, no. 2, pp. 605–636, 2020

    2020

  68. [76]

    Randomized algorithms for the low multilinear rank approxi- mations of tensors,

    ——, “Randomized algorithms for the low multilinear rank approxi- mations of tensors,” J. Comput. Appl. Math., vol. 390, p. 113380, 2021. JOURNAL OF LATEX CLASS FILES, VOL. , NO. , XX XXXX 19

    2021

  69. [77]

    An efficient randomized algorithm for computing the approx- imate tucker decomposition,

    ——, “An efficient randomized algorithm for computing the approx- imate tucker decomposition,” J. Sci. Comput. , vol. 88, no. 2, p. 32, 2021

    2021

  70. [78]

    Randomized algorithms for the com- putation of multilinear rank- (µ1, µ2, µ3) approximations,

    M. Che, Y . Wei, and Y . Xu, “Randomized algorithms for the com- putation of multilinear rank- (µ1, µ2, µ3) approximations,” J. Global Optim., vol. 87, no. 2, pp. 373–403, 2023

    2023

  71. [79]

    Practical sketching algorithms for low-rank tucker approximation of large tensors,

    W. Dong, G. Yu, L. Qi, and X. Cai, “Practical sketching algorithms for low-rank tucker approximation of large tensors,” J. Sci. Comput. , vol. 95, no. 2, p. 52, 2023

    2023

  72. [80]

    Streaming coresets for symmetric tensor factorization,

    R. Chhaya, J. Choudhari, A. Dasgupta, and S. Shit, “Streaming coresets for symmetric tensor factorization,” in Proc. Int. Conf. Mach. Learn. (ICML), 2020, pp. 1855–1865

    2020

  73. [81]

    Tensor decompositions and applica- tions,

    T. G. Kolda and B. W. Bader, “Tensor decompositions and applica- tions,” SIAM Rev., vol. 51, no. 3, pp. 455–500, 2009

    2009

  74. [82]

    An order- p tensor factorization with applications in imaging,

    C. D. Martin, R. Shafer, and B. LaRue, “An order- p tensor factorization with applications in imaging,” SIAM J. Sci. Comput. , vol. 35, no. 1, pp. A474–A490, 2013

    2013

  75. [83]

    High dimensional statistical estimation under uniformly dithered one-bit quantization,

    J. Chen, C.-L. Wang, M. K. Ng, and D. Wang, “High dimensional statistical estimation under uniformly dithered one-bit quantization,” IEEE Trans. Inf. Theory , vol. 69, no. 8, pp. 5151–5187, 2023

    2023

  76. [84]

    A new truncation strategy for the higher-order singular value decomposition,

    N. Vannieuwenhoven, R. Vandebril, and K. Meerbergen, “A new truncation strategy for the higher-order singular value decomposition,” SIAM J. Sci. Comput. , vol. 34, no. 2, pp. A1027–A1052, 2012

    2012

  77. [85]

    Randomized algorithms for low-rank tensor decompositions in the tucker format,

    R. Minster, A. K. Saibaba, and M. E. Kilmer, “Randomized algorithms for low-rank tensor decompositions in the tucker format,” SIAM J. Math. Data Sci. , vol. 2, no. 1, pp. 189–215, 2020

    2020

  78. [86]

    Randomized block krylov methods for stronger and faster approximate singular value decomposition,

    C. Musco and C. Musco, “Randomized block krylov methods for stronger and faster approximate singular value decomposition,” Proc. Adv. Neural Inf. Process. Syst. (NIPS) , vol. 28, 2015

    2015

  79. [87]

    Superlinear convergence of randomized block Lanczos algorithm,

    Q. Yuan, M. Gu, and B. Li, “Superlinear convergence of randomized block Lanczos algorithm,” in Proc. IEEE Int. Conf. Data Mining (ICDM). IEEE, 2018, pp. 1404–1409

    2018

  80. [88]

    On the unreasonable effectiveness of single vector krylov methods for low-rank approximation,

    R. Meyer, C. Musco, and C. Musco, “On the unreasonable effectiveness of single vector krylov methods for low-rank approximation,” in Proc. Annu. ACM-SIAM Symp. Discrete Algorithms (SODA) , 2024, pp. 811– 845

