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Optimization of Three-Dimensional (3D) Chemical Imaging by Soft X-Ray Spectro-Tomography Using a Compressed Sensing Algorithm

Published online by Cambridge University Press:  12 September 2017

Juan Wu ,
Mirna Lerotic ,
Sean Collins ,
Rowan Leary ,
Zineb Saghi ,
Paul Midgley ,
Slava Berejnov ,
Darija Susac ,
Juergen Stumper  and
Gurvinder Singh
...Show all authors
Juan Wu
Affiliation:
Department of Chemistry & Chemical Biology, McMaster University, Hamilton, ON L8S 4M1, Canada
Mirna Lerotic
Affiliation:
2nd Look Consulting, Hong Kong
Sean Collins
Affiliation:
Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB2 1TQ, UK
Rowan Leary
Affiliation:
Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB2 1TQ, UK
Zineb Saghi
Affiliation:
Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB2 1TQ, UK
Paul Midgley
Affiliation:
Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB2 1TQ, UK
Slava Berejnov
Affiliation:
Automotive Fuel Cell Cooperation (AFCC) Corporation, Burnaby, BC V5J 5J8, Canada
Darija Susac
Affiliation:
Automotive Fuel Cell Cooperation (AFCC) Corporation, Burnaby, BC V5J 5J8, Canada
Juergen Stumper
Affiliation:
Automotive Fuel Cell Cooperation (AFCC) Corporation, Burnaby, BC V5J 5J8, Canada
Gurvinder Singh
Affiliation:
Department of Materials Science and Engineering, Norwegian University of Science and Technology, Trondheim N-7491, Norway
Adam P. Hitchcock*
Affiliation:
Department of Chemistry & Chemical Biology, McMaster University, Hamilton, ON L8S 4M1, Canada
*
*Corresponding author. [email protected]
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Abstract

Soft X-ray spectro-tomography provides three-dimensional (3D) chemical mapping based on natural X-ray absorption properties. Since radiation damage is intrinsic to X-ray absorption, it is important to find ways to maximize signal within a given dose. For tomography, using the smallest number of tilt series images that gives a faithful reconstruction is one such method. Compressed sensing (CS) methods have relatively recently been applied to tomographic reconstruction algorithms, providing faithful 3D reconstructions with a much smaller number of projection images than when conventional reconstruction methods are used. Here, CS is applied in the context of scanning transmission X-ray microscopy tomography. Reconstructions by weighted back-projection, the simultaneous iterative reconstruction technique, and CS are compared. The effects of varying tilt angle increment and angular range for the tomographic reconstructions are examined. Optimization of the regularization parameter in the CS reconstruction is explored and discussed. The comparisons show that CS can provide improved reconstruction fidelity relative to weighted back-projection and simultaneous iterative reconstruction techniques, with increasingly pronounced advantages as the angular sampling is reduced. In particular, missing wedge artifacts are significantly reduced and there is enhanced recovery of sharp edges. Examples of using CS for low-dose scanning transmission X-ray microscopy spectroscopic tomography are presented.

