Abstract

A penalized maximum-likelihood estimation is proposed to perform hyperspectral (spatio-spectral) image reconstruction for X-ray fluorescence tomography. The approach minimizes a Poisson-based negative log-likelihood of the observed photon counts, and uses a penalty term that has the effect of encouraging local continuity of model parameter estimates in both spatial and spectral dimensions simultaneously. The performance of the reconstruction method is demonstrated with experimental data acquired from a seed of arabidopsis thaliana collected at the 13-ID-E microprobe beamline at the Advanced Photon Source. The resulting element distribution estimates with the proposed approach show significantly better reconstruction quality than the conventional analytical inversion approaches, and allows for a high data compression factor which can reduce data acquisition times remarkably. In particular, this technique provides the capability to tomographically reconstruct full energy dispersive spectra without compromising reconstruction artifacts that impact the interpretation of results.

© 2015 Optical Society of America

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References

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2014 (5)

H. M. Hertz, J. C. Larsson, U. Lundstrom, D. H. Larsson, and C. Vogt, “Laboratory x-ray fluorescence tomography for high-resolution nanoparticle bio-imaging,” Opt. Lett. 39, 2790–2793, (2014).
[Crossref] [PubMed]

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The Bionanoprobe: Hard X-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75, (2014).
[Crossref]

J. Moussouris, “Gibbs and Markov random systems with constraints,” J. Stat. Phys. 10, 11–33, (2014).
[Crossref]

F. De Carlo, D. Gürsoy, F. Marone, M. Rivers, D. Parkinson, F. Khan, N. Schwarz, D. Vine, S. Vogt, S. C. Gleber, S. Narayanan, M. Newville, A. Lanzirotti, Y. Sun, Y. Hong, and C. Jacobsen, “Scientific data exchange: a schema for HDF5-based storage of raw and analyzed data,” J. Synchrotron Radiat. 21, 1224–1230, (2014).
[Crossref] [PubMed]

D. Gürsoy, F. De Carlo, X. Xiao, and C. Jacobsen, “TomoPy: a framework for the analysis of synchrotron tomographic data,” J. Synchrotron Radiat. 21, 1185–1193, (2014).
[Crossref]

2012 (1)

H. Suhonen, F. Xu, L. Helfen, C. Ferrero, P. Vladimirov, and P. Cloetens, “X-ray phase contrast and fluorescence nanotomography for material studies,” Int. J. Mater. Res. 103, 179–183, (2012).
[Crossref]

2011 (2)

E. Lombi, M. D. Jonge, E. Donner, C. G. Ryan, and D. Paterson, “Trends in hard X-ray fluorescence mapping: environmental applications in the age of fast detectors,” Anal. Bioanal. Chem. 400, 1637–1644, (2011).
[Crossref] [PubMed]

E. X. Miqueles and A. R. De Pierro, “Iterative reconstruction in X-ray fluorescence tomography based on Radon inversion,” IEEE T. Med. Imaging 30, 438–450, (2011).
[Crossref]

2010 (1)

M. D. Jonge and S. Vogt, “Hard X-ray fluorescence tomography – an emerging tool for structural visualization,” Curr. Opin. Struc. Biol. 20, 606–614, (2010).
[Crossref]

2009 (1)

E. Lombi and J. Susini, “Synchrotron-based techniques for plant and soil science: opportunities, challenges and future perspectives,” Plant Soil 320, 1–35, (2009).
[Crossref]

2008 (1)

A. J. Brown, B. Sutter, and S. Dunagan, “The MARTE VNIR imaging spectrometer experiment: design and analysis,” Astrobiology 8, 1001–1011, (2008).
[Crossref] [PubMed]

2007 (3)

C. J. Fahrni, “Biological applications of X-ray fluorescence microscopy: exploring the subcellular topography and speciation of transition metals,” Curr. Opin. Chem. Biol. 11, 121–127, (2007).
[Crossref] [PubMed]

D. Bourassa, S. C. Gleber, S. Vogt, H. Yi, F. Will, H. Richter, C. H. Shin, and C. J. Fahrni, “3D imaging of transition metals in the zebrafish embryo by X-ray fluorescence microtomography,” Metallomics 9, 1648–1655, (2007).

