Abstract

Radiation dose is a concern in X-ray tomographic imaging; coded aperture compressive X-ray tomosynthesis is an approach used to reduce radiation. It places a coded aperture in front of an X-ray source in order to obtain 2D patterned projections of a three-dimensional object onto a detector plane. By using different coded apertures in a multiple source system, multiplexed projections can be obtained instead of sequential projections as in conventional tomosynthesis systems. Compressed sensing (CS) reconstruction algorithms are then used to recover the three-dimensional data cube. An optimization approach to design the structure of the coded apertures in a multiple source compressive X-ray tomosynthesis imaging system is presented. A uniform energy criteria on the voxels and detector elements is used so that the object is uniformly sensed and the elements of the detector plane uniformly sense the information. Simulations and experimental results for optimized coded apertures are shown, and their performance is compared to the use of random coded apertures.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Coded aperture optimization in compressive X-ray tomography: a gradient descent approach

Angela P. Cuadros and Gonzalo R. Arce
Opt. Express 25(20) 23833-23849 (2017)

Fast optimization of coded apertures in X-ray computed tomography

Tianyi Mao, Angela P. Cuadros, Xu Ma, Weiji He, Qian Chen, and Gonzalo R. Arce
Opt. Express 26(19) 24461-24478 (2018)

Spatiotemporal blue noise coded aperture design for multi-shot compressive spectral imaging

Claudia V. Correa, Henry Arguello, and Gonzalo R. Arce
J. Opt. Soc. Am. A 33(12) 2312-2322 (2016)

References

  • View by:
  • |
  • |
  • |

  1. J. T. Dobbins and D. J. Godfrey, “Digital X-ray tomosynthesis: current state of the art and clinical potential,” Phys. Med. Biol. 48(19), R65 (2003).
    [Crossref] [PubMed]
  2. R. Smith-Bindman, J. Lipson, R. Marcus, K.P. Kim, M. Mahesh, R. Gould, A. Berrington de Gonzalez, and D. L. Miglioretti, “Radiation dose associated with common computed tomography examinations and the associated lifetime attributable risk of cancer,” Arch. Internal Med. 169(22), 2078–2086 (2009).
    [Crossref]
  3. I. Reiser and S. Glick, Tomosynthesis Imaging (Taylor and Francis, 2014).
  4. F. Natterer, The Mathematics of Computerized Tomography (Vieweg Teubner Verlag, 1986).
  5. K. Hämäläinen, A. Kallonen, V. Kolehmainen, M. Lassas, K. Niinimäki, and S. Siltanen, “Sparse tomography,” Computational Methods in Science and Engineering, SIAM, 35, B644–B665 (2013).
  6. K. Choi and D. J. Brady, “Coded aperture computed tomography,” Proc. SPIE 7468, 74680B (2009).
    [Crossref]
  7. Y. Kaganovsky, D. Li, A. Holmgren, H. Jeon, K. MacCabe, D. Politte, J. O’Sullivan, L. Carin, and D. J. Brady, “Compressed Sampling Strategies for Tomography,” J. Opt. Soc. Am. A 31, 1369–1394 (2014).
    [Crossref]
  8. M. Slaney and A. Kak, Principles of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, 2001).
  9. E. Candes and M. Wakin, “An introduction to compressive sampling,” IEEE Sig. Proc. Mag. 25 (2), 21–30 (2008).
    [Crossref]
  10. A. Cuadros, G. R. Arce, and H. Arguello, “Coded aperture design in compressive X-ray tomography,” in IEEE Global Conference on Signal and Information Processing (GlobalSIP), 656–659Dec (2014).
  11. A. Cuadros, K. Wang, C. Peitch, H. Arguello, and G. R. Arce, “Coded aperture design for compressive X-ray tomosynthesis,” in Imaging and Applied Optics 2015. Optical Society of America, 2015, p. CW2F.2.
    [Crossref]
  12. J. P. Allebach, “DBS: retrospective and future directions,” Proc. SPIE 4300, 358–376 (2000).
    [Crossref]
  13. D. L. Lau and G. R. Arce, Modern Digital Halftoning (CRC Press; Taylor & Francis Group, 2008).
    [Crossref]
  14. W. Xu, F. Xu, M. Jones, B. Keszthelyi, J. Sedat, D. Agard, and K. Mueller, “High-performance iterative electron tomography reconstruction with long-object compensation using graphics processing units,” J. Structural Biol. 171 (2), 142–153 (2010).
    [Crossref]
  15. D. J. Brady, Optical Imaging and Spectroscopy (Wiley; Optical Society of America, 2009).
    [Crossref]
  16. N. Halko, P. G. Martinsson, and J. A. Tropp, “Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions,” SIAM Review 532217–288, (2011).
    [Crossref]
  17. M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Sig. Proc. 1(4), 586–597 (2007).
    [Crossref]
  18. G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive Coded Aperture Spectral Imaging: An Introduction,” IEEE Signal Processing Magazine, 105–115, January (2014).
    [Crossref]