Keywords

3D chemical mappingX-ray tomographycompressed sensingSTXMelectron tomography
Type
Instrumentation and Software
Information
Microscopy and Microanalysis , Volume 23 , Issue 5 , October 2017 , pp. 951 - 966
Copyright
© Microscopy Society of America 2017 

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References

Adcock, B., Hansen, A.C., Poon, C. & Roman, B. (2017). Breaking the coherence barrier: A new theory for compressed sensing. Forum of Mathematics, Sigma, 5, e4.Google Scholar
Ade, H. & Hitchcock, A.P. (2008). NEXAFS microscopy and resonant scattering: Composition and orientation probed in real and reciprocal space. Polymer 49, 643–675.Google Scholar
Al-Afeef, A., Alekseev, A., Maclaren, I. & Cockshott, P. (2015 a). Electron tomography based on a Total Generalized Variation minimization reconstruction technique. 31st Picture Coding Symposium, Cairns, Australia.Google Scholar
Al-Afeef, A., Bobynko, J., Cockshott, W.P., Craven, A.J., Zuazo, I.U., Barges, P. & Maclaren, I. (2016). Linear chemically sensitive electron tomography using DualEELS and dictionary-based compressed sensing. Ultramicroscopy 170, 96–106.CrossRefGoogle ScholarPubMed
Al-Afeef, A., Cockshott, W.P., Maclaren, I. & Mcvitie, S. (2015 b). Electron tomography image reconstruction using data-driven adaptive compressed sensing. Scanning 38, 251–276.CrossRefGoogle ScholarPubMed
Andersen, A.H. & Kak, A.C. (1984). Simultaneous algebraic reconstruction technique (SART): A superior implementation of the ART algorithm. Ultrason Imaging 6, 81–94.Google Scholar
Bandhopadhyay, S., Singh, G. & Glomm, W.R. (2017). Shape tunable synthesis of anisotropic gold nanostructures through binary surfactant mixtures. Materials Today Chemistry 3, 1–9.Google Scholar
Bangliang, S., Yiheng, Z., Lihui, P., Danya, Y. & Baofen, Z. (2000). The use of simultaneous iterative reconstruction technique for electrical capacitance tomography. Chem Eng J 77, 37–41.CrossRefGoogle Scholar
Baruchel, J., Buffiere, J.-Y., Cloetens, P., Di Michiel, M., Ferrie, E., Ludwig, W., Maire, E. & Salvo, L. (2006). Advances in synchrotron radiation microtomography. Scripta Materialia 55, 41–46.Google Scholar
Batenburg, K.J. & Sijbers, J. (2007). Dart: A fast Heuristic algebraic reconstruction algorithm for discrete tomography. In Proceedings of the 2007 IEEE International Conference on Image Processing. Piscataway, NJ: IEEE. doi:10.1109/ICIP.2007.4379972.CrossRefGoogle Scholar
Berejnov, V., Susac, D., Stumper, J. & Hitchcock, A.P. (2013). 3D chemical mapping of PEM fuel cell cathodes by scanning transmission soft X-ray spectro-tomography. ECS Trans 50, 361–368.Google Scholar
Blumensath, T. & Davies, M.E. (2009). Iterative hard thresholding for compressed sensing. Appl Comput Harmonic Anal 27, 265–274.Google Scholar
Boudin, F., Hours, M., Lacronique, J.-F., Salvo, L., Suéry, M., Marmottant, A., Limodin, N. & Bernard, D. (2010). 3D imaging in material science: Application of X-ray tomography. C R Phys 11, 641–649.Google Scholar
Bredies, K., Kunish, K. & Pock, T. (2010). Total generalized variation. SIAM J Imaging Sci 3, 492–526.Google Scholar
Candès, E.J., Romber, J. & Tao, T. (2006). Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inform Theory 52, 489–509.CrossRefGoogle Scholar
Censor, Y., Elfving, T., Herman, G.T. & Nikazad, T. (2008). On diagonally relaxed orthogonal projection methods. SIAM J Sci Comput 30, 473–504.CrossRefGoogle Scholar
