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Locally adaptive image denoising by a statistical multiresolution criterion

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  • Hotz, Thomas
  • Marnitz, Philipp
  • Stichtenoth, Rahel
  • Davies, Laurie
  • Kabluchko, Zakhar
  • Munk, Axel

Abstract

It is shown how to choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, an efficient method for locally adaptive image denoising is presented. As expected, the smoothing parameter serves as an edge detector in this framework. Numerical examples together with applications in confocal microscopy illustrate the usefulness of the approach.

Suggested Citation

  • Hotz, Thomas & Marnitz, Philipp & Stichtenoth, Rahel & Davies, Laurie & Kabluchko, Zakhar & Munk, Axel, 2012. "Locally adaptive image denoising by a statistical multiresolution criterion," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 543-558.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:3:p:543-558
    DOI: 10.1016/j.csda.2011.08.018
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    References listed on IDEAS

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    1. Qiu, Peihua, 2007. "Jump Surface Estimation, Edge Detection, and Image Restoration," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 745-756, June.
    2. Gonzalez Manteiga, W. & Martinez Miranda, M. D. & Perez Gonzalez, A., 2004. "The choice of smoothing parameter in nonparametric regression through Wild Bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 487-515, October.
    3. Thon, Kevin & Rue, Håvard & Skrøvseth, Stein Olav & Godtliebsen, Fred, 2012. "Bayesian multiscale analysis of images modeled as Gaussian Markov random fields," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 49-61, January.
    4. Charles, C. & Rasson, J. P., 2003. "Wavelet denoising of Poisson-distributed data and applications," Computational Statistics & Data Analysis, Elsevier, vol. 43(2), pages 139-148, June.
    5. Hardle, Wolfgang & Tsybakov, A. B., 1993. "How sensitive are average derivatives?," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 31-48, July.
    6. Axel Munk & Nicolai Bissantz & Thorsten Wagner & Gudrun Freitag, 2005. "On difference‐based variance estimation in nonparametric regression when the covariate is high dimensional," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 19-41, February.
    7. Kabluchko, Zakhar, 2011. "Extremes of the standardized Gaussian noise," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 515-533, March.
    8. P.L. Davies & M. Meise, 2008. "Approximating data with weighted smoothing splines," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(3), pages 207-228.
    9. Kolaczyk, Eric D. & Ju, Junchang & Gopal, Sucharita, 2005. "Multiscale, Multigranular Statistical Image Segmentation," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1358-1369, December.
    10. Bissantz, Nicolai & Hohage, T. & Munk, Axel & Ruymgaart, F., 2007. "Convergence rates of general regularization methods for statistical inverse problems and applications," Technical Reports 2007,04, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    11. Ogden, Todd & Parzen, Emanuel, 1996. "Data dependent wavelet thresholding in nonparametric regression with change-point applications," Computational Statistics & Data Analysis, Elsevier, vol. 22(1), pages 53-70, June.
    12. J. Polzehl & V. G. Spokoiny, 2000. "Adaptive weights smoothing with applications to image restoration," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 335-354.
    13. Hardle, Wolfgang & Tsybakov, A. B., 1993. "How sensitive are average derivatives?," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 31-48, July.
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    2. De Canditiis, Daniela, 2014. "A frame based shrinkage procedure for fast oscillating functions," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 142-150.

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