Geometric reconstruction methods for electron tomography

Ultramicroscopy

Volumn 128, Issue , 2013, Pages 42-54

  Alpers, Andreas ^a   Gardner, Richard J ^b   König, Stefan ^a   Pennington, Robert S ^c   Boothroyd, Chris B ^d   Houben, Lothar ^d   Dunin Borkowski, Rafal E ^d   Joost Batenburg, Kees ^e,f  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b WESTERN WASHINGTON UNIVERSITY   (United States)

^c TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^d FORSCHUNGSZENTRUM JÜLICH   (Germany)

^e CWI   (Netherlands)

^f UNIVERSITY OF ANTWERP   (Belgium)

Author keywords

Convexity; Electron tomography; Homogeneity; InAs nanowires; Reconstruction algorithms

Indexed keywords

CONVEXITY; ELECTRON TOMOGRAPHY; HOMOGENEITY; INAS NANOWIRES; RECONSTRUCTION ALGORITHMS;

ALGORITHMS; GEOMETRY; NANOWIRES;

ELECTRIC IMPEDANCE TOMOGRAPHY;

2N GON; ACCURACY; ARTICLE; BINARY ALGEBRAIC RECONSTRUCTION TECHNIQUE; CLASSIFICATION ALGORITHM; COMPUTER SIMULATION; DISCRETE ALGEBRAIC RECONSTRUCTION TECHNIQUE; ELECTRON TOMOGRAPHY; GARDNER KIDERLEN X RAY; GEOMETRY; IMAGE ANALYSIS; IMAGE QUALITY; IMAGE RECONSTRUCTION; IMAGING AND DISPLAY; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MODIFIED PRINCE WILLSKY ALGORITHM; PROBABILITY; PROCESS DEVELOPMENT; SIMULTANEOUS ITERATIVE RECONSTRUCTION TECHNIQUE; STATISTICAL DISTRIBUTION; UNFILTERED BACKPROJECTION;

EID: 84875017799     PISSN: 03043991     EISSN: 18792723     Source Type: Journal    
DOI: 10.1016/j.ultramic.2013.01.002     Document Type: Article

References (53)

