{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T10:41:57Z","timestamp":1776076917045,"version":"3.50.1"},"reference-count":14,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2015,5,20]],"date-time":"2015-05-20T00:00:00Z","timestamp":1432080000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/e17053461","type":"journal-article","created":{"date-parts":[[2015,5,20]],"date-time":"2015-05-20T11:05:46Z","timestamp":1432119946000},"page":"3461-3478","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":51,"title":["Nonparametric Denoising Methods Based on Contourlet Transform with Sharp Frequency Localization: Application to Low Exposure Time Electron Microscopy Images"],"prefix":"10.3390","volume":"17","author":[{"given":"Soumia","family":"Ahmed","sequence":"first","affiliation":[{"name":"Science and Technology Faculty, University of Mohamed El Bachir El Ibrahimi\u2013Bordj Bou Arr\u00e9ridj, 34030 Bordj Bou Arr\u00e9ridj, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zoubeida","family":"Messali","sequence":"additional","affiliation":[{"name":"Laboratory of Electrical Engineering, University of M'sila, 28000 M'sila, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6392-7693","authenticated-orcid":false,"given":"Abdeldjalil","family":"Ouahabi","sequence":"additional","affiliation":[{"name":"Polytech Tours, Graduate School of Engineering, University of Tours, 37200 Tours, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sylvain","family":"Trepout","sequence":"additional","affiliation":[{"name":"INSERM U1196, B\u00e2t. 112, Centre Universitaire, 91405 Orsay Cedex, France"},{"name":"Institut Curie, Centre de Recherche, B\u00e2t. 112, Centre Universitaire, 91405 Orsay Cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cedric","family":"Messaoudi","sequence":"additional","affiliation":[{"name":"INSERM U1196, B\u00e2t. 112, Centre Universitaire, 91405 Orsay Cedex, France"},{"name":"Institut Curie, Centre de Recherche, B\u00e2t. 112, Centre Universitaire, 91405 Orsay Cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sergio","family":"Marco","sequence":"additional","affiliation":[{"name":"INSERM U1196, B\u00e2t. 112, Centre Universitaire, 91405 Orsay Cedex, France"},{"name":"Institut Curie, Centre de Recherche, B\u00e2t. 112, Centre Universitaire, 91405 Orsay Cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,5,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1002\/(SICI)1097-0029(20000501)49:3<245::AID-JEMT4>3.0.CO;2-O","article-title":"Electron detection characteristics of a slow-scan CCD camera, imaging plates and film, and electron image restoration","volume":"49","author":"Zuo","year":"2000","journal-title":"Microsc. 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(2012). Signal and Image Multiresolution Analysis, Wiley-ISTE.","DOI":"10.1002\/9781118568767"},{"key":"ref_10","unstructured":"Fabrizio, R., and Brani, V. (2005). Bayesian Modeling in the Wavelet Domain, Elsevier."},{"key":"ref_11","unstructured":"Nikias, C.L., and Shao, M. (1995). Signal Processing with Alpha-Stable Distributions and Applications, Wiley. [1st]."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Lu, Y., and Do, M.N. (2006, January 8\u201311). A new contourlet transform with sharp frequency localization, Atlanta, GA, USA.","DOI":"10.1109\/ICIP.2006.312657"},{"key":"ref_13","first-page":"1","article-title":"Bilateral filtering and wavelet based image denoising: Application to electron microscopy images with low electron dose","volume":"1","author":"Messali","year":"2013","journal-title":"Int. J. Netw. 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Technol"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/5\/3461\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:46:38Z","timestamp":1760215598000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/5\/3461"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5,20]]},"references-count":14,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2015,5]]}},"alternative-id":["e17053461"],"URL":"https:\/\/doi.org\/10.3390\/e17053461","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,5,20]]}}}