Pith. sign in

REVIEW 2 major objections 5 minor 1 cited by

Learnable Scaled Gradient Descent for Guaranteed Robust Tensor PCA

T0 review · 2 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper claims that robust tensor PCA can be solved by scaled gradient descent on a t-SVD factorization, with a linear convergence rate independent of the condition number.

desk verdict A genuinely useful algorithm and a real sparsity condition, but the main recovery guarantee drops I1 I2 factors and is not proven as stated. read the letter →

arxiv 2501.04565 v2 pith:F74YH3WU submitted 2025-01-08 cs.CV

Lanlan Feng , Ce Zhu , Yipeng Liu , Saiprasad Ravishankar , Longxiu Huang This is my paper · ORCID
classification cs.CV MSC 15A6990C26
keywords robusttensorPCAscaledgradientdescentt-SVDtubalrankincoherencedeepunfoldingself-supervisedlearninglinearconvergence
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 aims to establish that robust tensor principal component analysis (RTPCA) under the t-SVD framework can be solved by factored scaled gradient descent rather than by convex tensor-nuclear-norm (TNN) minimization. The proposed RTPCA-SGD writes the low-rank tensor as $X = L * R^\top$ and alternates soft-thresholding of the sparse component with scaled gradient updates of the two factors. The paper's central theoretical claim is that, under tensor $\mu$-incoherence and a slice-based sparsity condition, the iterates converge linearly to the true low-rank and sparse components at a rate independent of the condition number. A self-supervised deep-unfolding version, RTPCA-LSGD, learns the step size and threshold parameters from the observed data alone. If the guarantee is correct, the practical payoff is a scalable RTPCA that avoids full t-SVD computations in every iteration while retaining recovery guarantees.

What carries the argument

The central object is the tensor distance metric $$\operatorname{dist}(L,R;L_\star,R_\star) = \inf_{Q\in GL(R)}\left(\|(L*Q-L_\star)*\Sigma_\$star^{{1/2}}$\|$_F^{2}$ + \|(R*$Q^{{-\top}}$-R_\star)*\Sigma_\$star^{{1/2}}$\|$_F^{2}$\right)^{1/2},$$ which removes the gauge ambiguity between the two factors by optimizing over invertible alignment tensors $Q$; Lemma 1 guarantees the optimal $Q$ exists and is invertible when the factors are close. The scaled gradient updates $$L_{k+1}=L_k-\eta\,(L_k*R_k^\top+S_{k+1}-Y)*R_k*(R_k^\top R_k)^{-1}, \quad R_{k+1}=R_k-\eta\,(L_k*R_k^\top+S_{k+1}-Y)^\top*L_k*(L_k^\top L_k)^{-1}$$ use the scaling factors $(R_k^\top R_k)^{-1}$ and $(L_k^\top L_k)^{-1}$ to remove the dependence on the condition number. The threshold schedule $\zeta_{k+1}=3\sqrt{I_1I_2}\,\mu R\sigma_{\min}(X_\star)\tau^k$ keeps the soft-thresholding step above $\|X_\star-X_k\|_\infty$, so by Lemma 3 it projects onto the support of $S_\star$; the t-product algebra (circular convolution along the third mode, computed as matrix products in the Fourier domain) is what makes the whole factorization and distance calculus possible.

What would settle it

Inspect the contraction estimate in the proof of Lemma 12: combining the slice-sparsity spectral bound of Lemma 5 with $\zeta_{k+1}=3\sqrt{I_1I_2}\,\mu R\sigma_{\min}\tau^k$ introduces $I_1$ and $I_2$ factors that the proof drops, and keeping them would force $\alpha$ down to about $O(1/(\mu R I_1^2 I_2^2 I_3))$. Numerically, run RTPCA-SGD with growing $I_1=I_2$ at $\alpha$ just below the theorem's stated value and check whether the measured error still contracts at rate $\tau$; a stall or slowdown with increasing spatial dimensions would falsify the guarantee as stated.

Watch

Extended reading notes

Core claim

Theorem 1 states that when the true low-rank tensor $X_\star$ has tubal rank $R$ and satisfies tensor $\mu$-incoherence, and the sparse tensor $S_\star$ is $\alpha$-sparse with $\alpha \le 1/(10^4\mu R^{1.5} I_3^{1.5}\kappa)$, then with threshold values $\zeta_0 \in [\|X_\star\|_\infty, 2\|X_\star\|_\infty]$, $\zeta_1 = 3\sqrt{I_1I_2}\mu R\sigma_{\min}(X_\star)$, and step size $\eta \in [1/4, 2/3]$, the RTPCA-SGD iterates satisfy $$\|X_k - X_\star\|_F \le 0.03\sqrt{I_3}\,\tau^k \sigma_{\min}(X_\star), \quad \|X_k-X_\star\|_\infty \le 3\sqrt{I_1I_2}\,\mu R\tau^k\sigma_{\min}(X_\star), \quad \|S_k-S_\star\|_\infty \le 6\sqrt{I_1I_2}\,\mu R\$tau^{{k-1}}$\sigma_{\min}(X_\star),$$ with rate $\tau = 1-0.6\eta$ independent of the condition number $\kappa$. The theorem also claims that the support of every sparse iterate lies inside the support of $S_\star$, so the thresholding step never introduces false outliers. The proof rests on a spectral initialization through the top-$R$ t-SVD, a threshold schedule that stays above the current entrywise error, and a tensor distance metric that measures the two factors under their best alignment.

Load-bearing premise

The load-bearing premise is that the sparse-error terms in the scaled gradient update can be bounded by constants independent of $I_1$ and $I_2$; if the dimension factors introduced by the threshold schedule are kept, the stated guarantee would require a much smaller corruption fraction, roughly $O(1/(\mu R I_1^2 I_2^2 I_3))$, than the $\alpha \le 1/(10^4\mu R^{1.5}I_3^{1.5}\kappa)$ stated in Theorem 1.

