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A Weighted Non-convex Restoration Model for Hyperspectral Image

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Image and Graphics (ICIG 2021)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12889))

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Abstract

Low-rank and sparsity are two popular regularization objects in hyperspectral image restoration. To generalize this decomposition, a weighted non-convex low-rank method is proposed by adopting non-convex \(l_p\)-norm (\(0<p<1\)) to recover the clean image more genuinely. The noise term including Gaussian noise, impulse noise, stripes, and deadlines, is assumed to be sparse, and the non-convex \(l_p\)-norm can better approach the \(l_0\)-norm when \(0<p<1\). For the clean image underlying a noised one, its low rank property is conducive to the capture of both spatial and spectral information by applying \(l_p\)-norm to the bases of the gradient of data. To remain faithful to the dissimilarity between the correlation along spatial and spectral directions, weights are assigned when computing the difference in each direction. Although being non-convex, the proposed model can be solved via ADMM algorithm. Extensive simulated experiments show that this model outperforms various existing methods visually and quantitatively.

This work was supported in part by the National Nature Science Foundation of China (62072312, 61972264, 61872429, 61772343), in part by Shenzhen Basis Research Project (JCYJ20180305125521534, JCYJ20170818091621856, JCYJ20170302144838601), in part by the Interdisciplinary Innovation Team of Shenzhen University (SZUGS2021SEMINAR06, JG2020060), in part by National Nature Science Foundation of Guangdong province (2019A1515010894).

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Notes

  1. 1.

    Casorati matrix is a matrix whose columns comprise vectorized bands of an HSI [5].

  2. 2.

    https://engineering.purdue.edu/~biehl/MultiSpec/hyperspectral.html.

References

  1. Goetz, A.F.: Three decades of hyperspectral remote sensing of the earth: a personal view. Remote Sens. Environ. 113, S5–S16 (2009)

    Article  Google Scholar 

  2. Goldfarb, D., Osher, S., Burger, M., Xu, J., Yin, W.: An iterative regularization method for total variation-based image restoration. Multiscale Model. Simul. 4(2), 460–489 (2005)

    Article  MathSciNet  Google Scholar 

  3. Gu, S., Zhang, L., Zuo, W., Feng, X.: Weighted nuclear norm minimization with application to image denoising. In: 2014 IEEE Conference on Computer Vision and Pattern Recognition, pp. 2862–2869 (2014)

    Google Scholar 

  4. He, W., Zhang, H., Zhang, L., Shen, H.: Hyperspectral image denoising via noise-adjusted iterative low-rank matrix approximation. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 8(6), 3050–3061 (2015)

    Article  Google Scholar 

  5. He, W., Zhang, H., Zhang, L., Shen, H.: Total-variation-regularized low-rank matrix factorization for hyperspectral image restoration. IEEE Trans. Geosci. Remote Sens. 54(1), 178–188 (2016)

    Article  Google Scholar 

  6. Krishnan, D., Fergus, R.: Fast image deconvolution using hyper-laplacian priors. In: Bengio, Y., Schuurmans, D., Lafferty, J.D., Williams, C.K.I., Culotta, A. (eds.) Advances in Neural Information Processing Systems 22: 23rd Annual Conference on Neural Information Processing Systems 2009. Proceedings of a Meeting Held 7–10 December 2009, Vancouver, British Columbia, Canada, pp. 1033–1041. Curran Associates, Inc. (2009)

    Google Scholar 

  7. Lu, C., Feng, J., Chen, Y., Liu, W., Lin, Z., Yan, S.: Tensor robust principal component analysis with a new tensor nuclear norm. IEEE Trans. Pattern Anal. Mach. Intell. 42(4), 925–938 (2020)

    Article  Google Scholar 

  8. Peng, J., Xie, Q., Zhao, Q., Wang, Y., Yee, L., Meng, D.: Enhanced 3DTV regularization and its applications on HSI denoising and compressed sensing. IEEE Trans. Image Process. 29, 7889–7903 (2020)

    Article  MathSciNet  Google Scholar 

  9. Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60(1), 259–268 (1992)

    Article  MathSciNet  Google Scholar 

  10. Wang, Y., Peng, J., Zhao, Q., Leung, Y., Zhao, X., Meng, D.: Hyperspectral image restoration via total variation regularized low-rank tensor decomposition. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 11(4), 1227–1243 (2018)

