Abstract

Reconstructing tomographic images of high resolution, as in x-ray microscopy or transmission electron microscopy, is often limited by the stability of the stages or sample drifts, which requires an image alignment prior to reconstruction. Feature-based image registration is routinely used to align images, but this technique relies on strong features in the sample or the application of gold tracer particles, for example. In this Letter, we present an analytic approach for achieving the vertical registration based on the inherent properties of the data acquired for tomographic reconstruction. It is computationally cheap to implement and can be easily integrated into existing reconstruction pipelines.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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2017 (1)

D. J. Ching and D. Gürsoy, J. Synchrotron Radiat. 24, 537 (2017).
[Crossref]

2014 (1)

D. Gürsoy, F. De Carlo, X. Xiao, and C. Jacobsen, J. Synchrotron Radiat. 21, 1188 (2014).
[Crossref]

2010 (2)

H. Lee, J. Lee, Y. G. Shin, R. Lee, and L. Xing, Phys. Med. Biol. 55, 3417 (2010).
[Crossref]

F. Cantele, E. Paccagnini, G. Pigino, P. Lupetti, and S. Lanzavecchia, J. Struct. Biol. 169, 192 (2010).
[Crossref]

2009 (1)

C. O. S. Sorzano, C. Messaoudi, M. Eibauer, J. Bilbao-Castro, R. Hegerl, S. Nickell, S. Marco, and J. Carazo, BMC Bioinf. 10, 124 (2009).
[Crossref]

2008 (1)

2006 (2)

2004 (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, IEEE Trans. Image Process. 13, 600 (2004).
[Crossref]

2003 (1)

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E86-A, 1925 (2003).

2001 (2)

S. Brandt, J. Heikkonen, and P. Engelhardt, J. Struct. Biol. 136, 201 (2001).
[Crossref]

S. Brandt, J. Heikkonen, and P. Engelhardt, J. Struct. Biol. 133, 10 (2001).
[Crossref]

1999 (1)

B. A. Dowd, G. H. Campbell, R. B. Marr, V. V. Nagarkar, S. V. Tipnis, L. Axe, and D. P. Siddons, Proc. SPIE 3772, 224 (1999).
[Crossref]

1996 (1)

J. C. Fung, W. Liu, W. de Ruijter, H. Chen, C. K. Abbey, J. W. Sedat, and D. A. Agard, J. Struct. Biol. 116, 181 (1996).
[Crossref]

1995 (1)

Y. Liu, P. A. Penczek, B. F. McEwen, and J. Frank, Ultramicroscopy 58, 393 (1995).
[Crossref]

1983 (1)

L. Grodzins, Nucl. Instrum. Methods Phys. Res. 206, 541 (1983).
[Crossref]

Abbey, C. K.

J. C. Fung, W. Liu, W. de Ruijter, H. Chen, C. K. Abbey, J. W. Sedat, and D. A. Agard, J. Struct. Biol. 116, 181 (1996).
[Crossref]

Agard, D. A.

J. C. Fung, W. Liu, W. de Ruijter, H. Chen, C. K. Abbey, J. W. Sedat, and D. A. Agard, J. Struct. Biol. 116, 181 (1996).
[Crossref]

Aoki, T.

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E86-A, 1925 (2003).

Axe, L.

B. A. Dowd, G. H. Campbell, R. B. Marr, V. V. Nagarkar, S. V. Tipnis, L. Axe, and D. P. Siddons, Proc. SPIE 3772, 224 (1999).
[Crossref]

Beckmann, F.

Bilbao-Castro, J.

C. O. S. Sorzano, C. Messaoudi, M. Eibauer, J. Bilbao-Castro, R. Hegerl, S. Nickell, S. Marco, and J. Carazo, BMC Bioinf. 10, 124 (2009).
[Crossref]

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, IEEE Trans. Image Process. 13, 600 (2004).
[Crossref]

Brandt, S.

S. Brandt, J. Heikkonen, and P. Engelhardt, J. Struct. Biol. 133, 10 (2001).
[Crossref]

S. Brandt, J. Heikkonen, and P. Engelhardt, J. Struct. Biol. 136, 201 (2001).
[Crossref]

Campbell, G. H.

B. A. Dowd, G. H. Campbell, R. B. Marr, V. V. Nagarkar, S. V. Tipnis, L. Axe, and D. P. Siddons, Proc. SPIE 3772, 224 (1999).
[Crossref]

Cantele, F.

F. Cantele, E. Paccagnini, G. Pigino, P. Lupetti, and S. Lanzavecchia, J. Struct. Biol. 169, 192 (2010).
[Crossref]

Carazo, J.