P. J. La Riviere, P. A. Vargas, M. Newville, and S. Sutton, “Reduced-scan schemes for X-ray fluorescence computed tomography,” IEEE Trans. Nucl. Sci. 54, 1535–1542, (2007).
[Crossref]

2006 (6)

J. Qi and R. M. Leahy, “Iterative reconstruction techniques in emission computed tomography,” Phys. Med. Biol. 51, R541 (2006).
[Crossref] [PubMed]

P. L. Riviere, P. Vargas, M. Rivers, and S. R. Sutton, “Penalized-likelihood image reconstruction for X-ray fluorescence computed tomography,” Opt. Eng. 45, 077005 (2006).
[Crossref]

S. Kim, T. Punshon, A. Lanzirotti, L. Li, J. Alonso, J. Ecker, J. Kaplan, and M. Guerinot, “Localization of iron in arabidopsis seed requires the vacuolar membrane transporter VIT1,” Science 314, 1295–1298, (2006).
[Crossref] [PubMed]

T. Paunesku, S. Vogt, J. Maser, B. Lai, and G. Woloschak, “X-ray fluorescence microprobe imaging in biology and medicine,” J. Cell Biochem. 99, 1489–1502, (2006).
[Crossref] [PubMed]

P. J. La Riviere and P. A. Vargas, “Monotonic penalized-likelihood image reconstruction for x-ray fluorescence computed tomography,” IEEE T. Med. Imaging 25, 1117–1129, (2006).
[Crossref]

A. J. Brown, “Spectral curve fitting for automatic hyperspectral data analysis,” IEEE Geosci Remote S 44, 1601 (2006).

2005 (2)

X. R. Wang, A. J. Brown, and B. Upcroft, “Applying incremental EM to Bayesian classifiers in the learning of hyperspectral remote sensing data,” Information Fusion Proc. 1, 606–613, (2005).

S. Bohic, A. Simionovici, X. Biquard, G. Martinez-Criado, and J. Susini, “Synchrotron X-ray microfluorescence and microspectroscopy: Application and perspectives in materials science,” Oil Gas Sci. Technol. 6, 979–993, (2005).
[Crossref]

2004 (1)

J. H. Chang, J. M. M. Anderson, and J. R. Votaw, “Regularized image reconstruction algorithms for positron emission tomography,” IEEE T. Med. Imaging 23, 1165–1175, (2004).
[Crossref]

2003 (1)

B. Golosio, A. Simionovici, A. Somogyi, L. Lemelle, M. Chukalina, and A. Brunetti, “Internal elemental micro-analysis combining x-ray fluorescence, Compton and transmission tomography,” J. Appl. Phys. 94, 145 (2003).
[Crossref]

2001 (1)

C. G. Schoer, “Reconstructing X-ray fluorescence microtomograms,” Appl. Phys. Lett. 79, 1912 (2001).
[Crossref]

1999 (1)

B. A. Dowd, G. H. Campbell, R. B. Marr, V. Nagarkar, S. Tipnis, L. Axe, and D. P. Siddons, “Developments in synchrotron x-ray computed microtomography at the National Synchrotron Light Source,” Proc. SPIE 3772, 224–236, (1999).
[Crossref]

1998 (1)

G-F. Rust and J. Weigelt, “X-Ray Fluorescent Computer Tomography with Synchrotron Radiation,” IEEE T. Nucl. Sci. 45, 75–88, (1998).
[Crossref]

1990 (2)

P. J. Green, “On the use of the EM algorithm for penalized likelihood estimation,” J. R. Stat. Soc. 52, 443–452, (1990).

K. Lange, “Convergence of EM image reconstruction algorithms with Gibbs smoothing,” IEEE T. Med. Imaging 9, 439–446, (1990).
[Crossref]

1987 (1)

E. Levitan and G. T. Herman, “A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography,” IEEE T. Med. Imaging 6, 185–192, (1987).
[Crossref]

Alonso, J.