1. Ercius P., Weyland M., Muller D.A., Gignac L.M. Three-dimensional imaging of nanovoids in copper interconnects using incoherent bright field tomography. Applied Physics Letters 2006, 88:243116.
2. Friedrich H., McCartney M.R., Buseck P.R. Comparison of intensity distributions in tomograms from BF TEM, ADF TEM, HAADF STEM, and calculated tilt series. Ultramicroscopy 2005, 106:18-27.
3. Janssen A.H., Yang C.-M., Wang Y., Schüth F., Koster A.J., de Jong K.P. Localization of small metal (oxide) particles in SBA-15 using bright-field electron tomography. Journal of Physical Chemistry B 2003, 107:10552-10556.
4. Midgley P.A., Dunin-Borkowski R.E. Electron tomography and holography in materials science. Nature Materials 2009, 8:271-280.
5. Midgley P.A., Weyland M. 3D electron microscopy in the physical sciences. the development of Z-contrast and EFTEM tomography. Ultramicroscopy 2003, 96:413-431.
6. Möbus G., Doole R.C., Inkson B.J. Spectroscopic electron tomography. Ultramicroscopy 2003, 96:433-451.
7. Pennington R.S., König S., Alpers A., Boothroyd C.B., Dunin-Borkowski R.E. Reconstruction of an InAs nanowire using geometric and algebraic tomography. Journal of Physics: Conference Series 2011, 326:012045.
8. Xu X., Peng Y., Saghi Z., Gay R., Inkson B.J., Möbus G. 3D reconstruction of SPM probes by electron tomography. Journal of Physics: Conference Series 2007, 61:810-814.
9. G.T. Herman, Fundamentals of computerized tomography: image reconstruction from projections, in: Advances in Pattern Recognition, 2nd edition, Springer, London, 2009.
10. A.C. Kak, M. Slaney, Principles of computerized tomographic imaging, in: Classics in Applied Mathematics, vol. 33, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2001 Reprint of the 1988 original.
11. Pan X., Sidky E.Y., Vannier M. Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction?. Inverse Problems 2009, 25:123009.
12. Fernandez J.-J. Computational methods for electron tomography. Micron 2012, 43:1010-1030.
13. R.J. Gardner, Geometric tomography, Encyclopedia of Mathematics and its Applications, vol. 58, 2nd edition, Cambridge University Press, New York, 2006.
14. G.T. Herman, A. Kuba (Eds.), Discrete Tomography: Foundations, Algorithms, and Applications, Applied and Numerical Harmonic Analysis, Birkhäuser Boston Inc., Boston, MA, 1999.
15. G.T. Herman, A. Kuba (Eds.), Advances in discrete tomography and its applications, in: Applied and Numerical Harmonic Analysis, Birkhäuser Boston Inc., Boston, MA, 2007.
16. Dick K.A. A review of nanowire growth promoted by alloys and non-alloying elements with emphasis on Au-assisted III-V nanowires. Progress in Crystal Growth and Characterization of Materials 2008, 54:138-173.
17. 1-xP core-shell nanowires. Journal of Crystal Growth 2010, 312:1755-1760.
18. R. Davidi, G.T. Herman, J. Klukowska, SNARK09: a programming system for the reconstruction of 2D images from 1D projections 〈〉, 2009 [Online accessed 10-August-2012]. http://www.dig.cs.gc.cuny.edu/software/snark09.
19. Petersen T.C., Ringer S.P. Electron tomography using a geometric surface-tangent algorithm. application to atom probe specimen morphology. Journal of Applied Physics 2009, 105:103518.
20. Saghi Z., Xu X., Möbus G. Electron tomography of regularly shaped nanostructures under non-linear image acquisition. Journal of Microscopy 2008, 232:186-195.
21. Goris B., van den Broek W., Batenburg K.J., Mezerji H.H., Bals S. Electron tomography based on a total variation minimization reconstruction technique. Ultramicroscopy 2012, 113:120-130.
22. Saghi Z., Holland D.J., Leary R., Falqui A., Bertoni G., Sederman A.J., Gladden L.F., Midgley P.A. Three-dimensional morphology of iron oxide nanoparticles with reactive concave surfaces. A compressed sensing-electron tomography (CS-ET) approach. Nano Letters 2011, 11:4666-4673.
23. Alpers A., Poulsen H.F., Knudsen E., Herman G.T. A discrete tomography algorithm for improving the quality of 3DXRD grain maps. Journal of Applied Crystallography 2006, 39:582-588.
24. Carvalho B.M., Herman G.T., Matej S., Salzberg C., Vardi E. Binary tomography for triplane cardiography. Information Processing in Medical Imaging 1999, vol. 1613:29-41. Springer, Berlin.
25. van Aert S., Batenburg K.J., Rossell M.D., Erni R., van Tendeloo G. Three-dimensional atomic imaging of crystalline nanoparticles. Nature 2011, 470:374-377.
26. Batenburg K.J., Bals S., Sijbers J., Kuebel C., Midgley P.A., Hernandez J.C., Kaiser U., Encina E.R., Coronado E.A., van Tendeloo G. 3D imaging of nanomaterials by discrete tomography. Ultramicroscopy 2009, 109:730-740.