C. O. S. Sorzano, C. Messaoudi, M. Eibauer, J. Bilbao-Castro, R. Hegerl, S. Nickell, S. Marco, and J. Carazo, BMC Bioinf. 10, 124 (2009).
[Crossref]

Chen, H.

J. C. Fung, W. Liu, W. de Ruijter, H. Chen, C. K. Abbey, J. W. Sedat, and D. A. Agard, J. Struct. Biol. 116, 181 (1996).
[Crossref]

Ching, D. J.

D. J. Ching and D. Gürsoy, J. Synchrotron Radiat. 24, 537 (2017).
[Crossref]

De Carlo, F.

D. Gürsoy, F. De Carlo, X. Xiao, and C. Jacobsen, J. Synchrotron Radiat. 21, 1188 (2014).
[Crossref]

de Ruijter, W.

J. C. Fung, W. Liu, W. de Ruijter, H. Chen, C. K. Abbey, J. W. Sedat, and D. A. Agard, J. Struct. Biol. 116, 181 (1996).
[Crossref]

Donath, T.

Dowd, B. A.

B. A. Dowd, G. H. Campbell, R. B. Marr, V. V. Nagarkar, S. V. Tipnis, L. Axe, and D. P. Siddons, Proc. SPIE 3772, 224 (1999).
[Crossref]

Eibauer, M.

C. O. S. Sorzano, C. Messaoudi, M. Eibauer, J. Bilbao-Castro, R. Hegerl, S. Nickell, S. Marco, and J. Carazo, BMC Bioinf. 10, 124 (2009).
[Crossref]

Engelhardt, P.

S. Brandt, J. Heikkonen, and P. Engelhardt, J. Struct. Biol. 136, 201 (2001).
[Crossref]

S. Brandt, J. Heikkonen, and P. Engelhardt, J. Struct. Biol. 133, 10 (2001).
[Crossref]

Fienup, J. R.

Frank, J.

Y. Liu, P. A. Penczek, B. F. McEwen, and J. Frank, Ultramicroscopy 58, 393 (1995).
[Crossref]

Fung, J. C.

J. C. Fung, W. Liu, W. de Ruijter, H. Chen, C. K. Abbey, J. W. Sedat, and D. A. Agard, J. Struct. Biol. 116, 181 (1996).
[Crossref]

Grodzins, L.

L. Grodzins, Nucl. Instrum. Methods Phys. Res. 206, 541 (1983).
[Crossref]

Guizar-Sicairos, M.

Gürsoy, D.

D. J. Ching and D. Gürsoy, J. Synchrotron Radiat. 24, 537 (2017).
[Crossref]

D. Gürsoy, F. De Carlo, X. Xiao, and C. Jacobsen, J. Synchrotron Radiat. 21, 1188 (2014).
[Crossref]

Hegerl, R.

C. O. S. Sorzano, C. Messaoudi, M. Eibauer, J. Bilbao-Castro, R. Hegerl, S. Nickell, S. Marco, and J. Carazo, BMC Bioinf. 10, 124 (2009).
[Crossref]

Heikkonen, J.

S. Brandt, J. Heikkonen, and P. Engelhardt, J. Struct. Biol. 133, 10 (2001).
[Crossref]

S. Brandt, J. Heikkonen, and P. Engelhardt, J. Struct. Biol. 136, 201 (2001).
[Crossref]

Higuchi, T.

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E86-A, 1925 (2003).

Jacobsen, C.

D. Gürsoy, F. De Carlo, X. Xiao, and C. Jacobsen, J. Synchrotron Radiat. 21, 1188 (2014).
[Crossref]

Kobayashi, K.

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E86-A, 1925 (2003).

Lanzavecchia, S.

F. Cantele, E. Paccagnini, G. Pigino, P. Lupetti, and S. Lanzavecchia, J. Struct. Biol. 169, 192 (2010).
[Crossref]

Lee, H.

H. Lee, J. Lee, Y. G. Shin, R. Lee, and L. Xing, Phys. Med. Biol. 55, 3417 (2010).
[Crossref]

Lee, J.

H. Lee, J. Lee, Y. G. Shin, R. Lee, and L. Xing, Phys. Med. Biol. 55, 3417 (2010).
[Crossref]

Lee, R.

H. Lee, J. Lee, Y. G. Shin, R. Lee, and L. Xing, Phys. Med. Biol. 55, 3417 (2010).
[Crossref]

Liu, W.

J. C. Fung, W. Liu, W. de Ruijter, H. Chen, C. K. Abbey, J. W. Sedat, and D. A. Agard, J. Struct. Biol. 116, 181 (1996).
[Crossref]

Liu, Y.