2014 (2)

Y. Kaganovsky, D. Li, A. Holmgren, H. Jeon, K. MacCabe, D. Politte, J. O’Sullivan, L. Carin, and D. J. Brady, “Compressed Sampling Strategies for Tomography,” J. Opt. Soc. Am. A 31, 1369–1394 (2014).
[Crossref]

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive Coded Aperture Spectral Imaging: An Introduction,” IEEE Signal Processing Magazine, 105–115, January (2014).
[Crossref]

2011 (1)

N. Halko, P. G. Martinsson, and J. A. Tropp, “Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions,” SIAM Review 532217–288, (2011).
[Crossref]

2010 (1)

W. Xu, F. Xu, M. Jones, B. Keszthelyi, J. Sedat, D. Agard, and K. Mueller, “High-performance iterative electron tomography reconstruction with long-object compensation using graphics processing units,” J. Structural Biol. 171 (2), 142–153 (2010).
[Crossref]

2009 (2)

R. Smith-Bindman, J. Lipson, R. Marcus, K.P. Kim, M. Mahesh, R. Gould, A. Berrington de Gonzalez, and D. L. Miglioretti, “Radiation dose associated with common computed tomography examinations and the associated lifetime attributable risk of cancer,” Arch. Internal Med. 169(22), 2078–2086 (2009).
[Crossref]

K. Choi and D. J. Brady, “Coded aperture computed tomography,” Proc. SPIE 7468, 74680B (2009).
[Crossref]

2008 (1)

E. Candes and M. Wakin, “An introduction to compressive sampling,” IEEE Sig. Proc. Mag. 25 (2), 21–30 (2008).
[Crossref]

2007 (1)

M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Sig. Proc. 1(4), 586–597 (2007).
[Crossref]

2003 (1)

J. T. Dobbins and D. J. Godfrey, “Digital X-ray tomosynthesis: current state of the art and clinical potential,” Phys. Med. Biol. 48(19), R65 (2003).
[Crossref] [PubMed]

2000 (1)

J. P. Allebach, “DBS: retrospective and future directions,” Proc. SPIE 4300, 358–376 (2000).
[Crossref]

Agard, D.

W. Xu, F. Xu, M. Jones, B. Keszthelyi, J. Sedat, D. Agard, and K. Mueller, “High-performance iterative electron tomography reconstruction with long-object compensation using graphics processing units,” J. Structural Biol. 171 (2), 142–153 (2010).
[Crossref]

Allebach, J. P.

J. P. Allebach, “DBS: retrospective and future directions,” Proc. SPIE 4300, 358–376 (2000).
[Crossref]

Arce, G. R.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive Coded Aperture Spectral Imaging: An Introduction,” IEEE Signal Processing Magazine, 105–115, January (2014).
[Crossref]

D. L. Lau and G. R. Arce, Modern Digital Halftoning (CRC Press; Taylor & Francis Group, 2008).
[Crossref]

A. Cuadros, K. Wang, C. Peitch, H. Arguello, and G. R. Arce, “Coded aperture design for compressive X-ray tomosynthesis,” in Imaging and Applied Optics 2015. Optical Society of America, 2015, p. CW2F.2.
[Crossref]

A. Cuadros, G. R. Arce, and H. Arguello, “Coded aperture design in compressive X-ray tomography,” in IEEE Global Conference on Signal and Information Processing (GlobalSIP), 656–659Dec (2014).

