The limited specimen tilting range that is typically available in electron tomography gives rise to a region in the Fourier space of the reconstructed object where experimental data are unavailable - the missing wedge. Since this region is sharply delimited from the area of available data, the reconstructed signal is typically hampered by convolution with its impulse response, which gives rise to the well-known missing wedge artefacts in 3D reconstructions. Despite the recent progress in the field of reconstruction and regularization techniques, the missing wedge artefacts remain untreated in most current reconstruction workflows in structural biology. Therefore we have designed a simple Fourier angular filter that effectively suppresses the ray artefacts in the single-axis tilting projection acquisition scheme, making single-axis tomographic reconstructions easier to interpret in particular at low signal-to-noise ratio in acquired projections. The proposed filter can be easily incorporated into current electron tomographic reconstruction schemes.

Centre for Biomedical Image Analysis Faculty of Informatics Masaryk University Brno Czech Republic

Charles University Prague 1st Faculty of Medicine Institute of Cellular Biology and Pathology Albertov 4 128 01 Prague 2 Czech Republic

Sir William Dunn School of Pathology University of Oxford South Parks Road Oxford OX1 3RE UK; MPI CBG Photenhauerstr 108 01307 Dresden Germany

Erratum v

J Struct Biol. 2014 Jul;187(1):93. doi: 10.1016/j.jsb.2014.05.008. PubMed

Zobrazit více v PubMed

Aganj, L., Bartesaghi, A., Borgnia, M., Liao, H.Y., Sapiro, G., Subramaniam, S., Ieee, 2007. Regularization for inverting the radon transform with wedge consideration, p. 217–220, 2007 4th Ieee International Symposium on Biomedical Imaging: Macro to Nano, vols 1–3, Ieee, New York.

Bartesaghi A., Sprechmann P., Liu J., Randall G., Sapiro G., Subramaniam S. Classification and 3D averaging with missing wedge correction in biological electron tomography. J. Struct. Biol. 2008;162:436–450. PubMed PMC

Batenburg K.J., Bals S., Sijbers J., Kubel 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. PubMed

Bellon P.L., Lanzavecchia S., Scatturin V. A two exposures technique of electron tomography from projections with random orientations and a quasi-Boolean angular reconstitution. Ultramicroscopy. 1998;72:177–186.

Capani F., Martone M.E., Deerinck T.J., Ellisman M.H. Selective localization of high concentrations of F-actin in subpopulations of dendritic spines in rat central nervous system: a three-dimensional electron microscopic study. J. Comp. Neurol. 2001;435:156–170. PubMed

Carazo J.M. The fidelity of 3D reconstructions from incomplete data and the use of restoration methods. In: Frank J., editor. Electron Tomography. Plenum Press; New York: 1992. pp. 117–166.

Crowther R.A., DeRosier D.J., Klug A. The reconstruction of a three-dimensional structure from projections and its application to electron microscopy. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. (1934–1990) 1970;(31):319–340.

Fanelli D., Oktem O. Electron tomography: a short overview with an emphasis on the absorption potential model for the forward problem. Inverse Probl. 2008;24:013001.

Fernandez J.J. TOMOBFLOW: feature-preserving noise filtering for electron tomography. BMC Bioinformatics. 2009;10:178. PubMed PMC

Fernandez J.J. Computational methods for electron tomography. Micron. 2012;43:1010–1030. PubMed

Forster F., Hegerl R. Structure determination in situ by averaging of tomograms. Elsevier Academic Press Inc.; San Diego: 2007. (Cellular Electron Microscopy). pp. 741–767. PubMed

Forster F., Medalia O., Zauberman N., Baumeister W., Fass D. Retrovirus envelope protein complex structure in situ studied by cryo-electron tomography. Proc. Natl. Acad. Sci. U.S.A. 2005;102:4729–4734. PubMed PMC

Frangakis A.S., Hegerl R. Noise reduction in electron tomographic reconstructions using nonlinear anisotropic diffusion. J. Struct. Biol. 2001;135:239–250. PubMed

Frangakis A.S., Hegerl R. Denoising of electron tomograms. In: Frank J., editor. Electron Tomography. Springer Science + Business Media; LLC, New York: 2006. pp. 331–352.