Y. Liu, P. A. Penczek, B. F. McEwen, and J. Frank, Ultramicroscopy 58, 393 (1995).
[Crossref]

Lupetti, P.

F. Cantele, E. Paccagnini, G. Pigino, P. Lupetti, and S. Lanzavecchia, J. Struct. Biol. 169, 192 (2010).
[Crossref]

Marco, S.

C. O. S. Sorzano, C. Messaoudi, M. Eibauer, J. Bilbao-Castro, R. Hegerl, S. Nickell, S. Marco, and J. Carazo, BMC Bioinf. 10, 124 (2009).
[Crossref]

Marr, R. B.

B. A. Dowd, G. H. Campbell, R. B. Marr, V. V. Nagarkar, S. V. Tipnis, L. Axe, and D. P. Siddons, Proc. SPIE 3772, 224 (1999).
[Crossref]

McEwen, B. F.

Y. Liu, P. A. Penczek, B. F. McEwen, and J. Frank, Ultramicroscopy 58, 393 (1995).
[Crossref]

Messaoudi, C.

C. O. S. Sorzano, C. Messaoudi, M. Eibauer, J. Bilbao-Castro, R. Hegerl, S. Nickell, S. Marco, and J. Carazo, BMC Bioinf. 10, 124 (2009).
[Crossref]

Nagarkar, V. V.

B. A. Dowd, G. H. Campbell, R. B. Marr, V. V. Nagarkar, S. V. Tipnis, L. Axe, and D. P. Siddons, Proc. SPIE 3772, 224 (1999).
[Crossref]

Nickell, S.

C. O. S. Sorzano, C. Messaoudi, M. Eibauer, J. Bilbao-Castro, R. Hegerl, S. Nickell, S. Marco, and J. Carazo, BMC Bioinf. 10, 124 (2009).
[Crossref]

Paccagnini, E.

F. Cantele, E. Paccagnini, G. Pigino, P. Lupetti, and S. Lanzavecchia, J. Struct. Biol. 169, 192 (2010).
[Crossref]

Penczek, P. A.

Y. Liu, P. A. Penczek, B. F. McEwen, and J. Frank, Ultramicroscopy 58, 393 (1995).
[Crossref]

Pigino, G.

F. Cantele, E. Paccagnini, G. Pigino, P. Lupetti, and S. Lanzavecchia, J. Struct. Biol. 169, 192 (2010).
[Crossref]

Sasaki, Y.

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E86-A, 1925 (2003).

Schreyer, A.

Sedat, J. W.

J. C. Fung, W. Liu, W. de Ruijter, H. Chen, C. K. Abbey, J. W. Sedat, and D. A. Agard, J. Struct. Biol. 116, 181 (1996).
[Crossref]

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, IEEE Trans. Image Process. 13, 600 (2004).
[Crossref]

Shin, Y. G.

H. Lee, J. Lee, Y. G. Shin, R. Lee, and L. Xing, Phys. Med. Biol. 55, 3417 (2010).
[Crossref]

Siddons, D. P.

B. A. Dowd, G. H. Campbell, R. B. Marr, V. V. Nagarkar, S. V. Tipnis, L. Axe, and D. P. Siddons, Proc. SPIE 3772, 224 (1999).
[Crossref]

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, IEEE Trans. Image Process. 13, 600 (2004).
[Crossref]

Sorzano, C. O. S.

C. O. S. Sorzano, C. Messaoudi, M. Eibauer, J. Bilbao-Castro, R. Hegerl, S. Nickell, S. Marco, and J. Carazo, BMC Bioinf. 10, 124 (2009).
[Crossref]

Takita, K.

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E86-A, 1925 (2003).

Taylor, K. A.

H. Winkler and K. A. Taylor, Ultramicroscopy 106, 240 (2006).
[Crossref]

Thurman, S. T.

Tipnis, S. V.

B. A. Dowd, G. H. Campbell, R. B. Marr, V. V. Nagarkar, S. V. Tipnis, L. Axe, and D. P. Siddons, Proc. SPIE 3772, 224 (1999).
[Crossref]

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, IEEE Trans. Image Process. 13, 600 (2004).
[Crossref]

Winkler, H.

H. Winkler and K. A. Taylor, Ultramicroscopy 106, 240 (2006).
[Crossref]

Xiao, X.

D. Gürsoy, F. De Carlo, X. Xiao, and C. Jacobsen, J. Synchrotron Radiat. 21, 1188 (2014).
[Crossref]

Xing, L.