    Article  Google Scholar 

  11. Wright, J., Ganesh, A., Rao, S.R., Peng, Y., Ma, Y.: Robust principal component analysis: exact recovery of corrupted low-rank matrices via convex optimization. In: Bengio, Y., Schuurmans, D., Lafferty, J.D., Williams, C.K.I., Culotta, A. (eds.) Advances in Neural Information Processing Systems 22: 23rd Annual Conference on Neural Information Processing Systems 2009. Proceedings of a Meeting Held 7–10 December 2009, Vancouver, British Columbia, Canada, pp. 2080–2088. Curran Associates, Inc. (2009)

    Google Scholar 

  12. Xie, Q., et al.: Multispectral images denoising by intrinsic tensor sparsity regularization. In: 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1692–1700 (2016)

    Google Scholar 

  13. Xie, Y., Qu, Y., Tao, D., Wu, W., Yuan, Q., Zhang, W.: Hyperspectral image restoration via iteratively regularized weighted Schatten \(p\)-norm minimization. IEEE Trans. Geosci. Remote Sens. 54(8), 4642–4659 (2016)

    Article  Google Scholar 

  14. Zhang, H., He, W., Zhang, L., Shen, H., Yuan, Q.: Hyperspectral image restoration using low-rank matrix recovery. IEEE Trans. Geosci. Remote Sens. 52(8), 4729–4743 (2014)

    Article  Google Scholar 

  15. Zhou, T., Tao, D.: GoDec: randomized low-rank and sparse matrix decomposition in noisy case. In: Proceeding of the Twenty-Eighth International Conference on Machine Learning, pp. 33–40. International Machine Learning Society (IMLS) (2011)

    Google Scholar 

  16. Fan, J., Li, R.: Variable selection via nonconcave penalized likelihood and its Oracle properties. J. Am. Stat. Assoc. 96, 1348–1361 (2001)

    Article  MathSciNet  Google Scholar 

  17. Nie, F., Wang, H., Cai, X., Huang, H., Ding, C.: Robust matrix completion via joint Schatten \(p\)-norm and \(l_p\)-norm minimization. IEEE International Conference on Data Mining, Brussels, Belgium, pp. 566–574 (2012)

    Google Scholar 

  18. Shang, F., Liu, Y., Cheng, J.: Scalable algorithms for tractable Schatten quasi-norm minimization. In: Computing Research Repository. arXiv:1606.01245 (2016)

  19. Xu, C., Lin, Z., Zha, H.: A unified convex surrogate for the Schatten-p norm. In: The Thirty-First AAAI Conference on Artificial Intelligence, San Francisco, California, USA, pp. 926–932 (2017)

    Google Scholar 

  20. Shang, F., Cheng, J., Liu, Y., Luo, Z., Lin, Z.: Bilinear linear factor matrix norm minimization for robust PCA: algorithms and applications. IEEE Trans. Pattern Anal. Mach. Intell. 50, 2066–2080 (2018)

    Article  Google Scholar 

  21. Zuo, W., Meng, D., Zhang, L., Feng, X., Zhang, D.: A generalized iterated shrinkage algorithm for non-convex sparse coding. In: IEEE International Conference on Computer Vision, pp. 217–224 (2013)

    Google Scholar 

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Authors and Affiliations

  1. College of Mathematics and Statistics, Shenzhen Key Laboratory of Advanced Machine Learning and Applications, Shenzhen University, Shenzhen, 518060, China

    Yijun Yu & Min Li

Authors
  1. Yijun Yu
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  2. Min Li
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Correspondence to Min Li .

Editor information

Editors and Affiliations

  1. Peking University, Beijing, China

    Yuxin Peng

  2. Tsinghua University, Beijing, China

    Shi-Min Hu

  3. Tampere University, Tampere, Finland

    Moncef Gabbouj

  4. Zhejiang University, Hangzhou, China

    Kun Zhou

  5. Technion – Israel Institute of Technology, Haifa, Israel

    Michael Elad

  6. Tsinghua University, Beijing, China

    Kun Xu

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Yu, Y., Li, M. (2021). A Weighted Non-convex Restoration Model for Hyperspectral Image. In: Peng, Y., Hu, SM., Gabbouj, M., Zhou, K., Elad, M., Xu, K. (eds) Image and Graphics. ICIG 2021. Lecture Notes in Computer Science(), vol 12889. Springer, Cham. https://doi.org/10.1007/978-3-030-87358-5_14

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  • DOI: https://doi.org/10.1007/978-3-030-87358-5_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-87357-8

  • Online ISBN: 978-3-030-87358-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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