Arguello, H.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive Coded Aperture Spectral Imaging: An Introduction,” IEEE Signal Processing Magazine, 105–115, January (2014).
[Crossref]

A. Cuadros, G. R. Arce, and H. Arguello, “Coded aperture design in compressive X-ray tomography,” in IEEE Global Conference on Signal and Information Processing (GlobalSIP), 656–659Dec (2014).

A. Cuadros, K. Wang, C. Peitch, H. Arguello, and G. R. Arce, “Coded aperture design for compressive X-ray tomosynthesis,” in Imaging and Applied Optics 2015. Optical Society of America, 2015, p. CW2F.2.
[Crossref]

Berrington de Gonzalez, A.

R. Smith-Bindman, J. Lipson, R. Marcus, K.P. Kim, M. Mahesh, R. Gould, A. Berrington de Gonzalez, and D. L. Miglioretti, “Radiation dose associated with common computed tomography examinations and the associated lifetime attributable risk of cancer,” Arch. Internal Med. 169(22), 2078–2086 (2009).
[Crossref]

Brady, D. J.

Y. Kaganovsky, D. Li, A. Holmgren, H. Jeon, K. MacCabe, D. Politte, J. O’Sullivan, L. Carin, and D. J. Brady, “Compressed Sampling Strategies for Tomography,” J. Opt. Soc. Am. A 31, 1369–1394 (2014).
[Crossref]

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive Coded Aperture Spectral Imaging: An Introduction,” IEEE Signal Processing Magazine, 105–115, January (2014).
[Crossref]

K. Choi and D. J. Brady, “Coded aperture computed tomography,” Proc. SPIE 7468, 74680B (2009).
[Crossref]

D. J. Brady, Optical Imaging and Spectroscopy (Wiley; Optical Society of America, 2009).
[Crossref]

Candes, E.

E. Candes and M. Wakin, “An introduction to compressive sampling,” IEEE Sig. Proc. Mag. 25 (2), 21–30 (2008).
[Crossref]

Carin, L.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive Coded Aperture Spectral Imaging: An Introduction,” IEEE Signal Processing Magazine, 105–115, January (2014).
[Crossref]

Y. Kaganovsky, D. Li, A. Holmgren, H. Jeon, K. MacCabe, D. Politte, J. O’Sullivan, L. Carin, and D. J. Brady, “Compressed Sampling Strategies for Tomography,” J. Opt. Soc. Am. A 31, 1369–1394 (2014).
[Crossref]

Choi, K.

K. Choi and D. J. Brady, “Coded aperture computed tomography,” Proc. SPIE 7468, 74680B (2009).
[Crossref]

Cuadros, A.

A. Cuadros, K. Wang, C. Peitch, H. Arguello, and G. R. Arce, “Coded aperture design for compressive X-ray tomosynthesis,” in Imaging and Applied Optics 2015. Optical Society of America, 2015, p. CW2F.2.
[Crossref]

A. Cuadros, G. R. Arce, and H. Arguello, “Coded aperture design in compressive X-ray tomography,” in IEEE Global Conference on Signal and Information Processing (GlobalSIP), 656–659Dec (2014).

Dobbins, J. T.

J. T. Dobbins and D. J. Godfrey, “Digital X-ray tomosynthesis: current state of the art and clinical potential,” Phys. Med. Biol. 48(19), R65 (2003).
[Crossref] [PubMed]

Figueiredo, M.

M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Sig. Proc. 1(4), 586–597 (2007).
[Crossref]

Glick, S.

I. Reiser and S. Glick, Tomosynthesis Imaging (Taylor and Francis, 2014).

Godfrey, D. J.

J. T. Dobbins and D. J. Godfrey, “Digital X-ray tomosynthesis: current state of the art and clinical potential,” Phys. Med. Biol. 48(19), R65 (2003).
[Crossref] [PubMed]

Gould, R.