Editorial extensions

If this is right

  • The per-iteration cost drops from $O(I_1I_2I_3\log I_3 + \lceil (I_3+1)/2\rceil I_1I_2\min(I_1,I_2))$ for TNN-based RTPCA to $O(I_1I_2I_3\log I_3 + \lceil (I_3+1)/2\rceil I_1I_2R)$ when $R\ll\min(I_1,I_2)$.
  • If Theorem 1 is correct, the recovery error contracts linearly at rate $\tau=1-0.6\eta$ regardless of the condition number $\kappa$, so ill-conditioned tensors are recovered as quickly as well-conditioned ones.
  • The support containment $\mathrm{supp}(S_k)\subseteq\mathrm{supp}(S_\star)$ means the sparse estimate never invents nonzero entries outside the true corruption support once the threshold schedule is active.
  • The $\alpha$-sparsity assumption applies slice-wise rather than fiber-wise, so it covers corruption patterns that would be fully dense under matrix row/column sparsity.
  • The self-supervised deep-unfolded variant RTPCA-LSGD can learn $\zeta_0,\zeta_1,\tau,\eta$ from observed data alone, removing the need for labeled ground truth in practical deployment.

Reading between the lines

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

  • The same factorized scaled-gradient machinery should transfer to other invertible transforms and to higher-order t-SVD generalizations, since the distance metric and thresholding arguments depend mainly on the norm identities of the t-product, not on the specific Fourier implementation.
  • Because the pure algorithm needs $\mu R\sigma_{\min}(X_\star)$ to set $\zeta_1$, the deep-unfolded model is implicitly learning a spectral quantity of the unknown tensor; this likely explains why it gains most in heavily corrupted settings where hand-set thresholds are unreliable.
  • A concrete extension would apply RTPCA-LSGD to tensor completion or tensor regression, where the same low-rank factorization and scaled updates can be used without a sparse component.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper proposes RTPCA-SGD, a scaled gradient descent method for t-SVD based robust tensor PCA, together with a deep-unfolding variant RTPCA-LSGD. The main theoretical claim (Theorem 1) is that under tensor µ-incoherence and α-t-sparsity with α ≤ 1/(10^4 μ R^{1.5} I3^{1.5} κ), the iterates converge linearly to the true low-rank tensor with a rate independent of the condition number, and that the sparse component is exactly support-recovered. The proof is organized as a spectral initialization guarantee (Theorem 3) plus a local linear convergence result (Theorem 2), with auxiliary lemmas in the supplementary material. The paper also reports synthetic and real-data experiments on video denoising and background initialization.

Significance. If the main theorem were established, this would be a useful contribution: it would provide the first ScaledGD-type recovery guarantee in the t-SVD framework, with a condition-number-independent linear rate and per-iteration cost O(I1 I2 I3 log I3 + ceil((I3+1)/2) I1 I2 R). The self-supervised deep-unfolding extension is a practical and timely addition, and the experimental section is extensive and mostly well presented. However, the central theoretical guarantee is not established as written: the proof of the key contraction step silently drops dimension factors that the stated sparsity condition cannot absorb. Since the advertised contribution is precisely the guaranteed recovery theorem, this gap is load-bearing for the paper's main claim.

major comments (2)
  1. [Supplementary, Lemma 12 (pages 23–24), Eq. (41)] The bounds for the sparse-error terms R2, R3, and R4 drop the I1 I2 factors that arise from the threshold ζ_{k+1} = 3 sqrt(I1 I2) μ R σ_min(X⋆) τ^k together with Lemma 5's bound ∥ΔS∥_2 ≤ α I3 sqrt(I1 I2) ∥ΔS∥_∞. For example, the R2 bound as displayed is proportional to I3 α μ R^{1.5} τ^k σ_min ∥ΔL Σ^{1/2}∥_F, but the preceding line contains I3 sqrt(I1 I2) sqrt(R) ∥ΔS∥_∞ and ∥ΔS∥_∞ ≤ 2 ζ_{k+1}, producing an extra factor I1 I2. The same omission occurs in R3, and in R4 the omitted factor is I1^2 I2^2. If these factors are retained, the second-to-last display of Eq. (41) gains terms proportional to I1 I2 sqrt(I3) α μ R^{1.5}/ε and I1^2 I2^2 I3^3 α^2 μ^2 R^3/ε^2 (up to constants), which are enormously larger than the displayed coefficients under the stated assumption α ≤ 1/(10^4 μ R^{1.5} I3^{1.5}) for generic dimensions such as I1 = I2 = 100, I3 = 50. Consequently the induction contraction in Eq. (41) is not established, and Theorem 1's linear convergence guarantee does not follow from the proof as written.
  2. [Supplementary, Lemma 13 (page 25), bound on T3] The same dimension-factor omission appears in the entrywise-error propagation. The displayed bound T3 ≤ 6 η sqrt(α I3)/(1−ε) · (1/sqrt(I1)) μ R τ^k σ_min(X⋆) is obtained from ∥ΔS∥_{2,∞} ≤ sqrt(α I2 I3) ∥ΔS∥_∞ and ∥ΔS∥_∞ ≤ 2 ζ_{k+1}, but substituting ζ_{k+1} = 3 sqrt(I1 I2) μ R τ^k σ_min gives an additional factor I1 I2. After multiplying by sqrt(I1), the retained bound is proportional to sqrt(α) I1 I2 sqrt(I3) μ R τ^k σ_min rather than sqrt(α I3) μ R τ^k σ_min. This affects the proof of the ∥X_k − X⋆∥_∞ and ∥S_k − S⋆∥_∞ claims in Theorem 2 and hence the corresponding statements in Theorem 1.
minor comments (5)
  1. [Assumption 2 and Theorem 1] The wording of Assumption 2 ('at most αt fraction of non-zero element in each slices') is imprecise; it should say that each slice contains at most an α fraction of nonzero entries, and the relation between the notation α_t in Assumption 2 and α in Theorem 1 should be stated explicitly.
  2. [Supplementary, Lemma 5] The proof cites a matrix bound as '[?, Lemma 1]'; the placeholder reference should be replaced with a proper citation, since Lemma 5 is used in the main proof.
  3. [Algorithm 2 and Figure 3] The caption of Figure 3 refers to 'ScaleGD iterative steps', but the method is called ScaledGD; this typo should be fixed.
  4. [Algorithm 2 and Theorem 1, threshold indexing] The relation ζ_{k+1} = τ^k ζ_1 for k ≥ 1 is stated, while the text elsewhere writes ζ_{k+1} = τ ζ_k; the indexing for k = 0 should be clarified.
  5. [Lemma 12 and Theorem 2, rate notation] Lemma 12 concludes with τ = 1 − 0.8η, whereas Theorem 2 and Theorem 1 state τ = 1 − 0.6η; the proof says 'substituting τ = 1 − 0.8η ≤ 1 − 0.6η', but the same symbol τ is used for the contraction rate and the threshold decay, which is confusing and should be disambiguated.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the RTPCA-SGD recovery guarantee is established via an internal induction fed by external matrix-perturbation lemmas and standard t-SVD algebra, not by a self-citation chain or by fitting.