Chao, W., Fischer, P., Tyliszczak, T., Rekawa, S., Anderson, E. & Naulleau, P. (2012). Real space soft x-ray imaging at 10 nm spatial resolution. Optics Express 20, 9777–9783.CrossRefGoogle ScholarPubMed
Cimmino, G. (1938). Calcolo approssimato per le soluzioni dei sistemi di equazioni lineari. La Ricerca Scienti ca, XVI, Series II, Anno IX 1, 326–333.Google Scholar
Donoho, D.L. (2006). Compressed sensing. IEEE Trans Inform Theory 52, 1289–1306.Google Scholar
Duarte-Carvajalino, J.M. & Sapiro, G. (2009). Learning to sense sparse signals: Simultaneous sensing matrix and sparsifying dictionary optimization. IEEE Trans Image Process 18, 1395–1408.Google Scholar
Elfving, T., Hansen, P.C. & Nikazad, T. (2012). Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM J Sci Comput 34, A2000–A2017.Google Scholar
Ercius, P., Alaidi, O., Rames, M.J. & Ren, G. (2015). Electron tomography: A three-dimensional analytic tool for hard and soft materials research. Adv Mater 27, 5638–5663.CrossRefGoogle ScholarPubMed
Folkesson, A., Andersson, C., Alvfors, P., Alaküla, M. & Overgaard, L. (2003). Real life testing of a hybrid PEM fuel cell bus. J Power Sources 118, 349–357.Google Scholar
Gilbert, P. (1972). Iterative methods for the three-dimensional reconstruction of an object from projections. J Theoretical Biol 36, 105–117.Google Scholar
Gregor, J. & Benson, T. (2008). Computational analysis and improvement of SIRT. IEEE Trans Med Imag 27, 918–924.Google Scholar
Haberfehlner, G., Orthacker, A., Albu, M., Li, J. & Kothleitner, G. (2014). Nanoscale voxel spectroscopy by simultaneous EELS and EDS tomography. Nanoscale 6, 14563–14569.Google Scholar
Hitchcock, A.P. (2012). Soft X-ray imaging and spectromicroscopy. In Handbook of Nanoscopy, Tendeloo G.V., Dyck D.V., & Pennycook S.J. (Eds.), pp. 745–791. Weinheim, Germany: Wiley-VCH Verlag GmbH & Co. KGaA.Google Scholar
Hitchcock, A.P., Berejnov, V., Lee, V., West, M.M., Dutta, M., Colbow, V. & Wessel, S. (2014). Carbon corrosion of proton exchange membrane fuel cell catalyst layers studied by scanning transmission X-ray microscopy. J Power Sources 266, 66–78.Google Scholar
Hitchcock, A.P., Johansson, G.A., Mitchell, G.E., Keefe, M.H. & Tyliszcak, T. (2008). 3-D chemical imaging using angle-scan nanotomography in a soft X-ray scanning transmission X-ray microscope. Appl Phys A 92, 447–452.CrossRefGoogle Scholar
Holler, M., Diaz, A., Guizar-Sicairos, M., Karvinen, P., Färm, E., Härkönen, E., Ritala, M., Menzel, A., Raabe, J. & Bunk, O. (2014). X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution. Sci Rep 4, 3857.CrossRefGoogle ScholarPubMed
Howells, M., Jacobsen, C., Warwick, T. & Van Den Bos, A. (2007). Principles and applications of zone plate X-ray microscopes. In Science of Microscopy, Hawkes, P.W. & Spence, J.C.H. (Eds.), pp. 835–926. New York, NY: Springer.CrossRefGoogle Scholar
Jacobsen, C., Wirick, S., Flynn, G. & Zimba, C. (2000). Soft X-ray spectroscopy from image sequences with sub-100 nm spatial resolution. J Microsc 197, 173–184.Google Scholar
Johansson, G.A., Dynes, J.J., Hitchcock, A.P., Tyliszczak, T., Swerhone, G.D. & Lawrence, J.R. (2006). Chemically sensitive tomography at 50 nm spatial resolution using a soft X-ray scanning transmission X-ray microscope. Microsc Microanal 12, 1412–1413.Google Scholar
Johansson, G.A., Tyliszczak, T., Mitchell, G.E., Keefe, M.H. & Hitchcock, A.P. (2007). Three-dimensional chemical mapping by scanning transmission X-ray spectromicroscopy. J Synchrotron Rad 14, 395–402.Google Scholar
