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arxiv: 2508.03049 · v2 · submitted 2025-08-05 · 🧮 math.NA · cs.NA

Low-rankness and Smoothness Meet Subspace: A Unified Tensor Regularization for Hyperspectral Image Super-resolution

Jun Zhang , Chao Yi , Mingxi Ma , Mengling He , Chao Wang This is my paper

Pith reviewed 2026-05-19 01:17 UTC · model grok-4.3

classification 🧮 math.NA cs.NA
keywords hyperspectral imagesuper-resolutiontensor regularizationlow-ranknesslocal smoothnesssubspace frameworktensor nuclear norm
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The pith

A unified tensor regularizer improves hyperspectral image super-resolution by applying low-rank and smoothness constraints in a subspace.

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

The paper proposes a method to enhance the resolution of hyperspectral images by using a new regularization technique. Hyperspectral images capture detailed information across many spectral bands but are often low resolution, making super-resolution important for applications like remote sensing. The approach introduces JLRST to combine low-rankness and local smoothness priors within a subspace framework, applying them to coefficient tensors rather than the full data to gain efficiency. Gradients are computed along all modes of clustered coefficients to capture correlations, and a logarithmic tensor nuclear norm is used to reduce bias in the regularization. An ADMM algorithm solves the model with proven convergence, leading to better performance than existing methods.

Core claim

The central discovery is a joint low-rank and smoothness tensor (JLRST) regularizer that encodes these priors under a subspace framework for hyperspectral image super-resolution. Gradients of the clustered coefficient tensors are computed along all three modes to exploit spectral correlations and nonlocal similarities. Priors are enforced on the subspace coefficients for improved accuracy and efficiency, and the mode-3 logarithmic tensor nuclear norm is applied to gradient tensors to mitigate bias from the standard tensor nuclear norm. The model is solved using the alternating direction method of multipliers with convergence guarantees.

What carries the argument

JLRST, the unified tensor regularizer that jointly applies low-rankness and local smoothness to gradients of clustered subspace coefficient tensors using mode-3 logarithmic tensor nuclear norm.

Load-bearing premise

Low-rankness and smoothness properties of the hyperspectral data are adequately preserved when the priors are applied only to the coefficients in the subspace representation rather than the original tensor.

What would settle it

Demonstrating on standard benchmark datasets that a competing method achieves higher peak signal-to-noise ratio or structural similarity index without using the subspace framework would challenge the claimed superiority in accuracy.

Figures

Figures reproduced from arXiv: 2508.03049 by Chao Wang, Chao Yi, Jun Zhang, Mengling He, Mingxi Ma.

Figure 1
Figure 1. Figure 1: Illustration of the proposed JLRST method. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Plots of PSNR against parameters L and N, respectively. TABLE I SELECTED PARAMETER SETS FOR THE PROPOSED METHOD Image α1 α2 α3 µ Pavia University 0.3 0.03 0.009 0.05 Indian Pines 0.02 0.03 0.03 0.04 Balloons 0.25 0.2 0.1 0.09 University of Houston 0.08 0.2 0.05 0.05 To investigate the impact of the subspace dimension L, we plot the PSNR values against L for four test images, as presented in [PITH_FULL_IMA… view at source ↗
Figure 3
Figure 3. Figure 3: The plots of PSNR (top) and UIQI (bottom) values versus the spectral band for four test images. (a) Pavia University, (b) Indian Pines, (c) Balloons, [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The first row represents the false color images of “Pavia University” generated by bands (R: 50, G: 66, and B: 69), and the second row displays the [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The first row shows the false color images of “Indian Pines” generated using bands (R: 60, G: 82, and B: 92), and the second row displays the error [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The first row shows the false color images of “Balloons” gained by bands (R: 16, G: 1, and B: 25), while the second row presents the error images [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The first row lists the false color images of “University of Houston” generated by bands (R: 29, G: 32, and B: 21), and the second row displays the [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Relative error [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
read the original abstract