full rationale

The paper's central claim, Theorem 1, is assembled from Theorem 2 (local linear convergence) and Theorem 3 (guaranteed initialization), both of which are proved in the supplementary material. The load-bearing technical inputs are external: Lemma 24 of [43] supplies the top-R SVD perturbation bound used in Theorem 3, and the t-product/t-SVD facts are cited to standard references [8], [10], [48] as well as to the authors' [49], but [49] is used only for well-known Fourier-domain t-product identities and soft-thresholding context, not to define the low-rank or sparse estimators or to force the convergence conclusion. The convergence induction in Lemma 12 estimates the contraction of dist(L_{k+1}, R_{k+1}; L*, R*) directly from the gradient update, the incoherence assumption, and the alpha-sparsity bound, with no fitted parameter being renamed as a prediction. The threshold values zeta0 and zeta1 are specified in terms of the ground-truth tensor X* (e.g., zeta1 := 3 sqrt(I1 I2) mu R sigma_min(X*)); this makes the guarantee oracle-dependent, which is a practical limitation, but it is not a circular reduction because the theorem does not define X* or S* through the algorithm's output and the claimed error bounds are not imposed on the algorithm as its inputs. The reviewer-identified gap in Lemma 12, where dimension factors I1 I2 are dropped when combining Lemma 5 with zeta_{k+1}, is a proof-correctness issue (the stated alpha condition may be insufficient for generic dimensions), not a circularity: it does not make any conclusion equivalent to its own premise by construction. I therefore find no circular step warranting a nonzero score.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper does not introduce new physical or mathematical entities. It relies on standard t-SVD machinery plus two domain assumptions on the data (incoherence and slice-wise sparsity). The main unstated pillars are the external perturbation lemma from [43] and a set of tensor norm inequalities collected in Lemma 5. The proof of the main theorem also depends on the boundedness of sparse-error terms, which is where the apparent algebraic errors appear.

free parameters (3)
  • learning rate eta = learned in RTPCA-LSGD; fixed in theory to [1/4, 2/3]
    The step size in Algorithm 2 is a learnable parameter in the deep-unfolded version; the theorem only states a feasible interval, not how to pick it from data. Experiments do not report the learned value.
  • thresholds zeta_0, zeta_1 and decay rate tau = learned in RTPCA-LSGD; zeta_0=1, zeta_1=1, tau=0.8 or 0.9 in real-data experiments
    These are learnable in the deep-unfolded model and hand-set in the non-learned experiments. The theoretical guarantee requires zeta_0 to satisfy ||X*||_infinity <= zeta_0 <= 2||X*||_infinity, which is not verified in experiments.
  • tubal rank R = 3 in real-data experiments
    The algorithm assumes the tubal rank is known; in practice it is chosen by the user. The theorem treats R as an input rather than a fitted number, but it is a free modeling choice affecting all theoretical constants.
assumptions (4)
  • domain assumption Tensor mu-incoherence conditions (Assumption 1) on the singular tensors of X*
    The recovery guarantee only holds for low-rank tensors with entries spread out across the tensor; stated in Assumption 1 and used throughout the proof.
  • domain assumption The sparse corruption S* is alpha-t-sparse, meaning every horizontal, lateral, and frontal slice has at most an alpha fraction of nonzeros
    Assumption 2 is the main modeling assumption on the corruption; the proof's bounds on the sparse error terms rely on the spectral and infinity-norm bounds for such tensors in Lemma 5.
  • standard math External perturbation lemma for top-R SVD (Lemma 24 of [43])
    The initialization analysis in Theorem 3 quotes a matrix perturbation bound from Tong et al. [43] without proof, and applies it frequency-by-frequency in the Fourier domain.
  • standard math Standard tensor properties: t-product via FFT, ||A||_F = (1/sqrt(I3))||bcirc(A)||_F, Weyl's inequality, and the relation between spectral norm and block circulant matrices
    These are used implicitly throughout the proofs in the supplementary and are attributed to prior t-SVD literature [8], [10], [48].

how reviews work

0 comments
Cite this review

Pith. "Pith review of Learnable Scaled Gradient Descent for Guaranteed Robust Tensor PCA." pith.science (2026). https://pith.science/paper/F74YH3WU

@misc{pith2026250104565,
  author       = {Pith},
  title        = {Pith review of: Learnable Scaled Gradient Descent for Guaranteed Robust Tensor PCA},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/F74YH3WU}},
  note         = {Machine review of arXiv:2501.04565}
}
read the original abstract

Robust tensor principal component analysis (RTPCA) aims to separate the low-rank and sparse components from multi-dimensional data, making it an essential technique in the signal processing and computer vision fields. Recently emerging tensor singular value decomposition (t-SVD) has gained considerable attention for its ability to better capture the low-rank structure of tensors compared to traditional matrix SVD. However, existing methods often rely on the computationally expensive tensor nuclear norm (TNN), which limits their scalability for real-world tensors. To address this issue, we explore an efficient scaled gradient descent (SGD) approach within the t-SVD framework for the first time, and propose the RTPCA-SGD method. Theoretically, we rigorously establish the recovery guarantees of RTPCA-SGD under mild assumptions, demonstrating that with appropriate parameter selection, it achieves linear convergence to the true low-rank tensor at a constant rate, independent of the condition number. To enhance its practical applicability, we further propose a learnable self-supervised deep unfolding model, which enables effective parameter learning. Numerical experiments on both synthetic and real-world datasets demonstrate the superior performance of the proposed methods while maintaining competitive computational efficiency, especially consuming less time than RTPCA-TNN.