Kak, A.C. & Slaney, M. (1988). Principles of Computerized Tomographic Imaging, Society for Industrial and Applied Mathematics, New York: IEEE Press.Google Scholar
Kremer, J.R., Mastronarde, D.N. & Mclntosh, J.R. (1996). Computer visualization of three-dimensional image data using IMOD. J Struct Biol 116, 71–76.Google Scholar
Landweber, L. (1951). An iteration formula for Fredholm integral equations of the first kind. Am J Math 73, 615–624.Google Scholar
Leary, R.K., Kumar, A., Straney, P.J., Collins, S.M., Yazdi, S., Dunin-Borkowski, R.E., Midgley, P.A., Millstone, J.E. & Ringe, E. (2016). Structural and optical properties of discrete dendritic Pt nanoparticles on colloidal Au nanoprisms. J Phys Chem C 120, 20843–20851.Google Scholar
Leary, R., Midgley, P.A. & Thomas, J.M. (2012). Recent advances in the application of electron tomography to materials chemistry. Acc Chem Res 45, 1782–1791.Google Scholar
Leary, R., Saghi, Z., Midgley, P.A. & Holland, D.J. (2013). Compressed sensing electron tomography. Ultramicroscopy 131, 70–91.Google Scholar
Lerotic, M., Mak, R., Wirick, S., Meirer, F. & Jacobsen, C. (2014). MANTiS: A program for the analysis of X-ray spectromicroscopy data. J Synchrotron Rad 21, 1206–1212.Google Scholar
Lustig, M., Donoho, D. & Pauly, J.M. (2007). Sparse MRI: The application of compressed sensing for rapid MR imaging. Magn Reson Med 58, 1182–1195.CrossRefGoogle ScholarPubMed
Mallat, S. (2008). A Wavelet Tour of Signal Processing, 3rd ed. Cambridge, MA: Academic Press.Google Scholar
Melo, L.G.A., Hitchcock, A.P., Berejnov, V., Susac, D., Stumper, J. & Botton, G.A. (2016). Evaluating focused ion beam and ultramicrotome sample preparation for analytical microscopies of the cathode layer of a polymer electrolyte membrane fuel cell. J Power Sources 312, 23–35.Google Scholar
Nicoletti, O., De La Peña, F., Leary, R.K., Holland, D.J., Ducati, C. & Midgley, P.A. (2013). Three-dimensional imaging of localized surface plasmon resonances of metal nanoparticles. Nature 502, 80–84.Google Scholar
Obst, M. & Schmid, G. (2014). 3D chemical mapping: Application of scanning transmission (soft) X-ray microscopy (STXM) in combination with angle-scan tomography in bio-, geo-, and environmental sciences. In Electron Microscopy, Kuo, J. (Ed.), pp. 757–781. New York: Humana Press.Google Scholar
Obst, M., Wang, J. & Hitchcock, A.P. (2009). Soft X-ray spectro-tomography study of cyanobacterial biomineral nucleation. Geobiology 7, 577–591.Google Scholar
Otsu, N. (1975). A threshold selection method from gray-level histograms. Automatica 11.285–296, 23–27.Google Scholar
Penczek, P.C. (2010). Fundamentals of three-dimensional reconstruction from projections. Methods Enzymol 482, 1–33.Google Scholar
Pettersen, E.F., Goddard, T.D., Huang, C.C., Couch, G.S., Greenblatt, D.M., Meng, E.C. & Ferrin, T.E. (2004). UCSF Chimera—A visualization system for exploratory research and analysis. J Comput Chem 25, 1605–1612.CrossRefGoogle ScholarPubMed
Saghi, Z., Divitini, G., Winter, B., Leary, R., Spiecker, E., Ducati, C. & Midgley, P.A. (2016). Compressed sensing electron tomography of needle-shaped biological specimens – Potential for improved reconstruction fidelity with reduced dose. Ultramicroscopy 160, 230–238.CrossRefGoogle ScholarPubMed