Hyperspectral image super-resolution (HSI-SR) has emerged as a challenging yet critical problem in remote sensing. Existing approaches primarily focus on regularization techniques that leverage low-rankness and local smoothness priors. Recently, correlated total variation has been introduced for tensor recovery, integrating these priors into a single regularization framework. Direct application to HSI-SR, however, is hindered by the high spectral dimensionality of hyperspectral data. In this paper, we propose a unified tensor regularizer, called JLRST, which jointly encodes low-rankness and local smoothness priors under a subspace framework. Specifically, we compute the gradients of the clustered coefficient tensors along all three tensor modes to fully exploit spectral correlations and nonlocal similarities in HSI. By enforcing priors on subspace coefficients rather than the entire HR-HSI data, the proposed method achieves improved computational efficiency and accuracy. Furthermore, to mitigate the bias introduced by the tensor nuclear norm (TNN), we introduce the mode-3 logarithmic TNN to process gradient tensors. An alternating direction method of multipliers with proven convergence is developed to solve the proposed model. Experimental results demonstrate that our approach significantly outperforms state-of-the-art model-based methods in HSI-SR.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 1 minor

Summary. The paper proposes JLRST, a unified tensor regularizer for hyperspectral image super-resolution that jointly encodes low-rankness and local smoothness priors under a subspace framework. It computes gradients of clustered coefficient tensors along all three modes to exploit spectral correlations and nonlocal similarities, introduces a mode-3 logarithmic TNN to mitigate bias from standard TNN, and solves the resulting model via ADMM with a proven convergence guarantee. Experiments are reported to show significant outperformance over state-of-the-art model-based HSI-SR methods.

Significance. If the central claims hold, the work would provide a computationally lighter regularization strategy for HSI-SR by moving low-rank and smoothness enforcement to the subspace coefficients rather than the full tensor, while retaining a convergent solver. The combination of established tensor priors with a logarithmic nuclear-norm variant and the subspace reduction could be of interest to the numerical analysis community working on tensor recovery and remote-sensing imaging.

major comments (2)
  1. [Abstract and model description] Abstract and model description: the central premise that 'enforcing priors on subspace coefficients rather than the entire HR-HSI data' simultaneously improves accuracy and reduces computational cost is stated as the key advantage but is neither theoretically derived nor supported by an ablation that compares enforcement on the full tensor versus the subspace coefficients on identical data and metrics. This premise is load-bearing for the claimed superiority and efficiency gains.
  2. [Abstract] Abstract: the claim of 'significantly outperforms state-of-the-art model-based methods' is made without reference to specific quantitative metrics, datasets, or error bars in the provided text, making independent verification of the experimental superiority difficult from the summary alone.
minor comments (1)
  1. The definition and exact formulation of the JLRST regularizer and the mode-3 logarithmic TNN would benefit from explicit equations early in the manuscript to aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment point by point below, providing clarifications based on the manuscript and proposing revisions where they strengthen the presentation without misrepresenting the work.

read point-by-point responses

  1. Referee: [Abstract and model description] Abstract and model description: the central premise that 'enforcing priors on subspace coefficients rather than the entire HR-HSI data' simultaneously improves accuracy and reduces computational cost is stated as the key advantage but is neither theoretically derived nor supported by an ablation that compares enforcement on the full tensor versus the subspace coefficients on identical data and metrics. This premise is load-bearing for the claimed superiority and efficiency gains.

    Authors: The manuscript explicitly notes that direct application of the regularizer to full HR-HSI data is hindered by high spectral dimensionality. Projecting to a subspace yields coefficient tensors of much lower rank and size (typically reducing spectral dimension from ~30 to a small number of basis vectors), which directly reduces the cost of gradient computations, clustering, and mode-3 logarithmic TNN operations. Accuracy benefits arise because the subspace isolates the dominant spectral correlations, enabling the joint low-rank and smoothness priors on clustered coefficients to capture nonlocal similarities more cleanly than on the noisy full tensor. While the original submission does not contain a side-by-side ablation on identical data and metrics, we will add such an experiment in the revision to supply the requested empirical support. revision: yes

  2. Referee: [Abstract] Abstract: the claim of 'significantly outperforms state-of-the-art model-based methods' is made without reference to specific quantitative metrics, datasets, or error bars in the provided text, making independent verification of the experimental superiority difficult from the summary alone.

