Skip to main content
Springer Nature Link
Log in

Tensor subspace learning and folded-concave function regularization for hyperspectral anomaly detection

  • Published:
The Journal of Supercomputing Aims and scope Submit manuscript

Abstract

Hyperspectral anomaly detection focuses on identifying and localizing the anomalous targets in remote sensing. The complex scenarios in hyperspectral images make it more difficult to effectively distinguish anomalous objects from background data, especially in noisy environments. Currently, available low-rank representation models capable of effective denoising often unfold hyperspectral cubic data into two-dimensional form, but this causes the structural knowledge to be lost. To surmount the above disadvantages, we propose a tensor subspace-based learning strategy with folded-concave regularization for hyperspectral anomaly detection. First, hyperspectral data undergo initial preprocessing through dimensional reduction and robust tensor principal component analysis to generate a dictionary representing the background. Then, a tensor subspace learning approach aims to factorize hyperspectral data into the background and anomaly tensors, in which the folded-concave function is leveraged to minimize minor components for denoising. Next, \(l_{F,1}\) norm on tensor is used to extract abnormal information from hyperspectral data. Finally, comprehensive experiments on several real datasets show that the proposed algorithm performs better than the comparative benchmark methods in detection performance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Algorithm 1
Algorithm 2
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Data availability

No datasets were generated or analyzed during the current study.

References

  1. Peng B, Yao Y, Lei J, Fang L, Huang Q (2023) Graph-based structural deep spectral-spatial clustering for hyperspectral image. IEEE Transact Instrum Meas. https://doi.org/10.1109/TIM.2023.3271762

    Article  Google Scholar 

  2. Gu Y, Huang Y, Liu T (2023) Intrinsic decomposition embedded spectral unmixing for satellite hyperspectral images with endmembers from uav platform. IEEE Transact Geosci Remote Sens. https://doi.org/10.1109/TGRS.2023.3307346

    Article  Google Scholar 

  3. Zhao C, Qin B, Feng S, Zhu W, Sun W, Li W, Jia X (2023) Hyperspectral image classification with multi-attention transformer and adaptive superpixel segmentation-based active learning. IEEE Transact Image Process 32:3606–3621. https://doi.org/10.1109/TIP.2023.3287738

    Article  Google Scholar 

  4. Ma F, Liu S, Yang F, Xu G (2023) Piecewise weighted smoothing regularization in tight framelet domain for hyperspectral image restoration. IEEE Access 11:1955–1969. https://doi.org/10.1109/ACCESS.2022.3233831

    Article  Google Scholar 

  5. Zhao X, Liu K, Gao K, Li W (2023) Hyperspectral time-series target detection based on spectral perception and spatial-temporal tensor decomposition. IEEE Transact Geosci Remote Sens. https://doi.org/10.1109/TGRS.2023.3307071

    Article  Google Scholar 

  6. Jiao J, Gong Z, Zhong P (2023) Triplet spectralwise transformer network for hyperspectral target detection. IEEE Transact Geosci Remote Sens. https://doi.org/10.1109/TGRS.2023.3306084

    Article  Google Scholar 

  7. Gao H, Zhang Y, Chen Z, Xu S, Hong D, Zhang B (2023) A multidepth and multibranch network for hyperspectral target detection based on band selection. IEEE Transact Geosci Remote Sens 61:1–18. https://doi.org/10.1109/TGRS.2023.3258061

    Article  Google Scholar 

  8. Feng S, Feng R, Wu D, Zhao C, Li W, Tao R (2023) A coarse-to-fine hyperspectral target detection method based on low-rank tensor decomposition. IEEE Transact Geosci Remote Sens. https://doi.org/10.1109/TGRS.2023.3329800

    Article  Google Scholar 

  9. Stein DWJ, Beaven SG, Hoff LE, Winter EM, Schaum AP, Stocker AD (2002) Anomaly detection from hyperspectral imagery. In: IEEE signal processing magazine, vol 19, no 1, pp 58–69. https://doi.org/10.1109/79.974730

  10. Schweizer SM, Moura JMF (2000) Hyperspectral imagery: clutter adaptation in anomaly detection. IEEE Transact Inf Theory 46(5):1855–1871