S. Kim, T. Punshon, A. Lanzirotti, L. Li, J. Alonso, J. Ecker, J. Kaplan, and M. Guerinot, “Localization of iron in arabidopsis seed requires the vacuolar membrane transporter VIT1,” Science 314, 1295–1298, (2006).
[Crossref] [PubMed]

Anderson, J. M. M.

J. H. Chang, J. M. M. Anderson, and J. R. Votaw, “Regularized image reconstruction algorithms for positron emission tomography,” IEEE T. Med. Imaging 23, 1165–1175, (2004).
[Crossref]

Axe, L.

B. A. Dowd, G. H. Campbell, R. B. Marr, V. Nagarkar, S. Tipnis, L. Axe, and D. P. Siddons, “Developments in synchrotron x-ray computed microtomography at the National Synchrotron Light Source,” Proc. SPIE 3772, 224–236, (1999).
[Crossref]

Bicer, T.

T. Bicer, “Supporting data-intensive scientific computing on bandwidth and space constrained environments”. PhD Dissertation, (2014).

Biquard, X.

S. Bohic, A. Simionovici, X. Biquard, G. Martinez-Criado, and J. Susini, “Synchrotron X-ray microfluorescence and microspectroscopy: Application and perspectives in materials science,” Oil Gas Sci. Technol. 6, 979–993, (2005).
[Crossref]

Bohic, S.

S. Bohic, A. Simionovici, X. Biquard, G. Martinez-Criado, and J. Susini, “Synchrotron X-ray microfluorescence and microspectroscopy: Application and perspectives in materials science,” Oil Gas Sci. Technol. 6, 979–993, (2005).
[Crossref]

Bolbat, M.

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The Bionanoprobe: Hard X-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75, (2014).
[Crossref]

Bourassa, D.

D. Bourassa, S. C. Gleber, S. Vogt, H. Yi, F. Will, H. Richter, C. H. Shin, and C. J. Fahrni, “3D imaging of transition metals in the zebrafish embryo by X-ray fluorescence microtomography,” Metallomics 9, 1648–1655, (2007).

Brister, K.

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The Bionanoprobe: Hard X-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75, (2014).
[Crossref]

Brown, A. J.

A. J. Brown, B. Sutter, and S. Dunagan, “The MARTE VNIR imaging spectrometer experiment: design and analysis,” Astrobiology 8, 1001–1011, (2008).
[Crossref] [PubMed]

A. J. Brown, “Spectral curve fitting for automatic hyperspectral data analysis,” IEEE Geosci Remote S 44, 1601 (2006).

X. R. Wang, A. J. Brown, and B. Upcroft, “Applying incremental EM to Bayesian classifiers in the learning of hyperspectral remote sensing data,” Information Fusion Proc. 1, 606–613, (2005).

Brunetti, A.

B. Golosio, A. Simionovici, A. Somogyi, L. Lemelle, M. Chukalina, and A. Brunetti, “Internal elemental micro-analysis combining x-ray fluorescence, Compton and transmission tomography,” J. Appl. Phys. 94, 145 (2003).
[Crossref]

Campbell, G. H.

B. A. Dowd, G. H. Campbell, R. B. Marr, V. Nagarkar, S. Tipnis, L. Axe, and D. P. Siddons, “Developments in synchrotron x-ray computed microtomography at the National Synchrotron Light Source,” Proc. SPIE 3772, 224–236, (1999).
[Crossref]

Chang, J. H.

J. H. Chang, J. M. M. Anderson, and J. R. Votaw, “Regularized image reconstruction algorithms for positron emission tomography,” IEEE T. Med. Imaging 23, 1165–1175, (2004).
[Crossref]

Chen, S.

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The Bionanoprobe: Hard X-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75, (2014).
[Crossref]

Chen, Z.

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The Bionanoprobe: Hard X-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75, (2014).
[Crossref]

Chukalina, M.

B. Golosio, A. Simionovici, A. Somogyi, L. Lemelle, M. Chukalina, and A. Brunetti, “Internal elemental micro-analysis combining x-ray fluorescence, Compton and transmission tomography,” J. Appl. Phys. 94, 145 (2003).
[Crossref]

Cloetens, P.