    Authors: The abstract is intentionally concise. The full manuscript reports concrete results in the Experiments section, including PSNR/SSIM tables on standard HSI-SR benchmarks (CAVE, Harvard, etc.) with comparisons to recent model-based methods and, where relevant, variability measures. To improve standalone readability of the abstract, we will insert a brief quantitative highlight (e.g., average PSNR gain) while respecting length constraints. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper introduces JLRST as a design choice that applies established low-rank and smoothness priors to subspace coefficients rather than the full tensor, solved via ADMM. This is presented as an engineering decision for efficiency and accuracy without reducing any claimed result to a self-defined quantity, fitted parameter renamed as prediction, or load-bearing self-citation chain. The model equations build on standard tensor nuclear norm variants and gradient computations without the target performance metrics being tautologically forced by the inputs. The derivation remains self-contained against external benchmarks and prior tensor recovery literature.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 2 invented entities

Only the abstract is available, so the ledger is necessarily incomplete. The method rests on standard tensor low-rank and smoothness assumptions plus the unproven claim that subspace projection preserves accuracy while reducing cost. No machine-checked proofs or external benchmarks are mentioned.

free parameters (1)
  • regularization weights
    Trade-off parameters balancing low-rank, smoothness, and data-fidelity terms; must be chosen or tuned for each dataset.
axioms (1)
  • domain assumption Subspace coefficients capture the essential spectral correlations and nonlocal similarities of the original hyperspectral data.
    Invoked when the authors move all regularization from the full tensor to the clustered subspace coefficients.
invented entities (2)
  • JLRST regularizer no independent evidence
    purpose: Jointly encode low-rankness and local smoothness under subspace framework
    Newly proposed unified tensor regularizer; no independent evidence supplied in abstract.
  • mode-3 logarithmic TNN no independent evidence
    purpose: Mitigate bias of standard tensor nuclear norm on gradient tensors
    Introduced specifically for processing the gradient tensors; no external validation given.

pith-pipeline@v0.9.0 · 5756 in / 1508 out tokens · 44132 ms · 2026-05-19T01:17:26.587354+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

55 extracted references · 55 canonical work pages

  1. [1]

    Hyperspectral face recognition with spatiospectral information fusion and PLS regression,

    M. Uzair, A. Mahmood, and A. Mian, “Hyperspectral face recognition with spatiospectral information fusion and PLS regression,” IEEE Trans- actions on Image Processing, vol. 24, no. 3, pp. 1127-1137, Mar. 2015

    work page 2015

  2. [2]

    Meta-Learning based hyperspectral target detection using Siamese network,

    Y . Wang, X. Chen, F. Wang, M. Song, and C. Yu, “Meta-Learning based hyperspectral target detection using Siamese network,” IEEE Transactions on Geoscience and Remote Sensing, vol. 60, 2022, Art. no. 5527913

    work page 2022

  3. [3]

    Hyperspectral image classifi- cation via cascaded spatial cross-attention network,

    B. Zhang, Y . Chen, S. Xiong, and X. Lu, “Hyperspectral image classifi- cation via cascaded spatial cross-attention network,” IEEE Transactions on Image Processing, vol. 34, pp. 899-913, 2025. 12

    work page 2025

  4. [4]

    An asymptotic multiscale symmetric fusion network for hyperspectral and multispectral image fusion,

    S. Liu, T. Shao, S. Liu, B. Li, and Y .-D. Zhang, “An asymptotic multiscale symmetric fusion network for hyperspectral and multispectral image fusion,” IEEE Transactions on Geoscience and Remote Sensing, vol. 63, 2025, Art. no. 5503016

    work page 2025

  5. [5]

    Hyperspectral image super- resolution meets deep learning: A survey and perspective,

    X. Wang, Q. Hu, Y . Cheng, and J. Ma, “Hyperspectral image super- resolution meets deep learning: A survey and perspective,” IEEE/CAA Journal of Automatica Sinica, vol. 10, no. 8, pp. 1668-1691, Aug. 2023

    work page 2023

  6. [6]

    Hyperspectral and multispectral image fusion: When model- driven meet data-driven strategies

    H.-F. Yan, Y .-Q. Zhao, J. C.-W. Chan, S. G. Kong, N. EI-Bendary, and M. Reda, “Hyperspectral and multispectral image fusion: When model- driven meet data-driven strategies” Information Fusion. vol. 116, Apr. 2025, Art. no. 102803

    work page 2025

  7. [7]

