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Simulation-Trained Sparse Coding for High-Precision Phase Imaging in Low-Dose Electron Holography

Published online by Cambridge University Press:  09 June 2020

Satoshi Anada ,
Yuki Nomura ,
Tsukasa Hirayama  and
Kazuo Yamamoto
Satoshi Anada*
Affiliation:
Nanostructures Research Laboratory, Japan Fine Ceramics Center, 2-4-1 Mutsuno, Atsuta-ku, Nagoya, Aichi456-8587, Japan
Yuki Nomura
Affiliation:
Technology Innovation Division, Panasonic Corporation, 3-1-1 Yagumo-Nakamachi, Moriguchi, Osaka570-8501, Japan
Tsukasa Hirayama
Affiliation:
Nanostructures Research Laboratory, Japan Fine Ceramics Center, 2-4-1 Mutsuno, Atsuta-ku, Nagoya, Aichi456-8587, Japan
Kazuo Yamamoto
Affiliation:
Nanostructures Research Laboratory, Japan Fine Ceramics Center, 2-4-1 Mutsuno, Atsuta-ku, Nagoya, Aichi456-8587, Japan
*
*Author for correspondence: Satoshi Anada, E-mail: [email protected]
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Abstract

We broaden the applicability of sparse coding, a machine learning method, to low-dose electron holography by using simulated holograms for learning and validation processes. The holograms, with shot noise, are prepared to generate a model, or a dictionary, that includes basic features representing interference fringes. The dictionary is applied to sparse representations of other simulated holograms with various signal-to-noise ratios (SNRs). Results demonstrate that this approach successfully removes noise for holograms with an extremely small SNR of 0.10, and that the denoised holograms provide the accurate phase distribution. Furthermore, this study demonstrates that the dictionary learned from the simulated holograms can be applied to denoising of experimental holograms of a p–n junction specimen recorded with different exposure times. The results indicate that the simulation-trained sparse coding is suitable for use over a wide range of imaging conditions, in particular for observing electron beam-sensitive materials.

Keywords

electron holographyhologram simulationimage denoisinglow-dose imagingmachine learningsparse coding
Type
Software and Instrumentation
Information
Microscopy and Microanalysis , Volume 26 , Issue 3 , June 2020 , pp. 429 - 438
Copyright
Copyright © Microscopy Society of America 2020