Figures

Figures reproduced from arXiv: 2501.04565 by the authors.

Figure 1
Figure 1. Illustration of RTPCA model. Tensors [5], as higher-order extensions of vectors and ma￾trices, offer powerful data structures that capture interactions across multiple dimensions, making them essential in many fields such as data science, machine learning, and signal processing [6]. Their multidimensional framework reveals unique properties that can be harnessed for a wide range of analytical and processing tasks su… view at source ↗
Figure 2
Figure 2. Illustration of t-SVD framework. √ 1 I3 ∥A∥b 2,∞ = ∥bcirc(A)∥2,∞. Definition 4 (Tensor ℓ1,∞ norm). The tensor ℓ1,∞ norm of an order-3 tensor A ∈ R I1×I2×I3 is defined as ∥A∥1,∞ = maxi1 PI2 i2=1 PI3 i3=1 |ai1,i2,i3 |. Definition 5 (Tensor infinity norm). The tensor infinity norm of an order-3 tensor A ∈ R I1×I2×I3 is defined as ∥A∥∞ = maxi1,i2,i3 |ai1,i2,i3 |. Definition 6 (Conjugate transpose). [8] The conjugate tra… view at source ↗
Figure 3
Figure 3. Network architecture. The observed tensor [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Comparison of tensor sparsity and matrix sparsity. Blue boxes denote [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Phase transition performance of RTPCA-SGD under different condi [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Convergence performance with respect to different error metrics, [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 8
Figure 8. Figure 8: Video denoising examples on the 11-th frame of “Akiyo” with 30% noise and the 24-th frame of “News” with 10% noise. experiments are conducted on a computer equipped with an Intel i5-11400F CPU, 16GB of RAM, and an RTX 3060 Ti GPU. Table I presents the comparison result…
Figure 9
Figure 9. Figure 9: Background initialization results by different methods on 3 scenes including the [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: Comparison reslults of RTPCA-SGD and RTPCA-LSGD on real-world datasets. The avarage PSNR values are shown on the top of the subfigure. [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Beyond Motion Cues and Structural Sparsity: Revisiting Small Moving Target Detection

    cs.CV 2025-09 conditional novelty 6.0 of 10

    TenRPCANet uses a Video Swin Transformer with low-rank tensor-inspired tokenization to separate dim moving targets from low-rank video backgrounds, reaching strong benchmark results in infrared and space imagery.

Reference graph

Works this paper leans on

74 extracted references · 64 canonical work pages · cited by 1 Pith paper

  1. [1]

    Robust principal component analysis?

    E. J. Candès, X. Li, Y . Ma, and J. Wright, “Robust principal component analysis?” Journal of the ACM (JACM) , vol. 58, no. 3, pp. 1–37, 2011

    work page 2011

  2. [2]

    Matrix and tensor completion algorithms for background model initialization: A comparative evaluation,

    A. Sobral and E.-h. Zahzah, “Matrix and tensor completion algorithms for background model initialization: A comparative evaluation,” Pattern Recognition Letters, vol. 96, pp. 22–33, 2017

    work page 2017

  3. [3]

    A novel anomaly detection scheme based on principal component classifier,

    M. Shyu, S. Chen, K. Sarinnapakorn, and L. Chang, “A novel anomaly detection scheme based on principal component classifier,” in Pro- ceedings of the IEEE foundations and new directions of data mining workshop. IEEE Press Piscataway, NJ, USA, 2003, pp. 172–179

    work page 2003

  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, 2018

    work page 2018

  5. [5]

    Tensor decompositions and applications,

    T. G. Kolda and B. W. Bader, “Tensor decompositions and applications,” SIAM review, vol. 51, no. 3, pp. 455–500, 2009

    2009

  6. [6]

    Tensor decomposition for signal processing and machine learning,

    N. D. Sidiropoulos, L. De Lathauwer, X. Fu, K. Huang, E. E. Papalex- akis, and C. Faloutsos, “Tensor decomposition for signal processing and machine learning,” IEEE Transactions on signal processing , vol. 65, no. 13, pp. 3551–3582, 2017

    work page 2017

  7. [7]

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

    work page 2022

  8. [8]

    Tensor robust principal component analysis: Exact recovery of corrupted low-rank tensors via convex optimization,

    C. Lu, J. Feng, Y . Chen, W. Liu, Z. Lin, and S. Yan, “Tensor robust principal component analysis: Exact recovery of corrupted low-rank tensors via convex optimization,” in Proceedings of the IEEE conference on computer vision and pattern recognition , 2016, pp. 5249–5257

    work page 2016

Show all 74 references
  1. [9]

    Novel methods for multilinear data completion and de-noising based on tensor-svd,

    Z. Zhang, G. Ely, S. Aeron, N. Hao, and M. Kilmer, “Novel methods for multilinear data completion and de-noising based on tensor-svd,” in Proceedings of the IEEE conference on computer vision and pattern recognition, 2014, pp. 3842–3849

    2014

  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 transactions on pattern analysis and machine intelligence, vol. 42, no. 4, pp. 925–938, 2019