    A convex formulation for hyperspectral image superresolution via subspace-based regularization,

    M. Sim ˜oes, J. Bioucas-Dias, L. B. Almeida, and J. Chanussot, “A convex formulation for hyperspectral image superresolution via subspace-based regularization,” IEEE Transactions on Geoscience and Remote Sensing, vol. 53, no. 6, pp. 3373-3388, Jun. 2015

    work page 2015

  8. [8]

    Hyperspectral image super-resolution via subspace- based low tensor multi-rank regularization,

    R. Dian and S. Li, “Hyperspectral image super-resolution via subspace- based low tensor multi-rank regularization,” IEEE Transactions on Image Processing, vol. 28, no. 10, pp. 5135-5146, Oct. 2019

    work page 2019

  9. [9]

    Hyperspec- tral super-resolution: A coupled tensor factorization approach,

    C. I. Kanatsoulis, X. Fu, N. D. Sidiropoulos, and W. K. Ma, “Hyperspec- tral super-resolution: A coupled tensor factorization approach,” IEEE Transactions on Signal Processing, vol. 66, no. 24, pp. 6503-6517, Dec. 2018

    work page 2018

  10. [11]

    NonRegSR- Net: A nonrigid registration hyperspectral super-resolution network,

    K. Zheng, L. Gao, D. Hong, B. Zhang, and J. Chanussot, “NonRegSR- Net: A nonrigid registration hyperspectral super-resolution network,” IEEE Transactions on Geoscience and Remote Sensing, vol. 60, 2022, Art. no. 5520216

    work page 2022

  11. [12]

    PSRT: Pyramid shuffle-and-reshuffle transformer for multispectral and hyperspectral image fusion,

    S.-Q. Deng, L.-J. Deng, X. Wu, R. Ran, D. Hong, and G. Vivone, “PSRT: Pyramid shuffle-and-reshuffle transformer for multispectral and hyperspectral image fusion,” IEEE Transactions on Geoscience and Remote Sensing, vol. 61, 2023, Art. no. 5503715

    work page 2023

  12. [13]

    High-resolution hyperspectral imaging via matrix factor- ization,

    R. Kawakami, Y . Matsushita, J. Wright, M. Ben-Ezra, Y .-W. Tai, and K. Ikeuchi, “High-resolution hyperspectral imaging via matrix factor- ization,” CVPR 2011, Colorado Springs, CO, USA, Jun. 2011, pp. 2329–2336

    work page 2011

  13. [14]

    Spatial and spectral image fusion using sparse matrix factorization,

    B. Huang, H. Song, H. Cui, J. Peng, and Z. Xu, “Spatial and spectral image fusion using sparse matrix factorization,” IEEE Transactions on Geoscience and Remote Sensing, vol. 52, no. 3, pp. 1693-1704, Mar. 2014

    work page 2014

  14. [15]

    Hyperspectral image super-resolution via non-negative structured sparse representation,

    W. Dong et al., “Hyperspectral image super-resolution via non-negative structured sparse representation,” IEEE Transactions on Image Process- ing, vol. 25, no. 5, pp. 2337-2352, May. 2016

    work page 2016

  15. [16]

    Self-similarity constrained sparse representation for hyperspectral image super-resolution,

    X.-H. Han, B. Shi, and Y . Zheng, “Self-similarity constrained sparse representation for hyperspectral image super-resolution,” IEEE Transac- tions on Image Processing, vol. 27, no. 11, pp. 5625-5637, Nov. 2018

    work page 2018

  16. [17]

    Spatial-spectral structured sparse low-rank representation for hyper- spectral image super-resolution,

    J. Xue, Y .-Q. Zhao, Y . Bu, W. Liao, J. C.-W. Chan, and W. Philips, “Spatial-spectral structured sparse low-rank representation for hyper- spectral image super-resolution,” IEEE Transactions on Image Process- ing, vol. 30, pp. 3084–3097, Feb. 2021

    work page 2021

  17. [18]

    Fusion of hyperspectral-multispectral images joining spatial-spectral dual-dictionary and structured sparse low-rank repre- sentation