Saghi, Z., Holland, D.J., Leary, R., Falqui, A., Bertoni, G., Sederman, A.J., Gladden, L.F. & Midgley, P.A. (2011). Three-dimensional morphology of iron oxide nanoparticles with reactive concave surfaces. A compressed sensing-electron tomography (CS-ET) approach. Nano Lett 11, 4666–4673.Google Scholar
Schmid, G., Obst, M., Wu, J. & Hitchcock, A.P. (2016). 3D chemical imaging of nanoscale biological, environmental and synthetic materials by soft X-ray spectro-tomography. In X-Ray and Neutron Techniques for Nanomaterials Characterization, Kumar, C.S.S.R. (Ed.), pp. 43–94. Berlin: Springer.Google Scholar
Schmid, G., Zeitvogel, F., Hao, L., Ingino, P., Kuerner, W., Dynes, J.J., Karunakaran, C., Wang, J., Lu, Y., Ayers, T., Schietinger, C., Hitchcock, A.P. & Obst, M. (2014). Synchrotron-based chemical nano-tomography of microbial cell-mineral aggregates in their natural, hydrated state. Microsc Microanal 20, 531–536.Google Scholar
Schneider, C.A., Rasband, W.S. & Eliceiri, K.W. (2012). NIH Image to ImageJ: 25 years of image analysis. Nature Methods 9, 671–675.CrossRefGoogle ScholarPubMed
Schrlau, M.G., Falls, E.M., Ziober, B.L. & Bau, H.H. (2008). Carbon nanopipettes for cell probes and intracellular injection. Nanotechnology 19, 015101.Google Scholar
Sidky, E.Y. & Pan, X.C. (2008). Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization. Phys Med Biol 53, 4777–4807.Google Scholar
Stöhr, J. (1992). NEXAFS Spectroscopy. Berlin: Springer-Verlag.Google Scholar
Susac, D., Berejnov, V., Hitchcock, A.P. & Stumper, J. (2011). STXM study of the ionomer distribution in the PEM fuel cell catalyst layers. ECS Trans 41, 629–635.Google Scholar
Susac, D., Berejnov, V., Hitchcock, A.P. & Stumper, J. (2013). STXM characterization of PEM fuel cell catalyst layers. ECS Trans 50, 405–413.Google Scholar
Torruella, P., Arenal, R., De La Peña, F., Saghi, S., Yedra, L., Eljarrat, A., López-Conesa, L., Estrader, M., López-Ortega, A., Salazar-Alvarez, G., Nogués, J., Ducati, C., Midgley, P.A., Peiró, F. & Estradé, S. (2016). 3D visualization of the iron oxidation state in FeO/Fe3O4 core–shell nanocubes from electron energy loss tomography. Nano Lett 16, 5068–5073.Google Scholar
Vainshtein, B.K. (1970). Finding the structure of objects from projections. Sov Phys Crystallogr 15, 781–787.Google Scholar
Wang, C., Mao, Z., Bao, F., Li, X. & Xie, X. (2005). Development and performance of 5 kW proton exchange membrane fuel cell stationary power system. Int J Hydrogen Energy 30, 1031–1034.CrossRefGoogle Scholar
Wang, J., Botton, G.A., West, M.M. & Hitchcock, A.P. (2009b). Quantitative evaluation of radiation damage to polyethylene terephthalate by soft X-rays and high-energy electrons. J Phys Chem B 113, 1869–1876.Google Scholar
Wang, J., Hitchcock, A.P., Karunakaran, C., Prange, A., Franz, B., Harkness, T., Lu, Y., Obst, M. & Hormes, J. (2011). 3D chemical and elemental imaging by STXM spectrotomography. AIP Conf Proc, 1365, 215–218.Google Scholar
Wang, J., Morin, C., Li, L., Hitchcock, A.P., Scholl, A. & Doran, A. (2009a). Radiation damage in soft X-ray microscopy. J Electron Spectrosc Relat Phenom 170, 25–36.Google Scholar
Xu, M. & Wang, L.V. (2005). Universal back-projection algorithm for photoacoustic computed tomography. Phys Rev E 71, 016706.Google Scholar
Zhang, X., Balhorn, R. & Mazrimas, J. (1996). Mapping and measuring DNA to protein ratios in mammalian sperm head by XANES imaging. J Struct Biol 116, 335–344.Google Scholar
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