H. Suhonen, F. Xu, L. Helfen, C. Ferrero, P. Vladimirov, and P. Cloetens, “X-ray phase contrast and fluorescence nanotomography for material studies,” Int. J. Mater. Res. 103, 179–183, (2012).
[Crossref]

De Carlo, F.

F. De Carlo, D. Gürsoy, F. Marone, M. Rivers, D. Parkinson, F. Khan, N. Schwarz, D. Vine, S. Vogt, S. C. Gleber, S. Narayanan, M. Newville, A. Lanzirotti, Y. Sun, Y. Hong, and C. Jacobsen, “Scientific data exchange: a schema for HDF5-based storage of raw and analyzed data,” J. Synchrotron Radiat. 21, 1224–1230, (2014).
[Crossref] [PubMed]

D. Gürsoy, F. De Carlo, X. Xiao, and C. Jacobsen, “TomoPy: a framework for the analysis of synchrotron tomographic data,” J. Synchrotron Radiat. 21, 1185–1193, (2014).
[Crossref]

De Pierro, A. R.

E. X. Miqueles and A. R. De Pierro, “Iterative reconstruction in X-ray fluorescence tomography based on Radon inversion,” IEEE T. Med. Imaging 30, 438–450, (2011).
[Crossref]

Deng, J.

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The Bionanoprobe: Hard X-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75, (2014).
[Crossref]

Donner, E.

E. Lombi, M. D. Jonge, E. Donner, C. G. Ryan, and D. Paterson, “Trends in hard X-ray fluorescence mapping: environmental applications in the age of fast detectors,” Anal. Bioanal. Chem. 400, 1637–1644, (2011).
[Crossref] [PubMed]

Dowd, B. A.

B. A. Dowd, G. H. Campbell, R. B. Marr, V. Nagarkar, S. Tipnis, L. Axe, and D. P. Siddons, “Developments in synchrotron x-ray computed microtomography at the National Synchrotron Light Source,” Proc. SPIE 3772, 224–236, (1999).
[Crossref]

Dunagan, S.

A. J. Brown, B. Sutter, and S. Dunagan, “The MARTE VNIR imaging spectrometer experiment: design and analysis,” Astrobiology 8, 1001–1011, (2008).
[Crossref] [PubMed]

Ecker, J.

S. Kim, T. Punshon, A. Lanzirotti, L. Li, J. Alonso, J. Ecker, J. Kaplan, and M. Guerinot, “Localization of iron in arabidopsis seed requires the vacuolar membrane transporter VIT1,” Science 314, 1295–1298, (2006).
[Crossref] [PubMed]

Fahrni, C. J.

D. Bourassa, S. C. Gleber, S. Vogt, H. Yi, F. Will, H. Richter, C. H. Shin, and C. J. Fahrni, “3D imaging of transition metals in the zebrafish embryo by X-ray fluorescence microtomography,” Metallomics 9, 1648–1655, (2007).

C. J. Fahrni, “Biological applications of X-ray fluorescence microscopy: exploring the subcellular topography and speciation of transition metals,” Curr. Opin. Chem. Biol. 11, 121–127, (2007).
[Crossref] [PubMed]

Ferrero, C.

H. Suhonen, F. Xu, L. Helfen, C. Ferrero, P. Vladimirov, and P. Cloetens, “X-ray phase contrast and fluorescence nanotomography for material studies,” Int. J. Mater. Res. 103, 179–183, (2012).
[Crossref]

Feser, M.

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The Bionanoprobe: Hard X-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75, (2014).
[Crossref]

Finney, L.

