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Denoising by Higher Order Statistics

  • A standard approach for deducing a variational denoising method is the maximum a posteriori strategy. Here, the denoising result is chosen in such a way that it maximizes the conditional density function of the reconstruction given its observed noisy version. Unfortunately, this approach does not imply that the empirical distribution of the reconstructed noise components follows the statistics of the assumed noise model. In this paper, we propose to overcome this drawback by applying an additional transformation to the random vector modeling the noise. This transformation is then incorporated into the standard denoising approach and leads to a more sophisticated data fidelity term, which forces the removed noise components to have the desired statistical properties. The good properties of our new approach are demonstrated for additive Gaussian noise by numerical examples. Our method shows to be especially well suited for data containing high frequency structures, where other denoising methods which assume a certain smoothness of the signal cannot restore the small structures.

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Author:Tanja Teuber, Steffen Remmele, Jürgen Hesser, Gabriele Steidl
URN (permanent link):urn:nbn:de:hbz:386-kluedo-27650
Document Type:Preprint
Language of publication:English
Publication Date:2011/10/05
Year of Publication:2011
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2011/10/06
Tag:additive Gaussian noise; denoising; higher-order moments; maximum a posteriori estimation
Number of page:22
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 27.05.2011