    2019

  3. [11]

    Foundations of the parafac procedure: Models and conditions for an “explanatory

    R. A. Harshman et al., “Foundations of the parafac procedure: Models and conditions for an “explanatory” multi-modal factor analysis,” UCLA working papers in phonetics , vol. 16, no. 1, p. 84, 1970

    1970

  4. [12]

    Tensor rank and the ill-posedness of the best low-rank approximation problem,

    V . De Silva and L. Lim, “Tensor rank and the ill-posedness of the best low-rank approximation problem,” SIAM Journal on Matrix Analysis and Applications, vol. 30, no. 3, pp. 1084–1127, 2008

    2008

  5. [13]

    Some mathematical notes on three-mode factor analysis,

    L. R. Tucker, “Some mathematical notes on three-mode factor analysis,” Psychometrika, vol. 31, no. 3, pp. 279–311, 1966

    1966

  6. [14]

    Square deal: Lower bounds and improved relaxations for tensor recovery,

    C. Mu, B. Huang, J. Wright, and D. Goldfarb, “Square deal: Lower bounds and improved relaxations for tensor recovery,” in International Conference on Machine Learning , 2014, pp. 73–81

    2014

  7. [15]

    Tree adaptive approximation in the hier- archical tensor format,

    J. Ballani and L. Grasedyck, “Tree adaptive approximation in the hier- archical tensor format,” SIAM journal on scientific computing , vol. 36, no. 4, pp. A1415–A1431, 2014

    2014

  8. [16]

    Tensor-train decomposition,

    I. V . Oseledets, “Tensor-train decomposition,” SIAM Journal on Scien- tific Computing, vol. 33, no. 5, pp. 2295–2317, 2011

    2011

  9. [17]

    Tensor ring decomposition,

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

    2016 arXiv

  10. [18]

    Facial recog- nition using tensor-tensor decompositions,

    N. Hao, M. E. Kilmer, K. Braman, and R. C. Hoover, “Facial recog- nition using tensor-tensor decompositions,” SIAM Journal on Imaging Sciences, vol. 6, no. 1, pp. 437–463, 2013

    2013

  11. [19]

    Outlier-robust tensor PCA,

    P. Zhou and J. Feng, “Outlier-robust tensor PCA,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , July 2017

    2017

  12. [20]

    Lateral-slice sparse tensor robust principal component analysis for hyperspectral image classification,

    W. Sun, G. Yang, J. Peng, and Q. Du, “Lateral-slice sparse tensor robust principal component analysis for hyperspectral image classification,” IEEE Geoscience and Remote Sensing Letters , vol. 17, no. 1, pp. 107– 111, 2019

    2019

  13. [21]

    Tensor–tensor products with invertible linear transforms,

    E. Kernfeld, M. Kilmer, and S. Aeron, “Tensor–tensor products with invertible linear transforms,” Linear Algebra and its Applications , vol. 485, pp. 545–570, 2015

    2015

  14. [22]

    Fourth-order tensors with multidimensional discrete transforms,

    X. Liu and X. Wang, “Fourth-order tensors with multidimensional discrete transforms,” arXiv preprint arXiv:1705.01576 , 2017

    2017 arXiv

  15. [23]

    A fast algorithm for cosine transform based tensor singular value decomposition,

    W. Xu, X. Zhao, and M. Ng, “A fast algorithm for cosine transform based tensor singular value decomposition,” arXiv preprint arXiv:1902.03070, 2019

    1902 arXiv

  16. [24]

    Robust tensor completion using transformed tensor singular value decomposition,

    G. Song, M. K. Ng, and X. Zhang, “Robust tensor completion using transformed tensor singular value decomposition,” Numerical Linear Algebra with Applications , vol. 27, no. 3, p. e2299, 2020

    2020

  17. [25]

    Dictionary learning with low-rank coding coefficients for tensor completion,

    T. Jiang, X. Zhao, H. Zhang, and M. K. Ng, “Dictionary learning with low-rank coding coefficients for tensor completion,” IEEE Transactions on Neural Networks and Learning Systems , vol. 34, no. 2, pp. 932 – 946, 2023

    2023

  18. [26]

    The twist tensor nuclear norm for video completion,

    W. Hu, D. Tao, W. Zhang, Y . Xie, and Y . Yang, “The twist tensor nuclear norm for video completion,” IEEE transactions on neural networks and learning systems, vol. 28, no. 12, pp. 2961–2973, 2016

    2016

  19. [27]

    Improved robust tensor principal com- ponent analysis via low-rank core matrix,

    Y . Liu, L. Chen, and C. Zhu, “Improved robust tensor principal com- ponent analysis via low-rank core matrix,” IEEE Journal of Selected Topics in Signal Processing , vol. 12, no. 6, pp. 1378–1389, 2018

    2018

  20. [28]

    Mixed noise removal in hyperspectral image via low-fibered-rank regularization,

    Y . Zheng, T. Huang, X. Zhao, T. Jiang, T. Ma, and T. Ji, “Mixed noise removal in hyperspectral image via low-fibered-rank regularization,” IEEE Transactions on Geoscience and Remote Sensing , vol. 58, no. 1, pp. 734–749, 2019

    2019

  21. [29]

    Multi-dimensional imaging data recovery via minimizing the partial sum of tubal nuclear norm,

    T. X. Jiang, T. Z. Huang, X. L. Zhao, and L. J. Deng, “Multi-dimensional imaging data recovery via minimizing the partial sum of tubal nuclear norm,” Journal of Computational and Applied Mathematics , vol. 372, p. 112680, 2020

    2020

  22. [30]

    Weighted tensor nuclear norm minimization for tensor completion using tensor-SVD,

    Y . Mu, P. Wang, L. Lu, X. Zhang, and L. Qi, “Weighted tensor nuclear norm minimization for tensor completion using tensor-SVD,” Pattern Recognition Letters, vol. 130, pp. 4–11, 2020