    Article  Google Scholar 

  11. Reed I, Yu X (1990) Adaptive multiple-band cfar detection of an optical pattern with unknown spectral distribution. IEEE Transact Acoust Speech Signal Process 38:1760–1770. https://doi.org/10.1109/29.60107

    Article  Google Scholar 

  12. Molero J, Garzon E, Garcia I, Plaza A (2013) Analysis and optimizations of global and local versions of the rx algorithm for anomaly detection in hyperspectral data. IEEE J Sel Top Appl Earth Obs Remote Sens 6:801–814. https://doi.org/10.1109/JSTARS.2013.2238609

    Article  Google Scholar 

  13. Taitano Y, Geier B, Bauer K (2010) A locally adaptable iterative RX detector. EURASIP J Adv Signal Process 2010: 341908. https://doi.org/10.1155/2010/341908

    Article  Google Scholar 

  14. Ma Y, Fan G, Jin Q (2020) Hyperspectral anomaly detection via integration of feature extraction and background purification. IEEE Geosci Remote Sens Lett 18:1436–1440. https://doi.org/10.1109/LGRS.2020.2998809

    Article  Google Scholar 

  15. Kwon H, Nasrabadi N (2005) Kernel rx-algorithm: a nonlinear anomaly detector for hyperspectral imagery. IEEE Transact Geosci Remote Sens 43:388–397. https://doi.org/10.1109/TGRS.2004.841487

    Article  Google Scholar 

  16. Li W, Du Q (2014) Collaborative representation for hyperspectral anomaly detection. IEEE Transact Geosci Remote Sens 53:1463–1474. https://doi.org/10.1109/TGRS.2014.2343955

    Article  Google Scholar 

  17. Hou Z, Li W, Tao R, Ma P, Shi W (2022) Collaborative representation with background purification and saliency weight for hyperspectral anomaly detection. Sci China Info Sci 65:1–12

    Google Scholar 

  18. Ma N, Peng Y, Wang S (2018) A fast recursive collaboration representation anomaly detector for hyperspectral image. IEEE Geosci Remote Sens Lett 16:588–592. https://doi.org/10.1109/LGRS.2018.2878869

    Article  Google Scholar 

  19. Lin S, Zhang M, Cheng X, Zhuo K, Zhao S, Wang H (2022) Hyperspectral anomaly detection via sparse representation and collaborative representation. IEEE J Sel Top Appl Earth Observations Remote Sens 16:946–961. https://doi.org/10.1109/JSTARS.2022.3229834

    Article  Google Scholar 

  20. Chen S, Yang S, Kalpakis K, Chang C (2013) Low-rank decomposition-based anomaly detection. Algorithms Technol Multispectral Hyperspectral Ultraspectral Imag XIX 8743:171–177

    Google Scholar 

  21. CandesCandes EJ, Li X, Ma Y, Wright J (2011) Robust principal component analysis. J. ACM 58(3):1–37

    Article  MathSciNet  Google Scholar 

  22. Vaswani N, Javed TBS, Narayanamurthy P (2018) Robust subspace learning: robust pca, robust subspace tracking, and robust subspace recovery. IEEE Signal Process Mag 35(4):32–55

    Article  Google Scholar 

  23. Farrell M, Mersereau R (2005) On the impact of covariance contamination for adaptive detection in hyperspectral imaging. IEEE Signal Process Lett 12:649–652. https://doi.org/10.1109/LSP.2005.853045

    Article  Google Scholar 

  24. Xu Y, Wu Z, Li J, Plaza A, Wei Z (2016) Anomaly detection in hyperspectral images based on low-rank and sparse representation. IEEE Transact Geosci Remote Sens 54:1990–2000. https://doi.org/10.1109/TGRS.2015.2493201

    Article  Google Scholar 

  25. Cheng T, Wang B (2020) Graph and total variation regularized low-rank representation for hyperspectral anomaly detection. IEEE Transact Geosci Remote Sens 58:391–406. https://doi.org/10.1109/TGRS.2019.2936609

    Article  Google Scholar 

  26. Li L, Wu Z, Wang B (2024) Hyperspectral anomaly detection via merging total variation into low-rank representation. IEEE J Sel Top Appl Earth Observations Remote Sens 17:14894–14907. https://doi.org/10.1109/JSTARS.2024.3447896

