An adaptive spatial–spectral total variation approach for Poisson noise removal in hyperspectral images

Abstract

Poisson distributed noise, such as photon noise, is an important noise source in multi- and hyperspectral images. We propose a variational-based denoising approach that accounts the vectorial structure of a spectral image cube, as well as the Poisson distributed noise. For this aim, we extend an approach initially developed for monochromatic images, by a regularisation term, which is spectrally and spatially adaptive and preserves edges. In order to take the high computational complexity into account, we derive a split Bregman optimisation for the proposed model. The results show the advantages of the proposed approach compared with a marginal approach on synthetic and real data.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

References

  1. 1.

    Bregman, L.: The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Comput. Math. Math. Phys. 7(3), 200–217 (1967)

    Article  Google Scholar 

  2. 2.

    Bresson, X., Chan, T.: Fast dual minimization of the vectorial total variation norm and applications to color image processing. Inverse Probl. Imaging 2(4), 455–484 (2008). doi:10.3934/ipi.2008.2.455

    Article  MathSciNet  MATH  Google Scholar 

  3. 3.

    Deger, F., Mansouri, A., Pedersen, M., Hardeberg, J.Y., Voisin, Y.: A variational approach for denoising hyperspectral images corrupted by Poisson distributed noise. In: Image Signal Processing, pp. 106–114. Springer (2014)

  4. 4.

    Delcourt, J., Mansouri, A., Sliwa, T., Voisin, Y.: A comparative study and an evaluation framework of multi/hyperspectral image compression. In: Fifth International Conference on Signal Image Technology Internet Based System, pp. 81–88 (2009). doi:10.1109/SITIS.2009.23

  5. 5.

    Fairchild, M.D., Johnson, G.M.: METACOW: a public-domain, high-extended-dynamic-range, spectral test target for imaging system analysis and simulation. In: Color Imaging Conference, pp. 239–245. IS&T (2004)

  6. 6.

    Getreuer, P.: Rudin–Osher–Fatemi total variation denoising using split Bregman. Image Process. On Line 10, 74–95 (2012). http://dx.doi.org/10.5201/ipol.2012.g-tvd

  7. 7.

    HySpex/Norsk Elektro Optikk AS: Imaging spectrometer (user manual). In: Technical Report (2013). www.hyspex.no

  8. 8.

    Krishnamurthy, K., Raginsky, M., Willett, R.: Multiscale photon-limited spectral image reconstruction. SIAM J. Imaging Sci. 3(3), 619–645 (2010). doi:10.1137/090756259

    Article  MathSciNet  MATH  Google Scholar 

  9. 9.

    Le, T., Chartrand, R., Asaki, T.J.: A variational approach to reconstructing images corrupted by Poisson noise. J. Math. Imaging Vis. 27(3), 257–263 (2007). doi:10.1007/s10851-007-0652-y

    Article  MathSciNet  Google Scholar 

  10. 10.

    Makitalo, M., Foi, A.: Optimal inversion of the Anscombe transformation in low-count Poisson image denoising. IEEE Trans. Image Process. 20(1), 99–109 (2011)

    Article  MathSciNet  Google Scholar 

  11. 11.

    Mansouri, A., Marzani, F., Gouton, P.: Development of a protocol for CCD calibration: application to a multispectral imaging system. Int. J. Robot. Autom. 20(2), 81–88 (2005). doi:10.2316/Journal.206.2005.2.206-2784

    Google Scholar 

  12. 12.

    Mansouri, A., Sliwa, T., Hardeberg, J.Y., Voisin, Y.: An adaptive-PCA algorithm for reflectance estimation from color images. In: 19th International Conference Pattern Recognition, vol. 1, pp. 1–4. IEEE (2008). doi:10.1109/ICPR.2008.4761120

  13. 13.

    Osher, S., Goldstein, T.: The split Bregman method for L1-regularized problems. SIAM J. Imaging Sci. 2(2), 323–343 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. 14.

    Othman, H., Qian, S.E.: Noise reduction of hyperspectral imagery using hybrid spatial–spectral derivative-domain wavelet shrinkage. IEEE Trans. Geosci. Remote Sens. 44(2), 397–408 (2006)

    Article  Google Scholar 

  15. 15.

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

    Article  MathSciNet  MATH  Google Scholar 

  16. 16.

    Salmon, J., Harmany, Z., Deledalle, C.A., Willett, R.: Poisson noise reduction with non-local PCA. J. Math. Imaging Vis. 48(2), 279–294 (2014). doi:10.1007/s10851-013-0435-6

    Article  MathSciNet  MATH  Google Scholar 

  17. 17.

    Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004). doi:10.1109/TIP.2003.819861

  18. 18.

    Yuan, Q., Zhang, L., Member, S., Shen, H.: Hyperspectral image denoising employing a spectral spatial adaptive total variation model. IEEE Trans. Geosci. Remote Sens. 50(10), 3660–3677 (2012)

  19. 19.

    Zanella, R., Boccacci, P., Zanni, L., Bertero, M.: Efficient gradient projection methods for edge-preserving removal of Poisson noise. Inverse Probl. 25(4), 1–24 (2009). doi:10.1088/0266-5611/25/4/045010

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

We would like to warmly thank the Regional Council of Burgundy for supporting this work. Support agreement FEDER 2011-9201AAO048S04661. The dataset of Kremer pigment chart was gratefully provided by Norsk Elektro Optikk AS.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Alamin Mansouri.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mansouri, A., Deger, F., Pedersen, M. et al. An adaptive spatial–spectral total variation approach for Poisson noise removal in hyperspectral images. SIViP 10, 447–454 (2016). https://doi.org/10.1007/s11760-015-0806-0

Download citation

Keywords

  • Adaptive total variation
  • Hyperspectral images
  • Poisson noise