R. Smith-Bindman, J. Lipson, R. Marcus, K.P. Kim, M. Mahesh, R. Gould, A. Berrington de Gonzalez, and D. L. Miglioretti, “Radiation dose associated with common computed tomography examinations and the associated lifetime attributable risk of cancer,” Arch. Internal Med. 169(22), 2078–2086 (2009).
[Crossref]

Halko, N.

N. Halko, P. G. Martinsson, and J. A. Tropp, “Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions,” SIAM Review 532217–288, (2011).
[Crossref]

Hämäläinen, K.

K. Hämäläinen, A. Kallonen, V. Kolehmainen, M. Lassas, K. Niinimäki, and S. Siltanen, “Sparse tomography,” Computational Methods in Science and Engineering, SIAM, 35, B644–B665 (2013).

Holmgren, A.

Jeon, H.

Jones, M.

W. Xu, F. Xu, M. Jones, B. Keszthelyi, J. Sedat, D. Agard, and K. Mueller, “High-performance iterative electron tomography reconstruction with long-object compensation using graphics processing units,” J. Structural Biol. 171 (2), 142–153 (2010).
[Crossref]

Kaganovsky, Y.

Kak, A.

M. Slaney and A. Kak, Principles of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, 2001).

Kallonen, A.

K. Hämäläinen, A. Kallonen, V. Kolehmainen, M. Lassas, K. Niinimäki, and S. Siltanen, “Sparse tomography,” Computational Methods in Science and Engineering, SIAM, 35, B644–B665 (2013).

Keszthelyi, B.

W. Xu, F. Xu, M. Jones, B. Keszthelyi, J. Sedat, D. Agard, and K. Mueller, “High-performance iterative electron tomography reconstruction with long-object compensation using graphics processing units,” J. Structural Biol. 171 (2), 142–153 (2010).
[Crossref]

Kim, K.P.

R. Smith-Bindman, J. Lipson, R. Marcus, K.P. Kim, M. Mahesh, R. Gould, A. Berrington de Gonzalez, and D. L. Miglioretti, “Radiation dose associated with common computed tomography examinations and the associated lifetime attributable risk of cancer,” Arch. Internal Med. 169(22), 2078–2086 (2009).
[Crossref]

Kittle, D. S.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive Coded Aperture Spectral Imaging: An Introduction,” IEEE Signal Processing Magazine, 105–115, January (2014).
[Crossref]

Kolehmainen, V.

K. Hämäläinen, A. Kallonen, V. Kolehmainen, M. Lassas, K. Niinimäki, and S. Siltanen, “Sparse tomography,” Computational Methods in Science and Engineering, SIAM, 35, B644–B665 (2013).

Lassas, M.

K. Hämäläinen, A. Kallonen, V. Kolehmainen, M. Lassas, K. Niinimäki, and S. Siltanen, “Sparse tomography,” Computational Methods in Science and Engineering, SIAM, 35, B644–B665 (2013).

Lau, D. L.

D. L. Lau and G. R. Arce, Modern Digital Halftoning (CRC Press; Taylor & Francis Group, 2008).
[Crossref]

Li, D.

Lipson, J.

R. Smith-Bindman, J. Lipson, R. Marcus, K.P. Kim, M. Mahesh, R. Gould, A. Berrington de Gonzalez, and D. L. Miglioretti, “Radiation dose associated with common computed tomography examinations and the associated lifetime attributable risk of cancer,” Arch. Internal Med. 169(22), 2078–2086 (2009).
[Crossref]

MacCabe, K.

Mahesh, M.

R. Smith-Bindman, J. Lipson, R. Marcus, K.P. Kim, M. Mahesh, R. Gould, A. Berrington de Gonzalez, and D. L. Miglioretti, “Radiation dose associated with common computed tomography examinations and the associated lifetime attributable risk of cancer,” Arch. Internal Med. 169(22), 2078–2086 (2009).
[Crossref]

Marcus, R.