    Article  Google Scholar 

  27. Niu Y, Wang B (2016) Hyperspectral anomaly detection based on low-rank representation and learned dictionary. Remote Sens 4:289

    Article  Google Scholar 

  28. Kiran B, RaDM Thomas, Parakkal R (2018) An overview of deep learning based methods for unsupervised and semi-supervised anomaly detection in videos. J Imaging 4(2):36

    Article  Google Scholar 

  29. Hu X, Xie C, Fan Z, Duan Q, Zhuang D, Jiang L, Chanussot J (2022) Hyperspectral anomaly detection using deep learning: a review. Remote Sens 14:14894–14907

    Google Scholar 

  30. Wang D, Zhuang L, Gao L, Sun L, Huang M, Plaza A (2023) Bocknet: blind-block reconstruction network with a guard window for hyperspectral anomaly detection. IEEE Transact Geosci Remote Sens 61:1–16

    Article  Google Scholar 

  31. Wang S, Wang X, Zhang L, Zhong Y (2021) Auto-ad: autonomous hyperspectral anomaly detection network based on fully convolutional autoencoder. IEEE Transact Geosci Remote Sens 60:1–14

    Google Scholar 

  32. Lian J, Wang L, Sun H, Huang H (2024) Gt-had: gated transformer for hyperspectral anomaly detection. IEEE Transact Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2024.3355166

    Article  Google Scholar 

  33. Sun S, Liu J, Chen X, Li W, Li H (2022) Hyperspectral anomaly detection with tensor average rank and piecewise smoothness constraints. IEEE Transact Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2022.3152252

    Article  Google Scholar 

  34. Wang J, Xia Y, Zhang Y (2020) Anomaly detection of hyperspectral image via tensor completion. IEEE Geosci Remote Sens Lett 18(6):1099–1103

    Article  Google Scholar 

  35. Li S, Wang W, Qi H, Kwan C, Vance S (2015) Low-rank tensor decomposition based anomaly detection for hyperspectral imagery. 2015 IEEE International Conference on Image Processing (ICIP) https://doi.org/10.1109/TGRS.2019.2936609

  36. Chen Z, Yang B, Wang B (2018) A preprocessing method for hyperspectral target detection based on tensor principal component analysis. Remote Sens. https://doi.org/10.3390/rs10071033

    Article  Google Scholar 

  37. Song S, Zhou H, Gu L, Yang Y, Yang Y (2019) Hyperspectral anomaly detection via tensor-based endmember extraction and low-rank decomposition. IEEE Geosci Remote Sens Lett 17:1772–1776. https://doi.org/10.1109/LGRS.2019.2953342

    Article  Google Scholar 

  38. Li L, Li W, Qu Y, Zhao C, Tao R, Du Q (2022) Prior-based tensor approximation for anomaly detection in hyperspectral imagery. IEEE Transact Neural Netw Learn Syst 33:1037–1050. https://doi.org/10.1109/TNNLS.2020.3038659

    Article  Google Scholar 

  39. Xu Y, Wu Z, Chanussot J, Wei Z (2018) Joint reconstruction and anomaly detection from compressive hyperspectral images using mahalanobis distance-regularized tensor rpca. IEEE Transact Geosci Remote Sens 56:2919–2930. https://doi.org/10.1109/TGRS.2017.2786718

    Article  Google Scholar 

  40. Wang M, Wang Q, Hong D, Roy SK, Chanussot J (2023) Learning tensor low-rank representation for hyperspectral anomaly detection. IEEE Transact Cybern 53:679–691. https://doi.org/10.1109/TCYB.2022.3175771

    Article  Google Scholar 

  41. He X, Wu J, Ling Q, Li Z, Lin Z, Zhou S (2023) Anomaly detection for hyperspectral imagery via tensor low-rank approximation with multiple subspace learning. IEEE Transact Geosci Remote Sens. https://doi.org/10.1109/TGRS.2023.3270667

    Article  Google Scholar 

  42. De Lathauwer L, De Moor B, Vandewalle J (2000) A multilinear singular value decomposition. SIAM J Matrix Anal Appl 21(4):1253–1278

    Article  MathSciNet  Google Scholar 

  43. Kilmer ME, Martin CD (2011) Factorization strategies for third-order tensors. Linear Algebr Appl 453:641–658

    Article  MathSciNet  Google Scholar 

  44. Kilmer ME, Martin CD, Hao N, Hoover RC (2013) Third-order tensors as operators on matrices: a theoretical and computational framework with applications in imaging. SIAM J Matrix Anal Appl 34(1):148–172