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S. Kim, T. Punshon, A. Lanzirotti, L. Li, J. Alonso, J. Ecker, J. Kaplan, and M. Guerinot, “Localization of iron in arabidopsis seed requires the vacuolar membrane transporter VIT1,” Science 314, 1295–1298, (2006).
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J. Qi and R. M. Leahy, “Iterative reconstruction techniques in emission computed tomography,” Phys. Med. Biol. 51, R541 (2006).
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F. De Carlo, D. Gürsoy, F. Marone, M. Rivers, D. Parkinson, F. Khan, N. Schwarz, D. Vine, S. Vogt, S. C. Gleber, S. Narayanan, M. Newville, A. Lanzirotti, Y. Sun, Y. Hong, and C. Jacobsen, “Scientific data exchange: a schema for HDF5-based storage of raw and analyzed data,” J. Synchrotron Radiat. 21, 1224–1230, (2014).
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S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The Bionanoprobe: Hard X-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75, (2014).
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B. Golosio, A. Simionovici, A. Somogyi, L. Lemelle, M. Chukalina, and A. Brunetti, “Internal elemental micro-analysis combining x-ray fluorescence, Compton and transmission tomography,” J. Appl. Phys. 94, 145 (2003).
[Crossref]

Spink, I.

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The Bionanoprobe: Hard X-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75, (2014).
[Crossref]

Steele, J.

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The Bionanoprobe: Hard X-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75, (2014).
[Crossref]

Suhonen, H.

H. Suhonen, F. Xu, L. Helfen, C. Ferrero, P. Vladimirov, and P. Cloetens, “X-ray phase contrast and fluorescence nanotomography for material studies,” Int. J. Mater. Res. 103, 179–183, (2012).
[Crossref]

Sun, Y.

F. De Carlo, D. Gürsoy, F. Marone, M. Rivers, D. Parkinson, F. Khan, N. Schwarz, D. Vine, S. Vogt, S. C. Gleber, S. Narayanan, M. Newville, A. Lanzirotti, Y. Sun, Y. Hong, and C. Jacobsen, “Scientific data exchange: a schema for HDF5-based storage of raw and analyzed data,” J. Synchrotron Radiat. 21, 1224–1230, (2014).
[Crossref] [PubMed]

Susini, J.

E. Lombi and J. Susini, “Synchrotron-based techniques for plant and soil science: opportunities, challenges and future perspectives,” Plant Soil 320, 1–35, (2009).
[Crossref]

S. Bohic, A. Simionovici, X. Biquard, G. Martinez-Criado, and J. Susini, “Synchrotron X-ray microfluorescence and microspectroscopy: Application and perspectives in materials science,” Oil Gas Sci. Technol. 6, 979–993, (2005).
[Crossref]

Sutter, B.

A. J. Brown, B. Sutter, and S. Dunagan, “The MARTE VNIR imaging spectrometer experiment: design and analysis,” Astrobiology 8, 1001–1011, (2008).
[Crossref] [PubMed]

Sutton, S.

P. J. La Riviere, P. A. Vargas, M. Newville, and S. Sutton, “Reduced-scan schemes for X-ray fluorescence computed tomography,” IEEE Trans. Nucl. Sci. 54, 1535–1542, (2007).
[Crossref]

Sutton, S. R.

P. L. Riviere, P. Vargas, M. Rivers, and S. R. Sutton, “Penalized-likelihood image reconstruction for X-ray fluorescence computed tomography,” Opt. Eng. 45, 077005 (2006).
[Crossref]

Tipnis, S.

B. A. Dowd, G. H. Campbell, R. B. Marr, V. Nagarkar, S. Tipnis, L. Axe, and D. P. Siddons, “Developments in synchrotron x-ray computed microtomography at the National Synchrotron Light Source,” Proc. SPIE 3772, 224–236, (1999).
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S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The Bionanoprobe: Hard X-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75, (2014).
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X. R. Wang, A. J. Brown, and B. Upcroft, “Applying incremental EM to Bayesian classifiers in the learning of hyperspectral remote sensing data,” Information Fusion Proc. 1, 606–613, (2005).

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P. L. Riviere, P. Vargas, M. Rivers, and S. R. Sutton, “Penalized-likelihood image reconstruction for X-ray fluorescence computed tomography,” Opt. Eng. 45, 077005 (2006).
[Crossref]

Vargas, P. A.