R. Smith-Bindman, J. Lipson, R. Marcus, K.P. Kim, M. Mahesh, R. Gould, A. Berrington de Gonzalez, and D. L. Miglioretti, “Radiation dose associated with common computed tomography examinations and the associated lifetime attributable risk of cancer,” Arch. Internal Med. 169(22), 2078–2086 (2009).
[Crossref]

Martinsson, P. G.

N. Halko, P. G. Martinsson, and J. A. Tropp, “Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions,” SIAM Review 532217–288, (2011).
[Crossref]

Miglioretti, D. L.

R. Smith-Bindman, J. Lipson, R. Marcus, K.P. Kim, M. Mahesh, R. Gould, A. Berrington de Gonzalez, and D. L. Miglioretti, “Radiation dose associated with common computed tomography examinations and the associated lifetime attributable risk of cancer,” Arch. Internal Med. 169(22), 2078–2086 (2009).
[Crossref]

Mueller, K.

W. Xu, F. Xu, M. Jones, B. Keszthelyi, J. Sedat, D. Agard, and K. Mueller, “High-performance iterative electron tomography reconstruction with long-object compensation using graphics processing units,” J. Structural Biol. 171 (2), 142–153 (2010).
[Crossref]

Natterer, F.

F. Natterer, The Mathematics of Computerized Tomography (Vieweg Teubner Verlag, 1986).

Niinimäki, K.

K. Hämäläinen, A. Kallonen, V. Kolehmainen, M. Lassas, K. Niinimäki, and S. Siltanen, “Sparse tomography,” Computational Methods in Science and Engineering, SIAM, 35, B644–B665 (2013).

Nowak, R.

M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Sig. Proc. 1(4), 586–597 (2007).
[Crossref]

O’Sullivan, J.

Peitch, C.

A. Cuadros, K. Wang, C. Peitch, H. Arguello, and G. R. Arce, “Coded aperture design for compressive X-ray tomosynthesis,” in Imaging and Applied Optics 2015. Optical Society of America, 2015, p. CW2F.2.
[Crossref]

Politte, D.

Reiser, I.

I. Reiser and S. Glick, Tomosynthesis Imaging (Taylor and Francis, 2014).

Sedat, J.

W. Xu, F. Xu, M. Jones, B. Keszthelyi, J. Sedat, D. Agard, and K. Mueller, “High-performance iterative electron tomography reconstruction with long-object compensation using graphics processing units,” J. Structural Biol. 171 (2), 142–153 (2010).
[Crossref]

Siltanen, S.

K. Hämäläinen, A. Kallonen, V. Kolehmainen, M. Lassas, K. Niinimäki, and S. Siltanen, “Sparse tomography,” Computational Methods in Science and Engineering, SIAM, 35, B644–B665 (2013).

Slaney, M.

M. Slaney and A. Kak, Principles of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, 2001).

Smith-Bindman, R.

R. Smith-Bindman, J. Lipson, R. Marcus, K.P. Kim, M. Mahesh, R. Gould, A. Berrington de Gonzalez, and D. L. Miglioretti, “Radiation dose associated with common computed tomography examinations and the associated lifetime attributable risk of cancer,” Arch. Internal Med. 169(22), 2078–2086 (2009).
[Crossref]

Tropp, J. A.

N. Halko, P. G. Martinsson, and J. A. Tropp, “Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions,” SIAM Review 532217–288, (2011).
[Crossref]

Wakin, M.

E. Candes and M. Wakin, “An introduction to compressive sampling,” IEEE Sig. Proc. Mag. 25 (2), 21–30 (2008).
[Crossref]

Wang, K.

A. Cuadros, K. Wang, C. Peitch, H. Arguello, and G. R. Arce, “Coded aperture design for compressive X-ray tomosynthesis,” in Imaging and Applied Optics 2015. Optical Society of America, 2015, p. CW2F.2.
[Crossref]

Wright, S.

M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Sig. Proc. 1(4), 586–597 (2007).
[Crossref]

Xu, F.

