Multiplicative noise cleaning via a variational method involving curvelets coefficients

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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Sylvain Durand, Jalal M. Fadili, Mila Nikolova. Multiplicative noise cleaning via a variational method involving curvelets coefficients. Scale Space and Variational Methods in Computer Vision, 2009, Voss, Norway. pp.282-294, ⟨10.1007/978-3-642-02256-2_24⟩. ⟨hal-00712105⟩



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