    N, Chen, et al. “Fusion of hyperspectral-multispectral images joining spatial-spectral dual-dictionary and structured sparse low-rank repre- sentation.” International Journal of Applied Earth Observation and Geoinformation, vol. 104, Dec. 2021, Art. no. 102570

    work page 2021

  18. [19]

    Hyperspectral image super- resolution via nonlocal low-rank tensor approximation and total variation regularization,

    Y . Wang, X. Chen, Z. Han, and S. He, “Hyperspectral image super- resolution via nonlocal low-rank tensor approximation and total variation regularization,” Remote Sensing, vol. 9, no. 12, 2017, Art. no. 1286

    work page 2017

  19. [20]

    Hyperspectral image fusion with a new hybrid regularization,

    J. Zhang, Z. Liu, and M. Ma, “Hyperspectral image fusion with a new hybrid regularization,” Computational and Applied Mathematics, vol. 41, no. 6, pp. 241, Sep. 2022

    work page 2022

  20. [21]

    Total variation regularized multi-matrices weighted Schatten p-norm minimization for image denoising,

    Z. Tan and H. Yang, “Total variation regularized multi-matrices weighted Schatten p-norm minimization for image denoising,” Applied Mathemat- ical Modelling, vol. 124, pp. 518-531, Dec. 2023

    work page 2023

  21. [22]

    Poisson tensor completion with transformed correlated total variation regularization,

    Q. Feng, J. Hou, W. Kong, C. Xu, and J. Wang “Poisson tensor completion with transformed correlated total variation regularization,” Pattern Recognition, vol. 156, Dec. 2024. Art. no. 110735

    work page 2024

  22. [23]

    Image denoising based on the adaptive weighted T V p regularization,

    Z.-F. Pang, H.-L. Zhang, S. Luo, and T. Zeng, “Image denoising based on the adaptive weighted T V p regularization,” Signal Processing, vol. 167, Feb. 2020. Art. no. 107325

    work page 2020

  23. [24]

    Poisson image restoration using a novel directional T V p regularization

    J. Zhang, P. Li, J. Yang, M. Ma, and C. Deng, “Poisson image restoration using a novel directional T V p regularization”, Signal Processing, vol. 193, Apr. 2022. Art. no. 108407

    work page 2022

  24. [25]

    Hyperspectral and multispectral image fusion using factor smoothed tensor ring de- composition,

    Y . Chen, J. Zeng, W. He, X.-L. Zhao, and T.-Z. Huang, “Hyperspectral and multispectral image fusion using factor smoothed tensor ring de- composition,” IEEE Transactions on Geoscience and Remote Sensing, vol. 60, 2022, Art. no. 5515417

    work page 2022

  25. [26]

    Hyperspectral and multispectral image fusion via logarithmic low-rank tensor ring decomposition,

    J. Zhang, L. Zhu, C. Deng, and S. Li, “Hyperspectral and multispectral image fusion via logarithmic low-rank tensor ring decomposition,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 17, pp. 11583-11597, Jun. 2024

    work page 2024

  26. [27]

    Hyperspectral sparse fusion us- ing adaptive total variation regularization and superpixel-based weighted nuclear norm

    J. Lu, J. Zhang, C. Wang, and C. Deng, “Hyperspectral sparse fusion us- ing adaptive total variation regularization and superpixel-based weighted nuclear norm.” Signal Processing. vol. 220, Jul. 2024. Art. no. 109449

    work page 2024

  27. [28]

    Adaptive total variation and second-order total variation-based model for low-rank tensor completion,

    X. Li, T.-Z. Huang, X.-L Zhao, T.-Y . Ji, Y .-B. Zheng, and L.-J. Deng “Adaptive total variation and second-order total variation-based model for low-rank tensor completion,” Numerical Algorithms, vol. 86, pp. 1–24, 2021

    work page 2021

  28. [29]

    Hyperspectral image denoising with weighted nonlocal low-rank model and adaptive total variation regularization,

    Y . Chen, W. Cao, L. Pang, and X. Cao, “Hyperspectral image denoising with weighted nonlocal low-rank model and adaptive total variation regularization,” IEEE Transactions on Geoscience and Remote Sensing. vol. 60, 2022, Art. no. 5544115

    work page 2022

  29. [30]