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References

Aharon, M, Elad, M & Bruckstein, A (2006). K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans Signal Process 54, 4311–4322.CrossRefGoogle Scholar
Anada, S, Nomura, Y, Hirayama, T & Yamamoto, K (2019). Sparse coding and dictionary learning for electron hologram denoising. Ultramicroscopy 206, 112818.CrossRefGoogle ScholarPubMed
Anderson, HS, Ilic-Helms, J, Rohrer, B, Wheeler, J & Larson, K (2013). Sparse imaging for fast electron microscopy. IS&T/SPIE Electr Imaging 8657, 86570C.Google Scholar
Bertsekas, DP (1999). Nonlinear Programming. Belmont: Athena Scientific.Google Scholar
Binev, P, Dahmen, W, DeVore, R & Lamby, P (2012). Compressed sensing and electron microscopy. In Modeling Nanoscale Imaging in Electron Microscopy, Nanostructure Science and Technology, Vogt, T, Dahmen, W & Binev, P (Eds.), pp. 73–126. New York: Springer.CrossRefGoogle Scholar
Candès, EJ & Donoho, DL (1999). Curvelets—a surprisingly effective nonadaptive representation for objects with edges. In Curves and Surfaces, Rabut, C, Cohen, A & Schumaker, LL (Eds.), Nashville: Vanderbilt University Press.Google Scholar
Deng, Y, Chen, Y, Zhang, Y, Wanga, S, Zhang, F & Sun, F (2016). ICON: 3D reconstruction with ‘missing-information’ restoration in biological electron tomography. J Struct Biol 195, 100–112.CrossRefGoogle ScholarPubMed
De Ruijter, WJ & Weiss, JK (1993). Detection limits in quantitative off-axis electron holography. Ultramicroscopy 50, 269–283.CrossRefGoogle Scholar
Dunin-Borkowski, RE, McCartney, MR, Frankel, RB, Bazylinski, DA, Posfai, M & Buseck, PR (1998). Magnetic microstructure of magnetotactic bacteria by electron holography. Science 282, 1868–1870.CrossRefGoogle ScholarPubMed
Efron, B, Hastie, T, Johnstone, I & Tibshirani, R (2004). Least angle regression. Ann Statist 32, 407–499.Google Scholar
Elad, M & Aharon, M (2006). Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans Image Process 15, 3736–3745.CrossRefGoogle ScholarPubMed
Engan, K, Aase, SO & Husoy, JH (1999). Method of optimal directions for frame design. IEEE Int Conf Acoust Speech Signal Process 5, 2443–2446.Google Scholar
Ferroni, M, Signoroni, A, Sanzogni, A, Masini, L, Migliori, A, Ortolani, L, Pezza, A & Morandi, V (2016). Biological application of compressed sensing tomography in the scanning electron microscope. Sci Rep 6, 33354.CrossRefGoogle ScholarPubMed
Frabboni, S, Matteucci, G & Pozzi, G (1987). Observation of electrostatic fields by electron holography: The case of reverse-biased p-n junctions. Ultramicroscopy 23, 29–38.CrossRefGoogle Scholar
Frabboni, S, Matteucci, G, Pozzi, G & Vanzi, M (1985). Electron holographic observations of the electrostatic field associated with thin reverse-biased p-n junctions. Phys Rev Lett 55, 2196–2199.CrossRefGoogle ScholarPubMed
Gabor, D (1948). A new microscopic principle. Nature 161, 777–778.CrossRefGoogle ScholarPubMed
Gribelyuk, MA, McCartney, MR, Li, J, Murthy, CS, Ronsheim, P, Doris, B, McMurray, JS, Hegde, S & Smith, DJ (2002). Mapping of electrostatic potential in deep submicron CMOS devices by electron holography. Phys Rev Lett 8, 025505.Google Scholar
Harada, K, Akashi, T, Togawa, Y, Matsuda, T & Tonomura, A (2005). Optical system for double-biprism electron holography. J Electron Microsc 54, 19–27.CrossRefGoogle ScholarPubMed
Harada, K, Tonomura, A, Togawa, Y, Akashi, T & Matsuda, T (2004). Double-biprism electron interferometry. Appl Phys Lett 84, 3229–3231.CrossRefGoogle Scholar
Harscher, A & Lichte, H (1996). Experimental study of amplitude and phase detection limits in electron holography. Ultramicroscopy 64, 57–66.CrossRefGoogle Scholar
Hastie, T, Tibshirani, R & Friedman, J (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd ed. New York: Springer.CrossRefGoogle Scholar
Hirayama, T, Ru, Q, Tanji, T & Tonomura, A (1993). Observation of magnetic domain states of barium ferrite particles by electron holography. Appl Phys Lett 63, 418–420.CrossRefGoogle Scholar
Kovarik, L, Stevens, A, Liyu, A & Browning, ND (2016). Implementing an accurate and rapid sparse sampling approach for low-dose atomic resolution STEM imaging. Appl Phys Lett 109, 164102.CrossRefGoogle Scholar
Lau, B & Pozzi, G (1978). Off axis electron micro-holography of magnetic domain walls. Optik 51, 287–296.Google Scholar
Leary, R, Saghi, Z, Midgley, PA & Holland, DJ (2013). Compressed sensing electron tomography. Ultramicroscopy 131, 70–91.CrossRefGoogle ScholarPubMed
Lee, TS (1996). Image representation using 2D Gabor wavelets. IEEE Trans Pattern Anal Mach Intell 18, 959–971.Google Scholar
Lenz, F (1988). Statistics of phase and contrast determination in electron holograms. Optik 79, 13–14.Google Scholar
Lichte, H (2008). Performance limits of electron holography. Ultramicroscopy 108, 256–262.CrossRefGoogle ScholarPubMed
Lichte, H, Geiger, D, Harscher, A, Heindl, E, Lehmann, M, Malamidis, D, Orchowski, A & Rau, W-D (1996). Artefacts in electron holography. Ultramicroscopy 64, 67–77.CrossRefGoogle Scholar
Mairal, J, Bach, F, Ponce, J & Sapiro, G (2010). Online learning for matrix factorization and sparse coding. J Mach Learn Res 11, 19–60.Google Scholar
Mallet, S (1999). A Wavelet Tour of Signal Processing, 2nd ed.New York: Academic Press.Google Scholar