    2020

  23. [31]

    t-Schatten- p norm for low-rank tensor recovery,

    H. Kong, X. Xie, and Z. Lin, “t-Schatten- p norm for low-rank tensor recovery,”IEEE Journal of Selected Topics in Signal Processing, vol. 12, no. 6, pp. 1405–1419, 2018

    2018

  24. [32]

    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 Transactions on Pattern Analysis and Machine Intelligence, vol. 43, no. 6, pp. 2133–2140, 2021

    2021

  25. [33]

    Low-rank tensor com- pletion based on self-adaptive learnable transforms,

    T. Wu, B. Gao, J. Fan, J. Xue, and W. L. Woo, “Low-rank tensor com- pletion based on self-adaptive learnable transforms,” IEEE Transactions on Neural Networks and Learning Systems , 2022

    2022

  26. [34]

    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 Transactions on Neural Networks and Learning Systems , vol. 33, no. 8, pp. 3305–3319, 2021

    2021

  27. [35]

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

    Y . Zheng, T. Huang, X. Zhao, T. Jiang, T. Ji, and T. Ma, “Tensor N-tubal rank and its convex relaxation for low-rank tensor recovery,”Information Sciences, vol. 532, pp. 170–189, 2020

    2020

  28. [36]

    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 Transactions on Image Processing , vol. 31, pp. 2433–2448, 2022

    2022

  29. [37]

    Multiplex trans- formed tensor decomposition for multidimensional image recovery,

    L. Feng, C. Zhu, Z. Long, J. Liu, and Y . Liu, “Multiplex trans- formed tensor decomposition for multidimensional image recovery,” IEEE Transactions on Image Processing , 2023

    2023

  30. [38]

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

    S. Liu, X. Zhao, J. Leng, B.-Z. Li, J.-H. Yang, and X. Chen, “Revisiting high-order tensor singular value decomposition from basic element perspective,” IEEE Transactions on Signal Processing , 2024

    2024

  31. [39]

    Tensor factorization for low-rank tensor completion,

    P. Zhou, C. Lu, Z. Lin, and C. Zhang, “Tensor factorization for low-rank tensor completion,” IEEE Transactions on Image Processing , vol. 27, no. 3, pp. 1152–1163, 2017

    2017

  32. [40]

    Unifying tensor factorization and tensor nuclear norm approaches for low-rank tensor completion,

    S. Du, Q. Xiao, Y . Shi, R. Cucchiara, and Y . Ma, “Unifying tensor factorization and tensor nuclear norm approaches for low-rank tensor completion,” Neurocomputing, vol. 458, pp. 204–218, 2021

    2021

  33. [41]

    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,” arXiv preprint arXiv:2401.11940, 2024

    2024 arXiv

  34. [42]

    A faster tensor robust PCA via tensor factorization,

    A. Wang, Z. Jin, and J. Yang, “A faster tensor robust PCA via tensor factorization,” International Journal of Machine Learning and Cybernetics, vol. 11, pp. 2771–2791, 2020. IEEE JOURNAL, VOL. XX, NO. XX, MONTH YEAR 13

    2020

  35. [43]

    Accelerating ill-conditioned low-rank matrix estimation via scaled gradient descent,

    T. Tong, C. Ma, and Y . Chi, “Accelerating ill-conditioned low-rank matrix estimation via scaled gradient descent,” Journal of Machine Learning Research, vol. 22, no. 150, pp. 1–63, 2021

    2021

  36. [44]

    Fast and provable tensor robust principal component analysis via scaled gradient descent,

    H. Dong, T. Tong, C. Ma, and Y . Chi, “Fast and provable tensor robust principal component analysis via scaled gradient descent,” Information and Inference: A Journal of the IMA , vol. 12, no. 3, pp. 1716–1758, 2023

    2023

  37. [45]

    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,” Advances in Neural Information Processing Systems , vol. 34, pp. 16 977–16 989, 2021

    2021

  38. [46]

    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 ICASSP 2023-2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2023, pp. 1–5

    2023

  39. [47]

    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 transac- tions on pattern analysis and machine intelligence , vol. 37, no. 9, pp. 1751–1763, 2015

    2015

  40. [48]

    Factorization strategies for third-order tensors,

    M. E. Kilmer and C. D. Martin, “Factorization strategies for third-order tensors,” Linear Algebra and its Applications , vol. 435, no. 3, pp. 641– 658, 2011

    2011

  41. [49]

    Robust block tensor principal component analysis,

    L. Feng, Y . Liu, L. Chen, X. Zhang, and C. Zhu, “Robust block tensor principal component analysis,” Signal Processing, vol. 166, p. 107271, 2020

    2020

  42. [50]

    Exact tensor completion using t-SVD,

    Z. Zhang and S. Aeron, “Exact tensor completion using t-SVD,” IEEE Transactions on Signal Processing, vol. 65, no. 6, pp. 1511–1526, 2016

    2016

  43. [51]

    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 Transactions on Pattern Analysis and Machine Intelligence , vol. 45, no. 9, pp. 10 990– 11 007, 2023

    2023

  44. [52]

    Deep unfolded robust PCA with application to clutter suppression in ultrasound,

    O. Solomon, R. Cohen, Y . Zhang, Y . Yang, Q. He, J. Luo, R. J. van Sloun, and Y . C. Eldar, “Deep unfolded robust PCA with application to clutter suppression in ultrasound,” IEEE transactions on medical imaging, vol. 39, no. 4, pp. 1051–1063, 2019

    2019

  45. [53]

    A deep-unfolded reference-based RPCA network for video foreground- background separation,

    H. Van Luong, B. Joukovsky, Y . C. Eldar, and N. Deligiannis, “A deep-unfolded reference-based RPCA network for video foreground- background separation,” in 2020 28th European Signal Processing Conference (EUSIPCO). IEEE, 2021, pp. 1432–1436

    2020

  46. [54]

    Interpretable neural networks for video separation: Deep unfolding RPCA with foreground masking,