    Robust subspace segmentation by low- rank representation,

    G. Liu, Z. Lin, and Y . Yu, “Robust subspace segmentation by low- rank representation,” Proceedings of the 27th international conference on machine learning (ICML-10), 2010, pp. 663-670

    work page 2010

  30. [31]

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

    Z. Lin, R. Liu, and Z. Su, “Linearized alternating direction method with adaptive penalty for low-rank representation,” Advances in neural information processing systems, Dec. 2011, pp. 612-620

    work page 2011

  31. [32]

    Hyperspectral and multispectral image fusion via superpixel-based weighted nuclear norm minimiza- tion,

    J. Zhang, J. Lu, C. Wang, and S. Li, “Hyperspectral and multispectral image fusion via superpixel-based weighted nuclear norm minimiza- tion,” IEEE Transactions on Geoscience and Remote Sensing, vol. 61, 2023, Art. no. 5521612

    work page 2023

  32. [33]

    Hyperspectral- multispectral image fusion via tensor ring and subspace decomposi- tions,

    H. Xu, M. Qin, S. Chen, Y . Zheng, and J. Zheng, “Hyperspectral- multispectral image fusion via tensor ring and subspace decomposi- tions,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol 14, pp. 8823–8837, Aug. 2021

    work page 2021

  33. [34]

    Hyperspectral image super- resolution via adaptive factor group sparsity regularization-based sub- space representation,

    Y . Peng, W. Li, X. Luo, and J. Du, “Hyperspectral image super- resolution via adaptive factor group sparsity regularization-based sub- space representation,” Remote Sensing, vol. 15, no. 19, 2023, Art. no. 4847

    work page 2023

  34. [35]

    H. Xu, C. Fang, Y . Ge, Y . Gu, and J. Zheng, ”Cascade-transform-based tensor nuclear norm for hyperspectral image super-resolution,” IEEE Transactions on Geoscience and Remote Sensing, vol. 62, pp. 1-16, 2024

    work page 2024

  35. [36]

    Hyperspectral image fusion via a novel generalized tensor nuclear norm regularization,

    R. Dian, Y . Liu, and S. Li, “Hyperspectral image fusion via a novel generalized tensor nuclear norm regularization,” IEEE Transactions on Neural Networks and Learning Systems, vol. 36, no. 4, pp. 7437-7448, Apr. 2025

    work page 2025

  36. [37]

    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 Journal of Selected Topics in Signal Processing, vol. 12, no. 6, pp. 1364-1377, Dec. 2018

    work page 2018

  37. [38]

    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

    work page 2021

  38. [39]

    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. 10990- 11007, Sep. 2023

    work page 2023

  39. [40]

    Fast hyperspectral image denoising and inpainting based on low-rank and sparse representations,

    L. Zhuang and J. M. Bioucas-Dias, “Fast hyperspectral image denoising and inpainting based on low-rank and sparse representations,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 11, no. 3, pp. 730–742, Mar. 2018

    work page 2018

  40. [41]

    K-means++: The advantages of careful seed- ing,

    A. David and V . Sergei, “K-means++: The advantages of careful seed- ing,” in Proc. Eighteenth Annu. ACM-SIAM Symp. Discrete Algorithms SODA’07, pp. 1027–1035, Jan. 2007

    work page 2007

  41. [42]

    Multiplicative denoising based on linearized alternating direction method using discrepancy function constraint,

    D.-Q. Chen and Y . Zhou, “Multiplicative denoising based on linearized alternating direction method using discrepancy function constraint,” Journal of Scientific Computing, vol. 60, no. 3, pp. 483–504, Sep. 2014

    work page 2014

  42. [43]

    Fast fusion of multi-band images based on solving a Sylvester equation,

    Q. Wei, N. Dobigeon, and J.-Y . Tourneret, “Fast fusion of multi-band images based on solving a Sylvester equation,” IEEE Transactions on Image Processing, vol. 24, no. 11, pp. 4109–4121, Nov. 2015

    work page 2015

  43. [44]

