A GENERALIZATION OF NEGATIVE NORM MODELS IN THE DISCRETE SETTING - Application to Stripe Denoising

Jérôme Fehrenbach, Pierre Weiss, Corinne Lorenzo

2012

Abstract

Starting with a book of Y.Meyer in 2001, negative norm models attracted the attention of the imaging community in the last decade. Despite numerous works, these norms seem to have provided only luckwarm results in practical applications. In this work, we propose a framework and an algorithm to remove stationary noise from images. This algorithm has numerous practical applications and we show it on 3D data from a newborn microscope called SPIM. We also show that this model generalizes Meyer’s model and its successors in the discrete setting and allows to interpret them in a Bayesian framework. It sheds a new light on these models and allows to pick them according to some a priori knowledge on the texture statistics. Further results are available on our webpage at http://www.math.univ-toulouse.fr/~weiss/PagePublications.html.

References

  1. Aujol, J.-F., Gilboa, G., Chan, T., and Osher, S. (2006). Structure-texture image decomposition - modeling, algorithms, and parameter selection. Int. J. Comput. Vision, vol. 67(1), pp. 111-136.
  2. Chambolle, A. and Pock, T. (2011). A first-order primaldual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40(1): 120-145.
  3. Fadili, M., Starck, J.-L., Bobin, J., and Moudden, Y. (2010). Image decomposition and separation using sparse representations: an overview. Proc. of the IEEE, Special Issue: Applications of Sparse Representation, vol. 98(6), pp. 983-994,.
  4. Garnett, J., Le, T., Meyer, Y., and Vese, L. (2007). Image decompositions using bounded variation and generalized homogeneous besov spaces. Appl. Comput. Harmon. Anal., 23, pp. 25-56.
  5. Huisken, J., Swoger, J., Bene, F. D., Wittbrodt, J., and Stelzer, E. (2004). Optical sectioning deep inside live embryos by selective plane illumination microscopy. Science, vol. 305, 5686, p.1007.
  6. Kowalski, M. (2009). Sparse regression using mixed norms. Appl. Comput. Harmon. A. 27, 3, 303-324.
  7. Meyer, Y. (2001). Oscillating patterns in image processing and in some nonlinear evolution equations, in 15th Dean Jacqueline B. Lewis Memorial Lectures. AMS.
  8. Ng, M., Weiss, P., and Yuan, X.-M. (2010). Solving constrained total-variation image restoration and reconstruction problems via alternating direction methods. SIAM Journal on Scientific Computing, 32.
  9. Osher, S., Sole, A., and Vese, L. (2003). Image decomposition and restoration using total variation minimization and the h-1 norm. SIAM Multiscale Model. Sim. 1(3), pp. 339-370.
  10. Rockafellar, T. (1970). Convex Analysis. Princeton University Press.
  11. Shiryaev, A. (1996). Probability, Graduate Texts in Mathematics 95. Springer.
  12. Starck, J., Elad, M., and Donoho, D. (2005). Image decomposition via the combination of sparse representations and a variational approach. IEEE Trans. Im. Proc., vol. 14(10).
  13. Vese, L. and Osher, S. (2003). Modeling textures with total variation minimization and oscillating patterns in image processing. J. Sci. Comput., 19(1-3), pp. 553-572.
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Paper Citation


in Harvard Style

Fehrenbach J., Weiss P. and Lorenzo C. (2012). A GENERALIZATION OF NEGATIVE NORM MODELS IN THE DISCRETE SETTING - Application to Stripe Denoising . In Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM, ISBN 978-989-8425-99-7, pages 337-342. DOI: 10.5220/0003742603370342


in Bibtex Style

@conference{icpram12,
author={Jérôme Fehrenbach and Pierre Weiss and Corinne Lorenzo},
title={A GENERALIZATION OF NEGATIVE NORM MODELS IN THE DISCRETE SETTING - Application to Stripe Denoising},
booktitle={Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM,},
year={2012},
pages={337-342},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003742603370342},
isbn={978-989-8425-99-7},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM,
TI - A GENERALIZATION OF NEGATIVE NORM MODELS IN THE DISCRETE SETTING - Application to Stripe Denoising
SN - 978-989-8425-99-7
AU - Fehrenbach J.
AU - Weiss P.
AU - Lorenzo C.
PY - 2012
SP - 337
EP - 342
DO - 10.5220/0003742603370342