Multiplicative Noise Cleaning via a Variational Method Involving Curvelet Coefficients

Authors:
Sylvain Durand;Jalal Fadili;Mila Nikolova
Affiliations:
M.A.P. 5 - CNRS, University Paris Descartes, France;GREYC CNRS-ENSICAEN-Université de Caen, France;CMLA - CNRS, ENS Cachan, PRES UniverSud, France
Venue:
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Year:
2009

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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 ***1 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.