    2024

  81. [89]

    Tensor nuclear norm-based low-rank approximation with total variation regularization,

    Y . Chen, S. Wang, and Y . Zhou, “Tensor nuclear norm-based low-rank approximation with total variation regularization,” IEEE J. Sel. Topics Signal Process., vol. 12, no. 6, pp. 1364–1377, 2018

    2018

  82. [90]

    Robust low-rank tensor completion via transformed tensor nuclear norm with total variation regularization,

    D. Qiu, M. Bai, M. K. Ng, and X. Zhang, “Robust low-rank tensor completion via transformed tensor nuclear norm with total variation regularization,” Neurocomputing, vol. 435, pp. 197–215, 2021

    2021

  83. [91]

    Waveshrink with firm shrinkage,

    H.-Y . Gao and A. G. Bruce, “Waveshrink with firm shrinkage,” Statistica Sinica, pp. 855–874, 1997

    1997

  84. [92]

    A general iterative shrinkage and thresholding algorithm for non-convex regularized opti- mization problems,

    P. Gong, C. Zhang, Z. Lu, J. Huang, and J. Ye, “A general iterative shrinkage and thresholding algorithm for non-convex regularized opti- mization problems,” in Proc. Int. Conf. Mach. Learn. (ICML). PMLR, 2013, pp. 37–45

    2013

  85. [93]

    On ℓq optimization and matrix comple- tion,

    G. Marjanovic and V . Solo, “On ℓq optimization and matrix comple- tion,” IEEE Trans. signal process. , vol. 60, no. 11, pp. 5714–5724, 2012

    2012

  86. [94]

    Variable selection via nonconcave penalized like- lihood and its oracle properties,

    J. Fan and R. Li, “Variable selection via nonconcave penalized like- lihood and its oracle properties,” J. Amer. Statist. Assoc. , vol. 96, no. 456, pp. 1348–1360, 2001

    2001

  87. [95]

    Nearly unbiased variable selection under minimax concave penalty,

    C.-H. Zhang, “Nearly unbiased variable selection under minimax concave penalty,” Ann. Statist., vol. 38, no. 2, pp. 894–942, 2010

    2010

  88. [96]

    Matrix completion via schatten capped p norm,

    G. Li, G. Guo, S. Peng, C. Wang, S. Yu, J. Niu, and J. Mo, “Matrix completion via schatten capped p norm,” IEEE Trans. Knowl. Data Eng., vol. 34, no. 1, pp. 394–404, 2020

    2020

  89. [97]

    Group sparse optimization for images recovery using capped folded concave functions,

    L. Pan and X. Chen, “Group sparse optimization for images recovery using capped folded concave functions,” SIAM J. Imag. Sci. , vol. 14, no. 1, pp. 1–25, 2021

    2021

  90. [98]

    Patched-tube unitary transform for robust tensor completion,

    M. K. Ng, X. Zhang et al., “Patched-tube unitary transform for robust tensor completion,” Pattern Recognit., vol. 100, p. 107181, 2020

    2020

  91. [99]

    Nonconvex optimization for robust tensor completion from grossly sparse observations,

    X. Zhao, M. Bai, and M. K. Ng, “Nonconvex optimization for robust tensor completion from grossly sparse observations,” J. Sci. Comput. , vol. 85, no. 2, p. 46, 2020

    2020

  92. [100]

    A generalized non-convex method for robust tensor completion,

    Z. Zhang, S. Liu, and Z. Lin, “A generalized non-convex method for robust tensor completion,” J. Sci. Comput., vol. 96, no. 3, p. 91, 2023

    2023

  93. [101]

    Robust low-tubal-rank tensor completion,

    A. Wang, X. Song, X. Wu, Z. Lai, and Z. Jin, “Robust low-tubal-rank tensor completion,” in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP), 2019, pp. 3432–3436

    2019

  94. [102]

    Generalized nonconvex regularization for tensor RPCA and its applications in visual inpainting,

    F. Zhang, H. Wang, W. Qin, X. Zhao, and J. Wang, “Generalized nonconvex regularization for tensor RPCA and its applications in visual inpainting,” Appl. Intell., vol. 53, no. 20, pp. 23 124–23 146, 2023

    2023

  95. [103]