H. Lee, J. Lee, Y. G. Shin, R. Lee, and L. Xing, Phys. Med. Biol. 55, 3417 (2010).
[Crossref]

BMC Bioinf. (1)

C. O. S. Sorzano, C. Messaoudi, M. Eibauer, J. Bilbao-Castro, R. Hegerl, S. Nickell, S. Marco, and J. Carazo, BMC Bioinf. 10, 124 (2009).
[Crossref]

IEEE Trans. Image Process. (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, IEEE Trans. Image Process. 13, 600 (2004).
[Crossref]

IEICE Trans. Fundam. Electron. Commun. Comput. Sci. (1)

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E86-A, 1925 (2003).

J. Opt. Soc. Am. A (1)

J. Struct. Biol. (4)

S. Brandt, J. Heikkonen, and P. Engelhardt, J. Struct. Biol. 136, 201 (2001).
[Crossref]

F. Cantele, E. Paccagnini, G. Pigino, P. Lupetti, and S. Lanzavecchia, J. Struct. Biol. 169, 192 (2010).
[Crossref]

J. C. Fung, W. Liu, W. de Ruijter, H. Chen, C. K. Abbey, J. W. Sedat, and D. A. Agard, J. Struct. Biol. 116, 181 (1996).
[Crossref]

S. Brandt, J. Heikkonen, and P. Engelhardt, J. Struct. Biol. 133, 10 (2001).
[Crossref]

J. Synchrotron Radiat. (2)

D. J. Ching and D. Gürsoy, J. Synchrotron Radiat. 24, 537 (2017).
[Crossref]

D. Gürsoy, F. De Carlo, X. Xiao, and C. Jacobsen, J. Synchrotron Radiat. 21, 1188 (2014).
[Crossref]

Nucl. Instrum. Methods Phys. Res. (1)

L. Grodzins, Nucl. Instrum. Methods Phys. Res. 206, 541 (1983).
[Crossref]

Opt. Lett. (1)

Phys. Med. Biol. (1)

H. Lee, J. Lee, Y. G. Shin, R. Lee, and L. Xing, Phys. Med. Biol. 55, 3417 (2010).
[Crossref]

Proc. SPIE (1)

B. A. Dowd, G. H. Campbell, R. B. Marr, V. V. Nagarkar, S. V. Tipnis, L. Axe, and D. P. Siddons, Proc. SPIE 3772, 224 (1999).
[Crossref]

Ultramicroscopy (2)

Y. Liu, P. A. Penczek, B. F. McEwen, and J. Frank, Ultramicroscopy 58, 393 (1995).
[Crossref]

H. Winkler and K. A. Taylor, Ultramicroscopy 106, 240 (2006).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. (a) Projection of the sphere phantom used for testing the registration. (b) shows an exemplary slice of the phantom, taken from the center of the phantom (slice no. 250). (c) shows a graph of the vertical displacement of each projection.
Fig. 2.
Fig. 2. Mθ profiles. (a) shows the profiles after applying the random movement and drift. (b) shows the same profiles after applying the correction.
Fig. 3.
Fig. 3. Visualization of the reconstructed backshifted data: (a) 3D ortho-slice, (b) xy-plane, (c) xz-plane, and (d) yz-plane. (e)–(h) show the difference between the original and the backshifted reconstruction: (e) 3D ortho-slice, (f) xy-plane, (g) xz-plane, and (h) yz-plane. The double bilinear interpolation creates rings in the xy-plane of the backshifted data.
Fig. 4.
Fig. 4. Difference between fitted and simulated drift values for different ADU levels: both the RMS variance σRMS and the maximum deviation Δmax asymptotically approach a value ϵ close to zero.
Fig. 5.
Fig. 5. Metrics for comparing the reconstruction from the original and backshifted data. The structural similarity index (MS-SSIM) of the original and backshifted data score very similar values at all noise levels. The integral of absolute value QIA, integral of negativity QIN, and histogram entropy QH are measures for the quality of reconstruction and show an actual improvement of the reconstruction for the backshifted data which can be attributed to a statistical averaging of noise between adjacent slices.
Fig. 6.
Fig. 6. (a) Projection of the test sample. (b) Deviations between induced and calculated shifts. Possible movements of the beam in the flat-field and optics imperfections lead to a slightly larger deviation than for perfect simulated data.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

pθ(t,z)=duμ(usinθ+tcosθ,ucosθ+tsinθ,z).
pθ(t,z)=dxdyμ(x,y,z)δ(xcosθ+ysinθt).
M(θ,z)=dtpθ(t,z).
M(θ,z)=dtpθ(t,z)=dtdxdyμ(x,y,z)δ(xcosθ+ysinθt)=dxdydtμ(x,y,z)δ(xcosθ+ysinθt)=dxdyμ(x,y,z)dtδ(xcosθ+ysinθt)=dxdyμ(x,y,z).
pθ=log(P(Nexp(T))P(N)).

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