W. Xu, F. Xu, M. Jones, B. Keszthelyi, J. Sedat, D. Agard, and K. Mueller, “High-performance iterative electron tomography reconstruction with long-object compensation using graphics processing units,” J. Structural Biol. 171 (2), 142–153 (2010).
[Crossref]

Xu, W.

W. Xu, F. Xu, M. Jones, B. Keszthelyi, J. Sedat, D. Agard, and K. Mueller, “High-performance iterative electron tomography reconstruction with long-object compensation using graphics processing units,” J. Structural Biol. 171 (2), 142–153 (2010).
[Crossref]

Arch. Internal Med. (1)

R. Smith-Bindman, J. Lipson, R. Marcus, K.P. Kim, M. Mahesh, R. Gould, A. Berrington de Gonzalez, and D. L. Miglioretti, “Radiation dose associated with common computed tomography examinations and the associated lifetime attributable risk of cancer,” Arch. Internal Med. 169(22), 2078–2086 (2009).
[Crossref]

IEEE J. Sel. Top. Sig. Proc. (1)

M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Sig. Proc. 1(4), 586–597 (2007).
[Crossref]

IEEE Sig. Proc. Mag. (1)

E. Candes and M. Wakin, “An introduction to compressive sampling,” IEEE Sig. Proc. Mag. 25 (2), 21–30 (2008).
[Crossref]

IEEE Signal Processing Magazine (1)

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive Coded Aperture Spectral Imaging: An Introduction,” IEEE Signal Processing Magazine, 105–115, January (2014).
[Crossref]

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

J. Structural Biol. (1)

W. Xu, F. Xu, M. Jones, B. Keszthelyi, J. Sedat, D. Agard, and K. Mueller, “High-performance iterative electron tomography reconstruction with long-object compensation using graphics processing units,” J. Structural Biol. 171 (2), 142–153 (2010).
[Crossref]

Phys. Med. Biol. (1)

J. T. Dobbins and D. J. Godfrey, “Digital X-ray tomosynthesis: current state of the art and clinical potential,” Phys. Med. Biol. 48(19), R65 (2003).
[Crossref] [PubMed]

Proc. SPIE (2)

K. Choi and D. J. Brady, “Coded aperture computed tomography,” Proc. SPIE 7468, 74680B (2009).
[Crossref]

J. P. Allebach, “DBS: retrospective and future directions,” Proc. SPIE 4300, 358–376 (2000).
[Crossref]

SIAM Review (1)

N. Halko, P. G. Martinsson, and J. A. Tropp, “Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions,” SIAM Review 532217–288, (2011).
[Crossref]

Other (8)

D. L. Lau and G. R. Arce, Modern Digital Halftoning (CRC Press; Taylor & Francis Group, 2008).
[Crossref]

A. Cuadros, G. R. Arce, and H. Arguello, “Coded aperture design in compressive X-ray tomography,” in IEEE Global Conference on Signal and Information Processing (GlobalSIP), 656–659Dec (2014).

A. Cuadros, K. Wang, C. Peitch, H. Arguello, and G. R. Arce, “Coded aperture design for compressive X-ray tomosynthesis,” in Imaging and Applied Optics 2015. Optical Society of America, 2015, p. CW2F.2.
[Crossref]