Frangakis A.S., Bohm J., Forster F., Nickell S., Nicastro D., Typke D., Hegerl R., Baumeister W. Identification of macromolecular complexes in cryoelectron tomograms of phantom cells. Proc. Natl. Acad. Sci. U.S.A. 2002;99:14153–14158. PubMed PMC

Gilbert P. Iterative methods for 3-dimensional reconstruction of an object from projections. J. Theor. Biol. 1972;36:105–117. PubMed

Gordon R., Bender R., Herman G.T. Algebraic reconstruction techniques (Art) for 3-dimensional electron microscopy and X-ray photography. J. Theor. Biol. 1970;29:471–476. PubMed

Gruebnau, A., Stierstorfer, K. 2004. Method for producing images in spiral computed tomography, and a spiral CT unit, G06K 9/00 ed., United States.

Grünewald K., Medalia O., Gross A., Steven A.C., Baumeister W. Prospects of electron cryotomography to visualize macromolecular complexes inside cellular compartments: implications of crowding. Biophys. Chem. 2003;100:577–591. PubMed

Hawkes P.W. The electron microscope as a structure projector. In: Frank J., editor. Electron Tomography. Springer Science; New York: 2006. pp. 83–112.

Hoog J.L., Bouchet-Marquis C., McIntosh J.R., Hoenger A., Gull K. Cryo-electron tomography and 3-D analysis of the intact flagellum in Trypanosoma brucei. J. Struct. Biol. 2012;178:189–198. PubMed PMC

Jarisch W.R. Computational approach of high efficiency CT (HECT)™ in TEM/STEM. Microsc. Microanal. 2010;16:1846–1847.

Kawase N., Kato M., Nishioka H., Jinnai H. Transmission electron microtomography without the “missing wedge” for quantitative structural analysis. Ultramicroscopy. 2007;107:8–15. PubMed

Komrska J. Fraunhofer-diffraction from sector stars. Opt. Acta. 1983;30:887–925.

Koster A.J., Barcena M. Cryotomography: low-dose automated tomography of frozen-hydrated specimens. In: Frank J., editor. Electron Tomography. Springer Science + Business Media; LLC, New York: 2006. pp. 113–161.

Kovacik L., Plitzko J.M., Grote M., Reichelt R. Electron tomography of structures in the wall of hazel pollen grains. J. Struct. Biol. 2009;166:263–271. PubMed

Kremer J.R., Mastronarde D.N., McIntosh J.R. Computer visualization of three-dimensional image data using IMOD. J. Struct. Biol. 1996;116:71–76. PubMed

Lanzavecchia S., Bellon P.L. Electron tomography in conical tilt geometry. The accuracy of a direct Fourier method (DFM) and the suppression of non-tomographic noise. Ultramicroscopy. 1996;63:247–261.

Lanzavecchia S., Bellon P.L., Scatturin V. Spark, a kernel of software programs for spatial reconstruction in electron-microscopy. J. Microsc. Oxford. 1993;171:255–266.

Lanzavecchia S., Cantele F., Bellon P.L., Zampighi L., Kreman M., Wright E., Zampighi G.A. Conical tomography of freeze-fracture replicas: a method for the study of integral membrane proteins inserted in phospholipid bilayers. J. Struct. Biol. 2005;149:87–98. PubMed

Lee E., Fahimian B.P., Iancu C.V., Suloway C., Murphy G.E., Wright E.R., Castano-Diez D., Jensen G.J., Miao J.W. Radiation dose reduction and image enhancement in biological imaging through equally-sloped tomography. J. Struct. Biol. 2008;164:221–227. PubMed PMC

Lu X.Q., Sun Y., Bai G.F. Adaptive wavelet–Galerkin methods for limited angle tomography. Image Vision Comput. 2010;28:696–703.

Marabini R., Rietzel E., Schroeder R., Herman G.T., Carazo J.M. Three-dimensional reconstruction from reduced sets of very noisy images acquired following a single-axis tilt schema: application of a new three-dimensional reconstruction algorithm and objective comparison with weighted backprojection. J. Struct. Biol. 1997;120:363–371. PubMed

Mastronarde D.N. Dual-axis tomography: an approach with alignment methods that preserve resolution. J. Struct. Biol. 1997;120:343–352. PubMed

Messaoudii C., Boudier T., Sanchez Sorzano C.O., Marco S. TomoJ: tomography software for three-dimensional reconstruction in transmission electron microscopy. BMC Bioinformatics. 2007;8:288. PubMed PMC

Miao J.W., Forster F., Levi O. Equally sloped tomography with oversampling reconstruction. Phys. Rev. B. 2005:72.