27. Gilbert P. Iterative methods for the three-dimensional reconstruction of an object from projections. Journal of Theoretical Biology 1972, 36:105-117.
28. Herman G.T. Reconstruction of binary patterns from a few projections. International Computing Symposium 1973 1974, 371-378. North-Holland Publ. Co., Amsterdam. A. Günther, B. Levrat, H. Lipps (Eds.).
29. Batenburg K.J., Sijbers J. DART. a practical reconstruction algorithm for discrete tomography. IEEE Transactions on Image Processing 2011, 20:2542-2553.
30. Gardner R.J., Kiderlen M. A solution to Hammer's X-ray reconstruction problem. Advances in Mathematics 2007, 214:323-343.
31. Gardner R.J., Kiderlen M. A new algorithm for 3D reconstruction from support functions. IEEE Transactions on Pattern Analysis and Machine Intelligence 2009, 31:556-562.
32. Marabini R., Herman G.T., Carazo J.M. 3D reconstruction in electron microscopy using ART with smooth spherically symmetric volume elements (blobs). Ultramicroscopy 1998, 72:53-65.
33. Obi T., Matej S., Lewitt R.M., Herman G.T 2.5-D simultaneous multislice reconstruction by series expansion methods from Fourier-rebinned PET data. IEEE Transactions on Medical Imaging 2000, 19:474-484.
34. Gregor J., Benson T. Computational analysis and improvement of SIRT. IEEE Transactions on Medical Imaging 2008, 27:918-924.
35. Bals S., Batenburg K.J., Liang D., Lebedev O., van Tendeloo G., Aerts A., Martens J.A., Kirschhock C.E.A. Quantitative three-dimensional modeling of Zeotile through discrete electron tomography. Journal of the American Chemical Society 2009, 131:4769-4773.
36. Bals S., Batenburg K.J., Verbeeck J., Sijbers J., van Tendeloo G. Quantitative 3D reconstruction of catalyst particles for bamboo-like carbon-nanotubes. Nano Letters 2007, 7:3669-3674.
37. Biermans E., Molina L., Batenburg K.J., Bals S., van Tendeloo G. Measuring porosity at the nanoscale by quantitative electron tomography. Nano Letters 2010, 10:5014-5019.
38. Leroux F., Gysemans M., Bals S., Batenburg K.J., Snauwaert J., Verbiest T., van Haesendonck C., van Tendeloo G. 3D characterization of helical silver nanochains mediated by protein assemblies. Advances in Materials 2010, 22:2193-2197.
39. Batenburg K.J., van Aarle W., Sijbers J. A semi-automatic algorithm for grey level estimation in tomography. Pattern Recognition Letters 2011, 32:1395-1405.
40. W. van Aarle, K.J. Batenburg, J. Sijbers, Automatic parameter estimation for the discrete algebraic reconstruction technique (DART), IEEE Transactions on Image Processing 21 (11) (2012) 4608-4621.
41. Gardner R.J., McMullen P. On Hammer's X-ray problem. Journal of the London Mathematical Society 1980, 21(2):171-175.
42. Gardner R., Gritzmann P. Discrete tomography. determination of finite sets by X-rays. Transactions of the American Mathematical Society 1997, 349:2271-2295.
43. Prince J.L., Willsky A.S. Estimating convex sets from noisy support line measurements. IEEE Transactions on Pattern Analysis and Machine Intelligence 1990, 12:377-389.
44. Gardner R.J., Kiderlen M., Milanfar P. Convergence of algorithms for reconstructing convex bodies and directional measures. Annals of Statistics 2006, 34:1331-1374.
45. Lia Y., Qian F., Xiang J., Lieber C.M. Nanowire electronic and optoelectronic devices. Materials Today 2006, 9:18-27.
46. Mokkapati S., Jagadish C. III-V compound SC for optoelectronic devices. Materials Today 2009, 12:22-32.
47. J. Banhart, Advanced tomographic methods in materials research and engineering, in: Monographs on the Physics and Chemistry of Materials, Oxford University Press, Oxford, 2008.
48. Möbus G., Inkson B.J. Nanoscale tomography in materials science. Materials Today 2007, 10:18-25.
49. Lyons R.G. Understanding Digital Signal Processing 2001, Prentice Hall, Upper Saddle River, NJ.
50. Klette R., Rosenfeld A. Digital Geometry 2004, Morgan Kaufmann, San Francisco, CA.
51. D. Colton, R. Kress, Inverse acoustic and electromagnetic scattering theory, in: Applied Mathematical Sciences, vol. 93, Springer, Berlin, 1992.
52. Kaipio J., Somersalo E. Statistical inverse problems. discretization model reduction and inverse crimes. Journal of Computational and Applied Mathematics 2007, 198:493-504.
53. Alpers A., Herman G.T., Poulsen H.F., Schmidt S. Phase retrieval for superposed signals from multiple binary objects. Journal of Optical Society of America A 2010, 27:1927-1937.