P. J. La Riviere, P. A. Vargas, M. Newville, and S. Sutton, “Reduced-scan schemes for X-ray fluorescence computed tomography,” IEEE Trans. Nucl. Sci. 54, 1535–1542, (2007).
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P. J. La Riviere and P. A. Vargas, “Monotonic penalized-likelihood image reconstruction for x-ray fluorescence computed tomography,” IEEE T. Med. Imaging 25, 1117–1129, (2006).
[Crossref]

Vine, D.

F. De Carlo, D. Gürsoy, F. Marone, M. Rivers, D. Parkinson, F. Khan, N. Schwarz, D. Vine, S. Vogt, S. C. Gleber, S. Narayanan, M. Newville, A. Lanzirotti, Y. Sun, Y. Hong, and C. Jacobsen, “Scientific data exchange: a schema for HDF5-based storage of raw and analyzed data,” J. Synchrotron Radiat. 21, 1224–1230, (2014).
[Crossref] [PubMed]

Vine, D. J.

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The Bionanoprobe: Hard X-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75, (2014).
[Crossref]

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H. Suhonen, F. Xu, L. Helfen, C. Ferrero, P. Vladimirov, and P. Cloetens, “X-ray phase contrast and fluorescence nanotomography for material studies,” Int. J. Mater. Res. 103, 179–183, (2012).
[Crossref]

Vogt, C.

Vogt, S.

F. De Carlo, D. Gürsoy, F. Marone, M. Rivers, D. Parkinson, F. Khan, N. Schwarz, D. Vine, S. Vogt, S. C. Gleber, S. Narayanan, M. Newville, A. Lanzirotti, Y. Sun, Y. Hong, and C. Jacobsen, “Scientific data exchange: a schema for HDF5-based storage of raw and analyzed data,” J. Synchrotron Radiat. 21, 1224–1230, (2014).
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T. Paunesku, S. Vogt, J. Maser, B. Lai, and G. Woloschak, “X-ray fluorescence microprobe imaging in biology and medicine,” J. Cell Biochem. 99, 1489–1502, (2006).
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S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The Bionanoprobe: Hard X-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75, (2014).
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J. H. Chang, J. M. M. Anderson, and J. R. Votaw, “Regularized image reconstruction algorithms for positron emission tomography,” IEEE T. Med. Imaging 23, 1165–1175, (2004).
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D. Bourassa, S. C. Gleber, S. Vogt, H. Yi, F. Will, H. Richter, C. H. Shin, and C. J. Fahrni, “3D imaging of transition metals in the zebrafish embryo by X-ray fluorescence microtomography,” Metallomics 9, 1648–1655, (2007).

Woloschak, G.

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The Bionanoprobe: Hard X-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75, (2014).
[Crossref]

T. Paunesku, S. Vogt, J. Maser, B. Lai, and G. Woloschak, “X-ray fluorescence microprobe imaging in biology and medicine,” J. Cell Biochem. 99, 1489–1502, (2006).
[Crossref] [PubMed]

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D. Gürsoy, F. De Carlo, X. Xiao, and C. Jacobsen, “TomoPy: a framework for the analysis of synchrotron tomographic data,” J. Synchrotron Radiat. 21, 1185–1193, (2014).
[Crossref]

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H. Suhonen, F. Xu, L. Helfen, C. Ferrero, P. Vladimirov, and P. Cloetens, “X-ray phase contrast and fluorescence nanotomography for material studies,” Int. J. Mater. Res. 103, 179–183, (2012).
[Crossref]

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D. Bourassa, S. C. Gleber, S. Vogt, H. Yi, F. Will, H. Richter, C. H. Shin, and C. J. Fahrni, “3D imaging of transition metals in the zebrafish embryo by X-ray fluorescence microtomography,” Metallomics 9, 1648–1655, (2007).

Yuan, Y.

