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Entropy 2015, 17(5), 3461-3478; doi:10.3390/e17053461

Nonparametric Denoising Methods Based on Contourlet Transform with Sharp Frequency Localization: Application to Low Exposure Time Electron Microscopy Images

1
Science and Technology Faculty, University of Mohamed El Bachir El Ibrahimi–Bordj Bou Arréridj, 34030 Bordj Bou Arréridj, Algeria
2
Laboratory of Electrical Engineering, University of M'sila, 28000 M'sila, Algeria
3
Polytech Tours, Graduate School of Engineering, University of Tours, 37200 Tours, France
4
INSERM U1196, Bât. 112, Centre Universitaire, 91405 Orsay Cedex, France
5
Institut Curie, Centre de Recherche, Bât. 112, Centre Universitaire, 91405 Orsay Cedex, France
This article is an extended version of our paper published in the 34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Château Clos Lucé, Parc Leonardo Da Vinci, Amboise, France, 21–26 September 2014.
*
Author to whom correspondence should be addressed.
Academic Editor: Kevin H. Knuth
Received: 24 February 2015 / Accepted: 29 April 2015 / Published: 20 May 2015
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Abstract

Image denoising is a very important step in cryo-transmission electron microscopy (cryo-TEM) and the energy filtering TEM images before the 3D tomography reconstruction, as it addresses the problem of high noise in these images, that leads to a loss of the contained information. High noise levels contribute in particular to difficulties in the alignment required for 3D tomography reconstruction. This paper investigates the denoising of TEM images that are acquired with a very low exposure time, with the primary objectives of enhancing the quality of these low-exposure time TEM images and improving the alignment process. We propose denoising structures to combine multiple noisy copies of the TEM images. The structures are based on Bayesian estimation in the transform domains instead of the spatial domain to build a novel feature preserving image denoising structures; namely: wavelet domain, the contourlet transform domain and the contourlet transform with sharp frequency localization. Numerical image denoising experiments demonstrate the performance of the Bayesian approach in the contourlet transform domain in terms of improving the signal to noise ratio (SNR) and recovering fine details that may be hidden in the data. The SNR and the visual quality of the denoised images are considerably enhanced using these denoising structures that combine multiple noisy copies. The proposed methods also enable a reduction in the exposure time. View Full-Text
Keywords: cryo-transmission electron microscopy; energy filtered transmission electron microscopy (EFTEM); contourlet; Bayesian denoiser; alpha-stable distributions cryo-transmission electron microscopy; energy filtered transmission electron microscopy (EFTEM); contourlet; Bayesian denoiser; alpha-stable distributions
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Ahmed, S.S.; Messali, Z.; Ouahabi, A.; Trepout, S.; Messaoudi, C.; Marco, S. Nonparametric Denoising Methods Based on Contourlet Transform with Sharp Frequency Localization: Application to Low Exposure Time Electron Microscopy Images. Entropy 2015, 17, 3461-3478.

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