D. J. Brady, Optical Imaging and Spectroscopy (Wiley; Optical Society of America, 2009).
[Crossref]

M. Slaney and A. Kak, Principles of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, 2001).

I. Reiser and S. Glick, Tomosynthesis Imaging (Taylor and Francis, 2014).

F. Natterer, The Mathematics of Computerized Tomography (Vieweg Teubner Verlag, 1986).

K. Hämäläinen, A. Kallonen, V. Kolehmainen, M. Lassas, K. Niinimäki, and S. Siltanen, “Sparse tomography,” Computational Methods in Science and Engineering, SIAM, 35, B644–B665 (2013).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1 (a) X-ray tomosynthesis. The system matrix Hi determines the mapping of the X-ray cone beam sources to the detector. Each row describes the sensing for a particular detector element and each column corresponds to the sensing of a particular voxel. (b) Coded aperture compressive X-ray tomosynthesis. The energy of each source is modulated by means of a coded aperture.
Fig. 2
Fig. 2 (a) To generate the initial set of codes, vector v m k is defined. It is formed by the values of the mth elements of the P coded apertures used in the kth shot. (b) Iteration Process for the DBS algorithm.
Fig. 3
Fig. 3 (a) Configuration for X-ray tomosynthesis simulation. 9 sources placed uniformly over a 128×128 phantom with 16 slices. The dimensions for a general scenario are shown in (a), for the particular simulation scenario that was studied here a = 128,b = 128,c = 675,d = 60,e = 150. (b) Mean of the transmittance of the optimal coded apertures for each shot.
Fig. 4
Fig. 4 (a) Singular Value Decomposition of the tomosynthesis matrix without coding, optimized codes and random codes for K=1 and K=2 shots (b) Singular Value Decomposition for the last 6900 components.
Fig. 5
Fig. 5 Histogram of the number of voxels measured by a detector element, d ¯. (a) Before the optimization, (b) After the optimization.
Fig. 6
Fig. 6 (a) Histogram of the number of detectors that measure a certain voxel, r ¯. (a) Before the optimization, (b) After the optimization.
Fig. 7
Fig. 7 (a) Thirteenth slice of the data cube. Sparse regularized reconstructions from: (b) Random coded X-ray projections using 3 snapshots (PSNR=25.96 dB); (c) Optimized coded apertures using 3 snapshots (PSNR=29.68 dB); (d) Uncoded X-ray projections using 1 snapshot (PSNR= 23.60 dB). Zoomed versions of: (e) Random coded X-ray projections; (f) Optimized coded apertures.
Fig. 8
Fig. 8 (a) First slice of the data cube. (b) Sparse regularized reconstructions from optimized coded apertures using 3 snapshots (PSNR=28.47 dB). (c) Least squares reconstruction using the full matrix (PSNR=28.27 dB); (d) 16th slice of the data cube. (e) Sparse regularized reconstructions from optimized coded apertures using 3 snapshots (PSNR=25.45 dB). (f) Least squares reconstruction using the full matrix (PSNR=25.46 dB). Note that LS reconstructions uses 3 times the amount of measurements than the compressive X-ray tomosynthesis.
Fig. 9
Fig. 9 Optimal coded apertures for: Two snapshots (K=2), (a) the central source and first snapshot, (b) the central source and second snapshot, (c) the source located in the lower right corner and first snapshot, (d) the source located in the lower right corner and second snapshot.
Fig. 10
Fig. 10 Optimal coded apertures for three snapshots (K=3) and the central source and a 1D cross section of the coded aperture elements in column 50, rows from 130 to 140.
Fig. 11
Fig. 11 (a) Convergence of DBS algorithm for different initial set of codes: (blue) checker board, (red) optimized set of codes, (black) random set of codes. (b) Convergence of DBS algorithm for the first 1.42 days (122,500 seconds)
Fig. 12
Fig. 12 Projections obtained from: (a) the central source, and (b) a source located 10 cm to the left of the center source. Reconstructions obtained using 2 shots and random coded apertures for: (c) the 6th and (d) 12th slice. Reconstructions obtained using 2 shots and optimized coded apertures for: (e) the 6th and (f) 12th slice.

Tables (2)

Tables Icon

Table 1 PSNR of the reconstructed image of the 13th slice for different number of shots (K)

Tables Icon

Table 2 PSNR of the reconstructed image of the 16 slices of the data-cube for K = 3 shots

Equations (3)

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

y = ( i = 0 P 1 C i H i ) f = CHf .
y ˜ = C ˜ H f = C ˜ H Ψ θ = A ˜ Ψ θ ,
arg min [ T 0 k , , T P 1 k ] k = 0 k = K 1 α m = 0 M 1 [ ( d ¯ ) m m 1 ] 2 + β j = 0 Q 1 [ ( r ¯ ) j m 2 ] 2 + γ c 3 Subject to ( d ¯ ) m > 0 and ( r ¯ ) j > 0 m , j ,

Metrics