Multiplicative Noise Cleaning via a Variational Method Involving Curvelet Coefficients

  • Sylvain Durand
  • Jalal Fadili
  • Mila Nikolova
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5567)

Abstract

Classical ways to denoise images contaminated with multiplicative noise (e.g. speckle noise) are filtering, statistical (Bayesian) methods, variational methods and methods that convert the multiplicative noise into additive noise (using a logarithmic function) in order to apply a shrinkage estimation for the log-image data and transform back the result using an exponential function.

We propose a new method that involves several stages: we apply a reasonable under-optimal hard-thresholding on the curvelet transform of the log-image; the latter is restored using a specialized hybrid variational method combining an ℓ1 data-fitting to the thresholded coefficients and a Total Variation regularization (TV) in the image domain; the restored image is an exponential of the obtained minimizer, weighted so that the mean of the original image is preserved. The minimization stage is realized using a properly adapted fast Douglas-Rachford splitting. The existence of a minimizer of our specialized criterion and the convergence of the minimization scheme are proved. The obtained numerical results outperform the main alternative methods.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Sylvain Durand
    • 1
  • Jalal Fadili
    • 2
  • Mila Nikolova
    • 3
  1. 1.M.A.P. 5 - CNRSUniversity Paris DescartesFrance
  2. 2.GREYC CNRS-ENSICAEN-Université de CaenFrance
  3. 3.CMLA - CNRS, ENS Cachan, PRES UniverSudFrance

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