Matsuda, T, Hasegawa, S, Igarashi, M, Kobayashi, T, Naito, M, Kajiyama, H, Endo, J, Osakabe, N, Tonomura, A & Aoki, R (1989). Magnetic field observation of a single flux quantum by electron-holographic interferometry. Phys Rev Lett 62, 2519–2522.CrossRefGoogle ScholarPubMed
McCartney, MR, Smith, DJ, Hull, R, Bean, JC, Voelkl, E & Frost, B (1994). Direct observation of potential distribution across Si/Si pn junctions using offaxis electron holography. Appl Phys Lett 65, 2603–2605.CrossRefGoogle Scholar
Mehdi, BL, Stevens, A, Kovarik, L, Jiang, N, Mehta, H, Liyu, A, Reehl, S, Stanfill, B, Luzi, L, Hao, W, Bramer, L & Browning, ND (2019). Controlling the spatio-temporal dose distribution during STEM imaging by subsampled acquisition: In-situ observations of kinetic processes in liquids. Appl Phys Lett 115, 063102.CrossRefGoogle Scholar
Möllenstedt, G & Düker, H (1956). Beobachtungen und messungen an biprisma-interferenzen mit elektronenwellen. Z Phys 145, 377–397.CrossRefGoogle Scholar
Möllenstedt, G & Wahl, H (1968). Elektronenholographie und Rekonstruktion mit Laserlicht. Naturwissenschaften 55, 340–341.CrossRefGoogle Scholar
Olshausen, BA & Field, DJ (1996). Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature 381, 607–609.CrossRefGoogle ScholarPubMed
Olshausen, BA & Field, DJ (2005). How close are we to understanding V1? Neural Comput 17, 1665–1699.CrossRefGoogle ScholarPubMed
Pozzi, G & Missiroli, GF (1973). Interference electron microscopy of magnetic domains. J Microsc 18, 103–108.Google Scholar
Rau, WD, Lichte, H, Völkl, E & Weierstall, U (1991). Real-time reconstruction of electron-off-axis holograms recorded with a high pixel CCD camera. J Comput-Assist Microsc 3, 51–63.Google Scholar
Rau, WD, Schwander, P, Baumann, FH, Höppner, W & Ourmazd, A (1999). Two-dimensional mapping of the electrostatic potential in transistors by electron holography. Phys Rev Lett 82, 2614–2617.CrossRefGoogle Scholar
Ru, Q, Endo, J, Tanji, T & Tonomura, A (1991). Phase-shifting electron holography by beam tilting. Appl Phys Lett 59, 2372–2374.CrossRefGoogle Scholar
Ru, Q, Hirayama, T, Endo, J & Tonomura, A (1992). Hologram-shifting method for high-speed electron hologram reconstruction. Jpn J Appl Phys 31, 1919–1921.CrossRefGoogle Scholar
Ru, Q, Lai, GL, Aoyama, K, Endo, J & Tonomura, A (1994). Principle and application of phase-shifting electron holography. Ultramicroscopy 55, 209–220.CrossRefGoogle Scholar
Saghi, Z, Divitini, G, Winter, B, Leary, R, Spiecker, E, Ducati, C & Midgley, PA (2016). Compressed sensing electron tomography of needle-shaped biological specimens – Potential for improved reconstruction fidelity with reduced dose. Ultramicroscopy 160, 230–238.CrossRefGoogle ScholarPubMed
Stevens, A, Kovarik, L, Abellan, P, Yuan, X, Carin, L & Browning, ND (2015). Applying compressive sensing to TEM video: A substantial frame rate increase on any camera. Adv Struct Chem Imaging 1, 10.CrossRefGoogle Scholar
Stevens, A, Luzi, L, Yang, H, Kovarik, L, Mehdi, BL, Liyu, A, Gehm, ME & Browning, ND (2018 a). A sub-sampled approach to extremely low-dose STEM. Appl Phys Lett 112, 043104.CrossRefGoogle Scholar
Stevens, A, Yang, H, Carin, L, Arslan, I & Browning, ND (2013). The potential for Bayesian compressive sensing to significantly reduce electron dose in high-resolution STEM images. Microscopy 63, 41–51.CrossRefGoogle ScholarPubMed
Stevens, A, Yang, H, Hao, Y, Jones, L, Ophus, C, Nellist, PD & Browning, ND (2018 b). Subsampled STEM-phychography. Appl Phys Lett 113, 033104.CrossRefGoogle Scholar
Tibshirani, R (1996). Regression shrinkage and section via the Lasso. J R Statist Soc B 58, 267–288.Google Scholar
Tonomura, A (1972). The electron interference method for magnetization measurement of thin films. Jpn J Appl Phys 11, 493–502.CrossRefGoogle Scholar
Tonomura, A, Matsuda, R, Endo, J, Arii, T & Mihara, K (1980). Direct observation of fine structure of magnetic domain walls by electron holography. Phys Rev Lett 44, 1430–1433.CrossRefGoogle Scholar
Tonomura, A, Matsuda, R, Tanabe, H, Osakabe, N, Endo, J, Fukuhara, A, Shinagawa, K & Fujiwara, H (1982). Electron holography technique for investigating thin ferromagnetic films. Phys Rev B 25, 6799–6804.CrossRefGoogle Scholar
Tsiper, S, Dicker, O, Kaizerman, I, Zohar, Z, Segev, M & Eldar, YC (2017). Sparsity-based super resolution for SEM images. Nano Lett 17, 5437–5445.CrossRefGoogle ScholarPubMed
Wang, Z, Hirayama, T, Sasaki, K, Saka, H & Kato, N (2002). Electron holographic characterization of electrostatic potential distributions in a transistor sample fabricated by focused ion beam. Appl Phys Lett 80, 246–248.CrossRefGoogle Scholar
Yamamoto, K, Hirayama, T & Tanji, T (2004). Off-axis electron holography without Fresnel fringes. Ultramicroscopy 101, 265–269.CrossRefGoogle ScholarPubMed
Yamamoto, K, Hirayama, T, Tanji, T & Hibino, M (2003). Evaluation of high-precision phase-shifting electron holography by using hologram simulation. Surf Interface Anal 35, 60–65.CrossRefGoogle Scholar
Yamamoto, K, Kawajiri, I, Tanji, T, Hibino, M & Hirayama, T (2000). High precision phase-shifting electron holography. J Electron Microsc 49, 31–39.CrossRefGoogle ScholarPubMed
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