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

  • Juan Wu (a1), Mirna Lerotic (a2), Sean Collins (a3), Rowan Leary (a3), Zineb Saghi (a3), Paul Midgley (a3), Slava Berejnov (a4), Darija Susac (a4), Juergen Stumper (a4), Gurvinder Singh (a5) and Adam P. Hitchcock (a1)...
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.

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* Corresponding author. aph@mcmaster.ca
References
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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.
Ade, H. & Hitchcock, A.P. (2008). NEXAFS microscopy and resonant scattering: Composition and orientation probed in real and reciprocal space. Polymer 49, 643675.
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.
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, 96106.
Al-Afeef, A., Cockshott, W.P., Maclaren, I. & Mcvitie, S. (2015 b). Electron tomography image reconstruction using data-driven adaptive compressed sensing. Scanning 38, 251276.
Andersen, A.H. & Kak, A.C. (1984). Simultaneous algebraic reconstruction technique (SART): A superior implementation of the ART algorithm. Ultrason Imaging 6, 8194.
Bandhopadhyay, S., Singh, G. & Glomm, W.R. (2017). Shape tunable synthesis of anisotropic gold nanostructures through binary surfactant mixtures. Materials Today Chemistry 3, 19.
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, 3741.
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, 4146.
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.
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, 361368.
Blumensath, T. & Davies, M.E. (2009). Iterative hard thresholding for compressed sensing. Appl Comput Harmonic Anal 27, 265274.
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, 641649.
Bredies, K., Kunish, K. & Pock, T. (2010). Total generalized variation. SIAM J Imaging Sci 3, 492526.
Candès, E.J., Romber, J. & Tao, T. (2006). Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inform Theory 52, 489509.
Censor, Y., Elfving, T., Herman, G.T. & Nikazad, T. (2008). On diagonally relaxed orthogonal projection methods. SIAM J Sci Comput 30, 473504.
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, 97779783.
Cimmino, G. (1938). Calcolo approssimato per le soluzioni dei sistemi di equazioni lineari. La Ricerca Scienti ca, XVI, Series II, Anno IX 1, 326333.
Donoho, D.L. (2006). Compressed sensing. IEEE Trans Inform Theory 52, 12891306.
Duarte-Carvajalino, J.M. & Sapiro, G. (2009). Learning to sense sparse signals: Simultaneous sensing matrix and sparsifying dictionary optimization. IEEE Trans Image Process 18, 13951408.
Elfving, T., Hansen, P.C. & Nikazad, T. (2012). Semiconvergence and relaxation parameters for projected SIRT algorithms. SIAM J Sci Comput 34, A2000A2017.
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, 56385663.
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, 349357.
Gilbert, P. (1972). Iterative methods for the three-dimensional reconstruction of an object from projections. J Theoretical Biol 36, 105117.
Gregor, J. & Benson, T. (2008). Computational analysis and improvement of SIRT. IEEE Trans Med Imag 27, 918924.
Haberfehlner, G., Orthacker, A., Albu, M., Li, J. & Kothleitner, G. (2014). Nanoscale voxel spectroscopy by simultaneous EELS and EDS tomography. Nanoscale 6, 1456314569.
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. 745791. Weinheim, Germany: Wiley-VCH Verlag GmbH & Co. KGaA.
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, 6678.
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, 447452.
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.
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. 835926. New York, NY: Springer.
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, 173184.
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, 14121413.
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, 395402.
Kak, A.C. & Slaney, M. (1988). Principles of Computerized Tomographic Imaging, Society for Industrial and Applied Mathematics, New York: IEEE Press.
Kremer, J.R., Mastronarde, D.N. & Mclntosh, J.R. (1996). Computer visualization of three-dimensional image data using IMOD. J Struct Biol 116, 7176.
Landweber, L. (1951). An iteration formula for Fredholm integral equations of the first kind. Am J Math 73, 615624.
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, 2084320851.
Leary, R., Midgley, P.A. & Thomas, J.M. (2012). Recent advances in the application of electron tomography to materials chemistry. Acc Chem Res 45, 17821791.
Leary, R., Saghi, Z., Midgley, P.A. & Holland, D.J. (2013). Compressed sensing electron tomography. Ultramicroscopy 131, 7091.
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, 12061212.
Lustig, M., Donoho, D. & Pauly, J.M. (2007). Sparse MRI: The application of compressed sensing for rapid MR imaging. Magn Reson Med 58, 11821195.
Mallat, S. (2008). A Wavelet Tour of Signal Processing, 3rd ed. Cambridge, MA: Academic Press.
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, 2335.
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, 8084.
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. 757781. New York: Humana Press.
Obst, M., Wang, J. & Hitchcock, A.P. (2009). Soft X-ray spectro-tomography study of cyanobacterial biomineral nucleation. Geobiology 7, 577591.
Otsu, N. (1975). A threshold selection method from gray-level histograms. Automatica 11.285–296, 2327.
Penczek, P.C. (2010). Fundamentals of three-dimensional reconstruction from projections. Methods Enzymol 482, 133.
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, 16051612.
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, 230238.
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, 46664673.
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. 4394. Berlin: Springer.
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, 531536.
Schneider, C.A., Rasband, W.S. & Eliceiri, K.W. (2012). NIH Image to ImageJ: 25 years of image analysis. Nature Methods 9, 671675.
Schrlau, M.G., Falls, E.M., Ziober, B.L. & Bau, H.H. (2008). Carbon nanopipettes for cell probes and intracellular injection. Nanotechnology 19, 015101.
Sidky, E.Y. & Pan, X.C. (2008). Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization. Phys Med Biol 53, 47774807.
Stöhr, J. (1992). NEXAFS Spectroscopy. Berlin: Springer-Verlag.
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, 629635.
Susac, D., Berejnov, V., Hitchcock, A.P. & Stumper, J. (2013). STXM characterization of PEM fuel cell catalyst layers. ECS Trans 50, 405413.
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, 50685073.
Vainshtein, B.K. (1970). Finding the structure of objects from projections. Sov Phys Crystallogr 15, 781787.
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, 10311034.
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, 18691876.
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.
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, 2536.
Xu, M. & Wang, L.V. (2005). Universal back-projection algorithm for photoacoustic computed tomography. Phys Rev E 71, 016706.
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, 335344.
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