    B. Joukovsky, Y . C. Eldar, and N. Deligiannis, “Interpretable neural networks for video separation: Deep unfolding RPCA with foreground masking,” IEEE Transactions on Image Processing , 2023

    2023

  47. [55]

    RPCANet: Deep unfolding RPCA based infrared small target detection,

    F. Wu, T. Zhang, L. Li, Y . Huang, and Z. Peng, “RPCANet: Deep unfolding RPCA based infrared small target detection,” in Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, 2024, pp. 4809–4818

    2024

  48. [56]

    Denise: Deep learning based robust PCA for positive semidefinite matrices,

    C. Herrera, F. Krach, A. Kratsios, P. Ruyssen, and J. Teichmann, “Denise: Deep learning based robust PCA for positive semidefinite matrices,” stat, vol. 1050, no. 5, 2020

    2020

  49. [57]

    Robust tensor CUR decompositions: Rapid low-tucker-rank tensor recovery with sparse corruptions,

    H. Cai, Z. Chao, L. Huang, and D. Needell, “Robust tensor CUR decompositions: Rapid low-tucker-rank tensor recovery with sparse corruptions,” SIAM Journal on Imaging Sciences , vol. 17, no. 1, pp. 225–247, 2024

    2024

  50. [58]

    Scene background initialization: A taxonomy,

    T. Bouwmans, L. Maddalena, and A. Petrosino, “Scene background initialization: A taxonomy,” Pattern Recognition Letters , vol. 96, pp. 3–11, 2017

    2017

  51. [59]

    Extensive benchmark and survey of modeling methods for scene background initialization,

    P.-M. Jodoin, L. Maddalena, A. Petrosino, and Y . Wang, “Extensive benchmark and survey of modeling methods for scene background initialization,” IEEE Transactions on Image Processing, vol. 26, no. 11, pp. 5244–5256, 2017

    2017

  52. [60]

    Guarantees of a preconditioned subgradient algorithm for overparameterized asymmetric low-rank ma- trix recovery,

    P. Giampouras, H. Cai, and R. Vidal, “Guarantees of a preconditioned subgradient algorithm for overparameterized asymmetric low-rank ma- trix recovery,” arXiv preprint arXiv:2410.16826 , 2024. LanlanFeng received the B.S. degree from the University of Electronic Science and Te...

    2024 arXiv

  53. [63]

    He was the recipient of the IEEE Signal Processing Society Young Author Best Paper Award in

    His research interests include biomedical and computational imaging, signal and image processing, machine learning, inverse problems, large-scale data processing, optimization, and neuroscience. He was the recipient of the IEEE Signal Processing Society Young Author Best Paper...

  54. [65]

    The first term tr(∆L ∗ Σ⋆ ∗ ∆⊤ L ) is closely related to dist(Lk, Rk; L⋆, R⋆), so we will focus on relating M1 and M2 to dist(Lk, Rk; L⋆, R⋆)

    Bound of R1: We can expand R1 as R1 =(1 − η)2 tr ∆L ∗ Σ⋆ ∗ ∆⊤ L − 2η(1 − η) tr L⋆ ∗ ∆⊤ R ∗ R♮ ∗ (R⊤ ♮ ∗ R♮)−1 ∗ Σ⋆ ∗ ∆⊤ L | {z } M1 + η2 L⋆ ∗ ∆⊤ R ∗ R♮ ∗ (R⊤ ♮ ∗ R♮)−1 ∗ Σ 1/2 ⋆ 2 F| {z } M2 . The first term tr(∆L ∗ Σ⋆ ∗ ∆⊤ L ) is closely related to dist(Lk, Rk; L⋆, R⋆), so we...

  55. [66]

    Bound of R2: Lemma 3 implies that ∆S = Sk+1 −S ⋆ is an α-sparse tensor. Thus, by the properties tr(A∗B ) ≤ ∥A∥2∥B∥∗; ∥A∥∗ ≤ √ R∥A∥F for A with the tubal rank R and Lemma 5 ; Lemma 3 and ∥A ∗ B∥F ≤ ∥A∥2∥B∥F; Lemma 11, 8 and 6 and denote ζk+1 = ζkτ = ζ1τ k := 3√I1I2 µRτ kσmin(X⋆...

  56. [67]

    IEEE JOURNAL, VOL

    Bound of R3: Similar to R2, we have | tr(∆S ∗ R♮ ∗ (R⊤ ♮ ∗ R♮)−1 ∗ Σ⋆ ∗ (R⊤ ♮ ∗ R♮)−1 ∗ R⊤ ♮ ∗ ∆R ∗ L⊤ ⋆ )| ≤ ∥∆S ∥2∥R♮ ∗ (R⊤ ♮ ∗ R♮)−1 ∗ Σ⋆ ∗ (R⊤ ♮ ∗ R♮)−1 ∗ R⊤ ♮ ∗ ∆R ∗ L⊤ ⋆ ∥∗ ≤ αI3 p I1I2 √ R∥∆S ∥∞∥R♮ ∗ (R⊤ ♮ ∗ R♮)−1 ∗ Σ⋆ ∗ (R⊤ ♮ ∗ R♮)−1 ∗ R⊤ ♮ ∗ ∆R ∗ L⊤ ⋆ ∥F ≤ αI3 p I1I2R...

  57. [68]

    Bound of R4: ∥∆S ∗ R♮ ∗ (R⊤ ♮ ∗ R♮)−1 ∗ Σ 1/2 ⋆ ∥2 F ≤ R∥∆S ∗ R♮ ∗ (R⊤ ♮ ∗ R♮)−1 ∗ Σ 1/2 ⋆ ∥2 2 ≤ R∥∆S ∥2 2∥R♮ ∗ (R⊤ ♮ ∗ R♮)−1 ∗ Σ 1/2 ⋆ ∥2 2 ≤ 4I3 2α2I1I2Rζ 2 k+1∥R♮ ∗ (R⊤ ♮ ∗ R♮)−1 ∗ Σ 1/2 ⋆ ∥2 2 ≤ 36I3 2α2µ2R3τ 2k 1 (1 − ε)2 σ2 min(X⋆). Hence, R4 ≤ 36I3 2η2α2µ2R3τ 2k 1 (1 −...