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The Bionanoprobe: Hard X-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75, (2014).
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A. J. Brown, B. Sutter, and S. Dunagan, “The MARTE VNIR imaging spectrometer experiment: design and analysis,” Astrobiology 8, 1001–1011, (2008).
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C. J. Fahrni, “Biological applications of X-ray fluorescence microscopy: exploring the subcellular topography and speciation of transition metals,” Curr. Opin. Chem. Biol. 11, 121–127, (2007).
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M. D. Jonge and S. Vogt, “Hard X-ray fluorescence tomography – an emerging tool for structural visualization,” Curr. Opin. Struc. Biol. 20, 606–614, (2010).
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A. J. Brown, “Spectral curve fitting for automatic hyperspectral data analysis,” IEEE Geosci Remote S 44, 1601 (2006).

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G-F. Rust and J. Weigelt, “X-Ray Fluorescent Computer Tomography with Synchrotron Radiation,” IEEE T. Nucl. Sci. 45, 75–88, (1998).
[Crossref]

IEEE Trans. Nucl. Sci. (1)

P. J. La Riviere, P. A. Vargas, M. Newville, and S. Sutton, “Reduced-scan schemes for X-ray fluorescence computed tomography,” IEEE Trans. Nucl. Sci. 54, 1535–1542, (2007).
[Crossref]

Information Fusion Proc. (1)

X. R. Wang, A. J. Brown, and B. Upcroft, “Applying incremental EM to Bayesian classifiers in the learning of hyperspectral remote sensing data,” Information Fusion Proc. 1, 606–613, (2005).

Int. J. Mater. Res. (1)

H. Suhonen, F. Xu, L. Helfen, C. Ferrero, P. Vladimirov, and P. Cloetens, “X-ray phase contrast and fluorescence nanotomography for material studies,” Int. J. Mater. Res. 103, 179–183, (2012).
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J. Cell Biochem. (1)

T. Paunesku, S. Vogt, J. Maser, B. Lai, and G. Woloschak, “X-ray fluorescence microprobe imaging in biology and medicine,” J. Cell Biochem. 99, 1489–1502, (2006).
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D. Gürsoy, F. De Carlo, X. Xiao, and C. Jacobsen, “TomoPy: a framework for the analysis of synchrotron tomographic data,” J. Synchrotron Radiat. 21, 1185–1193, (2014).
[Crossref]

F. De Carlo, D. Gürsoy, F. Marone, M. Rivers, D. Parkinson, F. Khan, N. Schwarz, D. Vine, S. Vogt, S. C. Gleber, S. Narayanan, M. Newville, A. Lanzirotti, Y. Sun, Y. Hong, and C. Jacobsen, “Scientific data exchange: a schema for HDF5-based storage of raw and analyzed data,” J. Synchrotron Radiat. 21, 1224–1230, (2014).
[Crossref] [PubMed]

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The Bionanoprobe: Hard X-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75, (2014).
[Crossref]

Metallomics (1)

D. Bourassa, S. C. Gleber, S. Vogt, H. Yi, F. Will, H. Richter, C. H. Shin, and C. J. Fahrni, “3D imaging of transition metals in the zebrafish embryo by X-ray fluorescence microtomography,” Metallomics 9, 1648–1655, (2007).

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S. Bohic, A. Simionovici, X. Biquard, G. Martinez-Criado, and J. Susini, “Synchrotron X-ray microfluorescence and microspectroscopy: Application and perspectives in materials science,” Oil Gas Sci. Technol. 6, 979–993, (2005).
[Crossref]

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P. L. Riviere, P. Vargas, M. Rivers, and S. R. Sutton, “Penalized-likelihood image reconstruction for X-ray fluorescence computed tomography,” Opt. Eng. 45, 077005 (2006).
[Crossref]

Opt. Lett. (1)

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J. Qi and R. M. Leahy, “Iterative reconstruction techniques in emission computed tomography,” Phys. Med. Biol. 51, R541 (2006).
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E. Lombi and J. Susini, “Synchrotron-based techniques for plant and soil science: opportunities, challenges and future perspectives,” Plant Soil 320, 1–35, (2009).
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Proc. SPIE (1)

B. A. Dowd, G. H. Campbell, R. B. Marr, V. Nagarkar, S. Tipnis, L. Axe, and D. P. Siddons, “Developments in synchrotron x-ray computed microtomography at the National Synchrotron Light Source,” Proc. SPIE 3772, 224–236, (1999).
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Science (1)

S. Kim, T. Punshon, A. Lanzirotti, L. Li, J. Alonso, J. Ecker, J. Kaplan, and M. Guerinot, “Localization of iron in arabidopsis seed requires the vacuolar membrane transporter VIT1,” Science 314, 1295–1298, (2006).
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P. C. Hansen, “Discrete Inverse Problems: Insight and Algorithms,” : (SIAM, Philadelphia, PA2010).