    Joint schatten p-norm and ℓp-norm robust matrix completion for missing value recovery,

    F. Nie, H. Wang, H. Huang, and C. Ding, “Joint schatten p-norm and ℓp-norm robust matrix completion for missing value recovery,” Knowl. Inf. Syst., vol. 42, no. 3, pp. 525–544, 2015

    2015

  96. [104]

    Nonconvex nonsmooth low rank minimization via iteratively reweighted nuclear norm,

    C. Lu, J. Tang, S. Yan, and Z. Lin, “Nonconvex nonsmooth low rank minimization via iteratively reweighted nuclear norm,” IEEE Trans. Image Process., vol. 25, no. 2, pp. 829–839, 2015

    2015

  97. [105]

    Large-scale low-rank matrix learning with nonconvex regularizers,

    Q. Yao, J. T. Kwok, T. Wang, and T.-Y . Liu, “Large-scale low-rank matrix learning with nonconvex regularizers,” IEEE Trans. Pattern Anal. Mach. Intell. , vol. 41, no. 11, pp. 2628–2643, 2018

    2018

  98. [106]

    Robust PCA using generalized nonconvex regularization,

    F. Wen, R. Ying, P. Liu, and R. C. Qiu, “Robust PCA using generalized nonconvex regularization,” IEEE Trans. Circuits Syst. Video Technol. , vol. 30, no. 6, pp. 1497–1510, 2019

    2019

  99. [107]

    Generalized nonconvex nonsmooth low-rank matrix recovery framework with feasible algorithm designs and convergence analysis,

    H. Zhang, F. Qian, P. Shi, W. Du, Y . Tang, J. Qian, C. Gong, and J. Yang, “Generalized nonconvex nonsmooth low-rank matrix recovery framework with feasible algorithm designs and convergence analysis,” IEEE Trans. Neural Netw. Learn. Syst. , vol. 34, no. 9, pp. 5342–5353, 2022

    2022

  100. [108]

    Iteratively capped reweighting norm minimization with global convergence guarantee for low-rank matrix learning,

    Z. Wang, D. Hu, Z. Liu, C. Gao, and Z. Wang, “Iteratively capped reweighting norm minimization with global convergence guarantee for low-rank matrix learning,” IEEE Trans. Pattern Anal. Mach. Intell. , vol. 47, no. 3, pp. 1923–1940, 2025

    1923

  101. [109]

    Distributed optimization and statistical learning via the alternating direction method of multipliers,

    S. Boyd, N. Parikh, E. Chu et al. , “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn., vol. 3, no. 1, pp. 1–122, 2011

    2011

  102. [110]

    A new alternating mini- mization algorithm for total variation image reconstruction,

    Y . Wang, J. Yang, W. Yin, and Y . Zhang, “A new alternating mini- mization algorithm for total variation image reconstruction,” SIAM J. Imaging Sci., vol. 1, no. 3, pp. 248–272, 2008

    2008

  103. [111]

    One-bit tensor completion via transformed tensor singular value decomposition,

    J. Hou, F. Zhang, and J. Wang, “One-bit tensor completion via transformed tensor singular value decomposition,” Appl. Math. Model., vol. 95, pp. 760–782, 2021

    2021

  104. [112]

    Learning tensors from partial binary measurements,

    N. Ghadermarzy, Y . Plan, and O. Yilmaz, “Learning tensors from partial binary measurements,” IEEE Trans. Signal Process. , vol. 67, no. 1, pp. 29–40, 2019

    2019

  105. [113]

    1-bit tensor completion,

    A. Aidini, G. Tsagkatakis, and P. Tsakalides, “ 1-bit tensor completion,” Electronic Imaging, vol. 30, pp. 1–6, 2018

    2018

  106. [114]

    1-bit matrix completion,

    M. A. Davenport, Y . Plan, E. Van Den Berg, and M. Wootters, “1-bit matrix completion,” Inf. Inference, vol. 3, no. 3, pp. 189–223, 2014

    2014

  107. [115]

    Revisiting nonlocal self-similarity from continuous representation,

    Y . Luo, X. Zhao, and D. Meng, “Revisiting nonlocal self-similarity from continuous representation,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 47, no. 1, pp. 450–468, 2025

    2025

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.