  58. [69]

    Lemma 13

    The proof is finished by substituting τ = 1 − 0.8η ≤ 1 − 0.6η. Lemma 13. If dist(Lk, Rk; L⋆, R⋆) ≤ ε√I3 τ kσmin(X⋆), p I1∥∆L ∗ Σ 1/2 ⋆ ∥2,∞ ∨ p I2∥∆R ∗ Σ 1/2 ⋆ ∥2,∞ ≤ p µRτ kσmin(X⋆), (42) IEEE JOURNAL, VOL. XX, NO. XX, MONTH YEAR 25 then p I1∥(Lk+1 ∗ Qk+1 − L⋆) ∗ Σ 1/2 ⋆ ∥2,∞...

  59. [70]

    Bound of T1: T1 ≤ (1 − η) q µR I1 τ kσmin(X⋆) directly follows from the assumption of this lemma

  60. [71]

    Together, we have T2 ≤ η∥L⋆ ∗ Σ −1/2 ⋆ ∥2,∞∥∆R ∗ Σ 1/2 ⋆ ∥2∥R♮ ∗ (R⊤ ♮ ∗ R♮)−1 ∗ Σ 1/2 ⋆ ∥2 ≤ η ε 1 − ε r µR I1 τ kσmin(X⋆)

    Bound of T2: Assumption 1 implies ∥L⋆ ∗ Σ −1/2 ⋆ ∥2,∞ ≤ q µR I1 , Lemma 6 implies ∥∆R ∗ Σ 1/2 ⋆ ∥2 ≤ ετ kσmin(X⋆), and Lemma 8 implies ∥R♮ ∗ (R⊤ ♮ ∗ R♮)−1 ∗ Σ 1/2 ⋆ ∥2 ≤ 1 1−ε. Together, we have T2 ≤ η∥L⋆ ∗ Σ −1/2 ⋆ ∥2,∞∥∆R ∗ Σ 1/2 ⋆ ∥2∥R♮ ∗ (R⊤ ♮ ∗ R♮)−1 ∗ Σ 1/2 ⋆ ∥2 ≤ η ε 1 ...

  61. [72]

    Thus, by Lemma 5, Lemma 3 and 11, we get T3 ≤ η∥∆S ∥2,∞∥R♮ ∗ (R⊤ ♮ ∗ R♮)−1 ∗ Σ 1/2 ⋆ ∥2 ≤ η √αI2I3 1 − ε ∥∆S ∥∞ ≤ 2η √αI2I3 1 − ε ζk+1 ≤ 6η √αI3 1 − ε 1√I1 µRτ kσmin(X⋆)

    Bound of T3: By Lemma 3, supp(∆S ) ⊆ supp(S⋆), which implies that ∆S is an α-sparse tensor. Thus, by Lemma 5, Lemma 3 and 11, we get T3 ≤ η∥∆S ∥2,∞∥R♮ ∗ (R⊤ ♮ ∗ R♮)−1 ∗ Σ 1/2 ⋆ ∥2 ≤ η √αI2I3 1 − ε ∥∆S ∥∞ ≤ 2η √αI2I3 1 − ε ζk+1 ≤ 6η √αI3 1 − ε 1√I1 µRτ kσmin(X⋆). Putting three ...

  62. [73]

    Bound with Qk+1: Note that Qk+1 does exist, according to Lemma 12 and 1. Applying (44), (45) and Lemma 10, we have ∥(Lk+1 ∗ Qk+1 − L⋆) ∗ Σ 1/2 ⋆ ∥2,∞ ≤ ∥(Lk+1 ∗ Qk − L⋆) ∗ Σ 1/2 ⋆ ∥2,∞ + ∥Lk+1(Qk+1 − Qk) ∗ Σ 1/2 ⋆ ∥2,∞ = ∥(Lk+1 ∗ Qk − L⋆) ∗ Σ 1/2 ⋆ ∥2,∞ + ∥Lk+1 ∗ QkΣ −1/2 ⋆ Σ ...

  63. [74]

    The proof is concluded by substituting τ = 1 − 0.6η

    A similar result can be derived for ∥(Rk+1 ∗ Q−⊤ k+1 − R⋆) ∗ Σ 1/2 ⋆ ∥2,∞. The proof is concluded by substituting τ = 1 − 0.6η. Now we have all the necessary ingredients, we proceed to prove Theorem 2 (local linear convergence). IEEE JOURNAL, VOL. XX, NO. XX, MONTH YEAR 26 Pro...

  64. [2016]

    Learnable Scaled Gradient Descent for Guaranteed Robust Tensor PCA

    A paper he co-authored won a Best Student Paper Award at the IEEE International Symposium on Biomedical Imaging (ISBI) 2018 and other papers were award finalists at the IEEE International Workshop on Machine Learning for Signal Processing (MLSP) 2017, ISBI 2020, and Optica Ima...

    2018

  65. [2019]

    IEEE JOURNAL, VOL

    He is the APSIPA Distinguished Lecturer 2022-2023. IEEE JOURNAL, VOL. XX, NO. XX, MONTH YEAR 14 Saiprasad Ravishankar (Senior Member, IEEE) received the B.Tech. degree in Electrical Engineering from the Indian Institute of Technology Madras, Chennai, India, in 2008, and the M....

    2022

  66. [2023]

    Tensor Computation for Data Analysis

    His research interest is tensor for data processing. He has published over 100 papers, co-authored two books “Tensor Computation for Data Analysis” by Springer and “Tensor Regression” by Foundations and Trends® in Machine Learning of NOW Publishers, and edited one book “Tensor...

    2022

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.