    Article  MathSciNet  Google Scholar 

  45. Lu C, Feng J, Chen Y, Liu W, Lin Z, Yan S (2016) Tensor robust principal component analysis with a new tensor nuclear norm. IEEE Transact Pattern Anal Mach Intell 42:925–938. https://doi.org/10.1109/TPAMI.2019.2891760

    Article  Google Scholar 

  46. Wang X, Wu Z, Xu Y, Wei Z, Xia L (2021) Hyperspectral anomaly detection based on tensor truncated nuclear norm and linear total variation regularization. In Image and Graphics: 11th International Conference, ICIG 2021, Haikou, August 6–8, 2021, Proceedings, Part II 11, pp 250–261

  47. Zhang T (2010) Analysis of multi-stage convex relaxation for sparse regularization. J Mach Learn Res 11:1081–1081

    MathSciNet  Google Scholar 

  48. Cao W, Wang Y, Yang C, Chang X, Han Z, Xu Z (2015) Folded-concave penalization approaches to tensor completion. Neurocomputing 152:261–273

    Article  Google Scholar 

  49. Ma F, Huo S, Yang F (2021) Graph-based logarithmic low-rank tensor decomposition for the fusion of remotely sensed images. IEEE J Sel Top Appl Earth Observations Rem Sens 58:11271–11286. https://doi.org/10.1109/JSTARS.2021.3123466

    Article  Google Scholar 

  50. Zheng YB, Huang TZ, Zhao XL, Jiang TX, Ma TH, Ji TY (2019) Mixed noise removal in hyperspectral image via low-fibered-rank regularization. IEEE Transact Geosci Remote Sens 58:734–749. https://doi.org/10.1109/TGRS.2019.2940534

    Article  Google Scholar 

  51. Zhang Z, Ely G, Aeron S, Hao N, Kilmer M (2014) 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 (CVPR), pp 3842–3849

  52. Voronin S, Chartrand R (2013) A new generalized thresholding algorithm for inverse problems with sparsity constraints. In: 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, pp 1636–1640

  53. Liu S, Zhu C, Ran D, Wen G (2023) Anomaly detection via tensor multisubspace learning and nonconvex low-rank regularization. IEEE J Sel Top Appl Earth Observations Remote Sens 16:8178–8190. https://doi.org/10.1109/JSTARS.2023.3311095

    Article  Google Scholar 

  54. Chang CI (2020) An effective evaluation tool for hyperspectral target detection: 3d receiver operating characteristic curve analysis. IEEE Transact Geosci Remote Sens 59(6):5131–5153

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the Natural science foundation project of Liaoning Science and Technology Department under Grant 2023-MS-314, and by the Scientific Research Project of Colleges from Liaoning Department of Education (P.R.C) under Grant LJ242410147006.

Author information

Authors and Affiliations

  1. School of Electronic and Information Engineering, Liaoning Technology University, Huludao, 125105, Liaoning, China

    Fei Ma, Aihua Hou & Guangxian Xu

  2. Liaoning Key Laboratory of Radio Frequency and Big Data for Intelligent Applications, Liaoning Technology University, Huludao, 125105, Liaoning, China

    Fei Ma & Aihua Hou

  3. School of Electronic and Control Engineering, Liaoning Technology University, Huludao, 125105, Liaoning, China

    Feixia Yang

Authors
  1. Fei Ma
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Aihua Hou
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Feixia Yang
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Guangxian Xu
    View author publications

    You can also search for this author inPubMed Google Scholar

Contributions

Fei Ma and Aihua Hou put forward folded-concave function and HOSVD for hyperspectral anomaly detection and wrote the main manuscript text. Feixia Yang and Guangxian Xu prepared the whole figures and tables. All authors reviewed the manuscript.

Corresponding author

Correspondence to Aihua Hou.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ma, F., Hou, A., Yang, F. et al. Tensor subspace learning and folded-concave function regularization for hyperspectral anomaly detection. J Supercomput 81, 320 (2025). https://doi.org/10.1007/s11227-024-06791-6

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11227-024-06791-6

Keywords