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      Contrast Transfer Function-Based Exit-Wave Reconstruction and Denoising of Atomic-Resolution Transmission Electron Microscopy Images of Graphene and Cu Single Atom Substitutions by Deep Learning Framework

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          Abstract

          The exit wave is the state of a uniform plane incident electron wave exiting immediately after passing through a specimen and before the atomic-resolution transmission electron microscopy (ARTEM) image is modified by the aberration of the optical system and the incoherence effect of the electron. Although exit-wave reconstruction has been developed to prevent the misinterpretation of ARTEM images, there have been limitations in the use of conventional exit-wave reconstruction in ARTEM studies of the structure and dynamics of two-dimensional materials. In this study, we propose a framework that consists of the convolutional dual-decoder autoencoder to reconstruct the exit wave and denoise ARTEM images. We calculated the contrast transfer function (CTF) for real ARTEM and assigned the output of each decoder to the CTF as the amplitude and phase of the exit wave. We present exit-wave reconstruction experiments with ARTEM images of monolayer graphene and compare the findings with those of a simulated exit wave. Cu single atom substitution in monolayer graphene was, for the first time, directly identified through exit-wave reconstruction experiments. Our exit-wave reconstruction experiments show that the performance of the denoising task is improved when compared to the Wiener filter in terms of the signal-to-noise ratio, peak signal-to-noise ratio, and structural similarity index map metrics.

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          Most cited references30

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          The rise of graphene.

          Graphene is a rapidly rising star on the horizon of materials science and condensed-matter physics. This strictly two-dimensional material exhibits exceptionally high crystal and electronic quality, and, despite its short history, has already revealed a cornucopia of new physics and potential applications, which are briefly discussed here. Whereas one can be certain of the realness of applications only when commercial products appear, graphene no longer requires any further proof of its importance in terms of fundamental physics. Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena, some of which are unobservable in high-energy physics, can now be mimicked and tested in table-top experiments. More generally, graphene represents a conceptually new class of materials that are only one atom thick, and, on this basis, offers new inroads into low-dimensional physics that has never ceased to surprise and continues to provide a fertile ground for applications.
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            Reducing the dimensionality of data with neural networks.

            High-dimensional data can be converted to low-dimensional codes by training a multilayer neural network with a small central layer to reconstruct high-dimensional input vectors. Gradient descent can be used for fine-tuning the weights in such "autoencoder" networks, but this works well only if the initial weights are close to a good solution. We describe an effective way of initializing the weights that allows deep autoencoder networks to learn low-dimensional codes that work much better than principal components analysis as a tool to reduce the dimensionality of data.
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              The electronic properties of graphene

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                Author and article information

                Journal
                Nanomaterials (Basel)
                Nanomaterials (Basel)
                nanomaterials
                Nanomaterials
                MDPI
                2079-4991
                06 October 2020
                October 2020
                : 10
                : 10
                : 1977
                Affiliations
                [1 ]Center for Multidimensional Carbon Materials, Institute for Basic Science (IBS), Ulsan 44919, Korea; jong022@ 123456unist.ac.kr (J.L.); lyd1227@ 123456unist.ac.kr (Y.L.); jmkim17@ 123456unist.ac.kr (J.K.)
                [2 ]Department of Materials Science and Engineering, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Korea
                Author notes
                [* ]Correspondence: zhlee@ 123456unist.ac.kr
                Author information
                https://orcid.org/0000-0003-3246-4072
                Article
                nanomaterials-10-01977
                10.3390/nano10101977
                7601262
                33036252
                199d6699-ec8b-4a90-b6cd-e4340ae413d6
                © 2020 by the authors.

                Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).

                History
                : 12 September 2020
                : 02 October 2020
                Categories
                Article

                deep learning,exit-wave reconstruction,denoising,single atom substitution,graphene,atomic resolution transmission electron microscopy

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