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T. Bicer, “Supporting data-intensive scientific computing on bandwidth and space constrained environments”. PhD Dissertation, (2014).

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Figures (7)

Fig. 1
Fig. 1 A schematic representation of a typical XRF data collection system. The sample is illuminated by a focused monochromatic X-ray beam (for example using a Fresnel zone plate or elliptically figured X-ray reflective mirrors) to stimulate emission of fluorescence X-rays from elements whose binding energies lie below the incident beam energy. The fluorescent X-rays on beam trajectory are considered to be emitted isotropically and the escaped photons are typically measured using solid state energy-resolving X-ray detector placed close to the specimen. X-ray attenuation though the sample can be measured using a variety of different transmission detectors placed downstream of the sample (ion chambers, photodiodes, etc.)
Fig. 2
Fig. 2 Schematic representations of the traditional and the proposed joint XFM elemental reconstruction approaches. The drawing on the left illustrates the traditional XFM data analysis, where each 1D energy-dispersive pixel data is converted into individual elemental maps (1) before performing a 3D tomographic reconstruction (2). The drawing on the right depicts a joint approach that uses the complete spatio-spectral data to perform reconstruction in a single step. In this way, the variations in both spatial (3) and energy (4) dimensions can be regularized in the reconstruction domain simultaneously, which in turn leads to a significantly reduced reconstruction uncertainty, and better interpretation of results.
Fig. 3
Fig. 3 A three-dimensional ”data cube” (with 2D spatial and 1D spectral variations of model parameters), and the interactions among neighboring voxels in spatial and spectral dimensions are illustrated at the top. The regularization function for various δ values are plotted at the bottom.
Fig. 4
Fig. 4 The absolute values of the reconstructed energy spectrum (in an arbitrary location inside the sample) using FBP (blue), absolute value of FBP (green) and sPML (red) are plotted on the top. The corresponding overlaid elemental maps of Mn, Fe, and Zn are shown on the bottom. The size of the seed is about 250 μm.
Fig. 5
Fig. 5 Individual 2D elemental maps of Mn, Fe, and Zn and their cross-section plots for both FBP and sPML.
Fig. 6
Fig. 6 The effect of angular sampling on reconstructed images at Fe-peak energy is presented for both reconstruction methods. The columns from right to left show the reconstructions obtained using a tilt step angle of 0.5, 1, 2, and 4 degrees, respectively. Bottom row shows the difference images between sPML and FBP. All the images are scaled to the same intensity range indicated by the color bar, and only the non-negative values are presented.
Fig. 7
Fig. 7 Relative error plots of FBP and sPML reconstructions as a function of X-ray energy.

Equations (8)

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x ^ E = arg max x E 0 { ( x E , y E ) β ( x E ) } ,
( x E ) = i j V w i j ψ ( x E , i x E , j ) ,
ψ ( x E ) = δ 2 [ | x E δ | log ( 1 + | x E δ | ) ] ,
RE E = | i [ x i ] E P 1 j [ d j ] E P 1 j [ d j ] E | ,
x j ( n + 1 ) = G j ( n ) + G j 2 ( n ) 8 E j ( n ) F j ( n ) 4 F j ( n )
E j ( n ) = j p j k x j ( n ) d i [ P x ( n ) ] i
F j ( n ) = 2 β k N j w j k γ ( x j ( n ) x k ( n ) )
G j ( n ) = j p j k 2 β k N j w j k γ ( x j ( n ) x k ( n ) ) ( x j ( n ) + x k ( n ) )

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