Preserving Time Structures While Denoising a Dynamical Image

  • Yves RozenholcEmail author
  • Markus Reiß
Part of the Computational Imaging and Vision book series (CIVI, volume 41)


In restoration or denoising of a movie, the classical procedures often do not take into account the full information provided by the movie. These procedures are either applied spatially “image per image” or locally on some neighborhood combining both closeness in one image and closeness in time. The local information is then combined homogeneously in order to realize the treatment. There is one type of movie where both approaches fail to provide a relevant treatment. Such a movie, called dynamical image, represents the same scene along the time with only variations, not in the positions of the objects in the scene but, in their gray levels, colors or contrasts. Hence, at each point of the image, one observes some regular temporal dynamics. This is the typical output using Dynamic Contrast Enhanced Computed Tomography (DCE-CT) or Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI) where at each spatial location (called voxel) of the image a time series is recorded.

In such a case, in order to preserve the full temporal information in the image, a proper denoising procedure should be based on averaging over spatial neighborhoods, but using the full dynamics of all pixels (or voxels) within the neighborhood. It is thus necessary to search homogeneous spatial neighborhoods with respect to the full dynamical information.

We introduce a new algorithm which meets these requirements. It is based on two main tools: a multiple hypothesis testing for the zero mean of a vector and an adaptive construction of homogeneous neighborhoods. For both tools, results of mathematical statistics ensure the quality of the global procedure. Illustrations from medical image sequences show a very good practical performance.


Dynamical Image Dynamic Contrast Enhance Magnetic Resonance Image Multiple Hypothesis Test Spatial Neighborhood Dynamic Contrast Enhanced Compute Tomography 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was supported in 2008 by a grant “Bonus Qualité Recherche” from the University Paris Descartes for the project “Cancer Angiogénèse et Outils Mathématiques”.


  1. 22.
    Baraud, Y., Huet, S., Laurent, B.: Adaptive tests of linear hypotheses by model selection. Ann. Stat. 31(1), 225–251 (2003) CrossRefzbMATHMathSciNetGoogle Scholar
  2. 30.
    Benjamini, Y., Hochberg, Y.: Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. R. Stat. Soc., Ser. B, Stat. Methodol. 57(1), 289–300 (1995) zbMATHMathSciNetGoogle Scholar
  3. 56.
    Buades, A., Coll, B., Morel, J.-M.: Nonlocal image and movie denoising. Int. J. Comput. Vis. 76(2), 123–139 (2008) CrossRefGoogle Scholar
  4. 120.
    Durot, C., Rozenholc, Y.: An adaptive test for zero mean. Math. Methods Stat. 15(1), 26–60 (2006) MathSciNetGoogle Scholar
  5. 180.
    Gayraud, G., Pouet, C.: Adaptive minimax testing in the discrete regression scheme. Probab. Theory Relat. Fields 133(4), 531–558 (2005) CrossRefzbMATHMathSciNetGoogle Scholar
  6. 285.
    Lepskiĭ, O.V.: A problem of adaptive estimation in Gaussian white noise. Theory Probab. Appl. 35(3), 454–466 (1990) CrossRefMathSciNetGoogle Scholar
  7. 286.
    Lepskiĭ, O.V.: Asymptotically minimax adaptive estimation. I. Upper bounds. Optimally adaptive estimates. Theory Probab. Appl. 36(4), 682–697 (1991/1992) CrossRefGoogle Scholar
  8. 287.
    Lepskiĭ, O.V., Spokoiny, V.G.: Optimal pointwise adaptive methods in nonparametric estimation. Ann. Stat. 25(6), 2512–2546 (1997) CrossRefMathSciNetGoogle Scholar
  9. 339.
    Polzehl, J., Spokoiny, V.: Adaptive weights smoothing with applications to image restoration. J. R. Stat. Soc., Ser. B, Stat. Methodol. 62(2), 335–354 (2000) CrossRefMathSciNetGoogle Scholar
  10. 356.
    Reiß, M., Rozenholc, Y., Cuenod, C.-A.: Pointwise adaptive estimation for robust and quantile regression. Technical report, ArXiv:0904.0543v1 (2009)
  11. 363.
    Rozenholc, Y., Reiß, M., Balvay, D., Cuenod, C.-A.: Growing time homogeneous neighborhoods for denoising and clustering dynamic contrast enhanced-CT sequences. Technical report, University Paris Descartes (2009) Google Scholar

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.MAP5, UMR CNRS 8145University Paris DescartesParisFrance
  2. 2.Institute of MathematicsHumboldt University BerlinBerlinGermany

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