    Multispectral images denoising by intrinsic tensor sparsity regularization,

    Q. Xie et al., “Multispectral images denoising by intrinsic tensor sparsity regularization,” in Proceedings of the IEEE conference on computer vision and pattern recognition, 2016, pp. 1692–1700

    work page 2016

  44. [45]

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

    Y .-B. Zheng, T.-Z. Huang, X.-L. Zhao, T.-X. Jiang, T.-H. Ma, and T.-Y . 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, Jan. 2020

    work page 2020

  45. [46]

    Exploiting spectral and spatial information in 13 hyperspectral urban data with high resolution,

    F. Dell’Acqua, P. Gamba, A. Ferrari, J. A. Palmason, J. A. Benedik- tsson, and K. Arnason, “Exploiting spectral and spatial information in 13 hyperspectral urban data with high resolution,” in IEEE Geoscience and Remote Sensing Letters, vol. 1, no. 4, pp. 322-326, Oct. 2004,

    work page 2004

  46. [47]

    Imaging spectroscopy and the airborne visi- ble/infrared imaging spectrometer (A VIRIS),

    R. O. Green et al., “Imaging spectroscopy and the airborne visi- ble/infrared imaging spectrometer (A VIRIS),” Remote Sensing of En- vironment, vol. 65, no. 3, pp. 227–248, Sep. 1998

    work page 1998

  47. [48]

    Generalized assorted pixel camera: postcapture control of resolution, dynamic range, and spectrum,

    F. Yasuma, T. Mitsunaga, D. Iso, and S. K. Nayar, “Generalized assorted pixel camera: postcapture control of resolution, dynamic range, and spectrum,” IEEE Transactions on Image Processing, vol. 19, no. 9, pp. 2241-2253, Sep. 2010

    work page 2010

  48. [49]

    2018 IEEE GRSS data fusion contest: Multimodal land use classification [technical committees],

    B. Le Saux, N. Yokoya, R. Hansch, and S. Prasad, “2018 IEEE GRSS data fusion contest: Multimodal land use classification [technical committees],” IEEE geoscience and remote sensing magazine, vol. 6, no. 1, pp. 52–54, 2018

    work page 2018

  49. [50]

    Hyperspectral super- resolution via coupled tensor ring factorization

    W. He, Y . Chen, N. Yokoya, C. Li, and Q. Zhao, “Hyperspectral super- resolution via coupled tensor ring factorization”, Pattern Recognition, vol. 122, 2022. Art. no. 108280

    work page 2022

  50. [51]

    Image quality assessment: from error visibility to structural similarity

    Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity”, IEEE Transactions on Image Processing, vol. 13, no. 4, pp. 600-612, Apr. 2004

    work page 2004

  51. [52]

    Quality of high resolution synthesised images: Is there a simple criterion?

    L. Wald, “Quality of high resolution synthesised images: Is there a simple criterion?” in Third conference” Fusion of Earth data: merging point measurements, raster maps and remotely sensed images, 2000, pp. 99–103

    work page 2000

  52. [53]

    Discrimination among semi-arid landscape endmembers using the spectral angle mapper (SAM) algorithm,

    R. H. Yuhas, A. F. H. Goetz, and J. W. Boardman, “Discrimination among semi-arid landscape endmembers using the spectral angle mapper (SAM) algorithm,” JPL, Summaries of the Third Annual JPL Airborne Geoscience Workshop, 1992, pp. 147–149

    work page 1992

  53. [54]

    A universal image quality index,

    Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Processing Letters, vol. 9, no. 3, pp. 81–84, Mar. 2002

    work page 2002

  54. [55]

    Fusing hyperspectral and multispectral images via coupled sparse tensor factorization,

    S. Li, R. Dian, L. Fang, and J. M. Bioucas-Dias, “Fusing hyperspectral and multispectral images via coupled sparse tensor factorization,” IEEE Transactions on Image Processing, vol. 27, no. 8, pp. 4118-4130, Aug. 2018

    work page 2018

  55. [56]

    Hyper- spectral image superresolution using unidirectional total variation with Tucker decomposition,

    T. Xu, T. -Z. Huang, L. -J. Deng, X. -L. Zhao, and J. Huang, “Hyper- spectral image superresolution using unidirectional total variation with Tucker decomposition,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 13, pp. 4381-4398, 2020

    work page 2020