Martone M.E., Gupta A., Wong M., Qian X., Sosinsky G., Ludascher B., Ellisman M.H. A cell-centered database for electron tomographic data. J. Struct. Biol. 2002;138:145–155. PubMed

Narasimha R., Aganj I., Bennett A.E., Borgnia M.J., Zabransky D., Sapiro G., McLaughlin S.W., Milne J.L.S., Subramaniam S. Evaluation of denoising algorithms for biological electron tomography. J. Struct. Biol. 2008;164:7–17. PubMed PMC

Natterer F. Fourier reconstruction in tomography. Numer. Math. 1985;47:343–353.

Norlen L., Oktem O., Skoglund U. Molecular cryo-electron tomography of vitreous tissue sections: current challenges. J. Microsc. Oxford. 2009;235:293–307. PubMed

Ofverstedt L.G., Zhang K., Isaksson L.A., Bricogne G., Skoglund U. Automated correlation and averaging of three-dimensional reconstructions obtained by electron tomography. J. Struct. Biol. 1997;120:329–342. PubMed

Penczek P., Marko M., Buttle K., Frank J. Double-tilt electron tomography. Ultramicroscopy. 1995;60:393–410. PubMed

Penczek P.A., Frank J. Resolution in electron tomography. In: Frank J., editor. Electron Tomography. Springer Science + Business Media; LLC, New York: 2006. pp. 307–330.

Persson M., Bone D., Elmqvist H. Total variation norm for three-dimensional iterative reconstruction in limited view angle tomography. Phys. Med. Biol. 2001;46:853–866. PubMed

Quinto E.T., Skoglund U., Oktem O. Electron lambda-tomography. Proc. Natl. Acad. Sci. U.S.A. 2009;106:21842–21847. PubMed PMC

Radermacher M. 3-Dimensional reconstruction of single particles from random and nonrandom tilt series. J. Electron. Micr. Tech. 1988;9:359–394. PubMed

Radermacher M. Weighted back-projection methods. In: Frank J., editor. Electron Tomography. Plenum Press; New York: 1992. pp. 91–115.

Radermacher M. Weighted back-projection methods. In: Frank J., editor. Electron Tomography. Springer Science + Business Media; LLC, New York: 2006. pp. 245–275.

Schroeter J.P., Bretaudiere J.P. SUPRIM: easily modified image processing software. J. Struct. Biol. 1996;116:131–137. PubMed

Skoglund U., Ofverstedt L.G., Burnett R.M., Bricogne G. Maximum-entropy three-dimensional reconstruction with deconvolution of the contrast transfer function: a test application with adenovirus. J. Struct. Biol. 1996;117:173–188. PubMed

Smigova J., Juda P., Cmarko D., Raska I. Fine structure of the “PcG body” in human U-2 OS cells established by correlative light-electron microscopy. Nucleus. 2011;2:219–228. PubMed PMC

Sorzano C.O.S., Marabini R., Boisset N., Rietzel E., Schroder R., Herman G.T., Carazo J.M. The effect of overabundant projection directions on 3D reconstruction algorithms. J. Struct. Biol. 2001;133:108–118. PubMed

Straubel R. Zwei allgemeine Sätze über Frauhofer‘sche Beugungserscheinungen. Annal. Phys. Chem. 1895;56:746–761.

Tam K.C., Perez-Mendez V. Tomographical imaging with limited-angle input. J. Opt. Soc. Am. 1981;71:582–592.

Tam K.C., Perez-Mendez V. Limited-angle 3-dimensional reconstructions using Fourier-transform iterations and radon-transform iterations. Opt. Eng. 1981;20:586–589.

Turner J.N., Valdre U. Tilting stages for biological applications. In: Frank J., editor. Electron Tomography. Plenum Press; New York: 1992. pp. 167–196.

Zampighi G.A., Zampighi L., Fain N., Wright E.M., Cantele F., Lanzavecchia S. Conical tomography II: a method for the study of cellular organelles in thin sections. J. Struct. Biol. 2005;151:263–274. PubMed