Abstract

Tomosynthesis is an emerging technique with potential to replace mammography, since it gives 3D information at a relatively small increase in dose and cost. We present an analytical singular-value decomposition of a tomosynthesis system, which provides the measurement component of any given object. The method is demonstrated on an example object. The measurement component can be used as a reconstruction of the object, and can also be utilized in future observer studies of tomosynthesis image quality.

© 2010 OSA

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  1. J. T. Dobbins and D. J. Godfrey, “Digital x-ray tomosynthesis: current state of the art and clinical potential,” Phys. Med. Biol. 48, R65–R106 (2003).
    [PubMed]
  2. J. T. Dobbins, “Tomosynthesis: at translational crossroads,” Med. Phys. 36, 1956–1967 (2009).
    [PubMed]
  3. L. T. Niklason, “Digital tomosynthesis in breast imaging,” Radiology 1997, 399–406 (1997).
  4. G. Gennaro, A. Toledano, C. di Maggio, E. Baldan, E. Bezzon, M. La Grassa, L. Pescarini, I. Polico, A. Proietti, A. Toffoli, and P. C. Muzzio, “Digital breast tomosynthesis versus digital mammography: a clinical performance study,” Eur. Radiol. (2009).
    [PubMed]
  5. I. Andersson, D. M. Ikeda, S. Zackrisson, M. Ruschin, T. Svahn, P. Timberg, and A. Tingberg, “Breast tomosynthesis and digital mammography: a comparison of breast cancer visibility and BIRADS classification in a population of cancers with subtle mammographic findings,” Eur. Radiol. 18, 2817–2825 (2008).
    [PubMed]
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  7. S. P. Poplack, T. D. Tosteson, C. A. Kogel, and H. M. Nagy, “Digital breast tomosyntheis: Initial experiance in 98 women with abnormal digital screening mammography,” Am. J. Radiology 189, 616–623 (2007).
  8. A. S. Chawla, J. Y. Lo, J. A. Baker, and E. Samei, “Optimized image acquisition for breast tomosynthesis in projection and reconstruction space,” Med. Phys. 36, 4859–4869 (2009).
    [PubMed]
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    [PubMed]
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    [PubMed]
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  13. H. H. Barrett, J. N. Aarsvold, and T. J. Roney, “Null functions and eigenfunctions: tools for the analysis of imaging systems,” Lect. Notes. Comput. Sci. 11, 211–226 (1991).
  14. A. Burvall, H. H. Barrett, C. Dainty, and K. J. Myers, “Singular-value decomposition for through-focus imaging systems,” J. Opt. Soc. Am. A 23, 2440–2448 (2006).
  15. J. Yao and H. H. Barrett, “Predicting human performance by a channelized Hotelling observer,” Proc. SPIE 1768, 161–168 (1992).
  16. H. H. Barrett, J. Yao, J. P. Rolland, and K. J. Myers, “Model observers for assessment of image quality,” Proc. Natl. Acad. Sci. USA 90, 9758–9765 (1993).
    [PubMed]
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  20. C. Lanczos, Linear differential operators (Van Nostrand, London, 1961).
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  22. I. Reiser and R. M. Nishikawa, “Task-based assessment of breast tomosynthesis: Effects of acquisition parameters and quantum noise,” Med. Phys. 37, 1591–1600 (2010).
    [PubMed]
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  24. K. G. Metheany, C. K. Abbey, N. Packard, and J. M. Boone, “Characterizing anatomical variability in breast CT images,” Med. Phys. 35, 4685–4694 (2008).
    [PubMed]
  25. C. K. Abbey and J. M. Boone, “An ideal observer for a model of x-ray imaging in breast parenchymal tissue,” (E.A. Krupinski, Ed.): IWDM 2008, LNCS5116, 393–400 (2008).
  26. C. Zhang, P. R. Bakic, and A. D. A. Maidment, “Development of an anthropomorphic breast software phantom based on region growing algorithm,” Proc. SPIE 6918, 69180V (2008).
  27. S. Park, J. M. Witten, and K. J. Myers, “Singular vectors of a linear imaging system as efficient channels for the bayesian ideal observer,” IEEE Trans. Med. Imaging 28, 657–668 (2009).
    [PubMed]

2010 (1)

I. Reiser and R. M. Nishikawa, “Task-based assessment of breast tomosynthesis: Effects of acquisition parameters and quantum noise,” Med. Phys. 37, 1591–1600 (2010).
[PubMed]

2009 (4)

S. Park, J. M. Witten, and K. J. Myers, “Singular vectors of a linear imaging system as efficient channels for the bayesian ideal observer,” IEEE Trans. Med. Imaging 28, 657–668 (2009).
[PubMed]

G. Gennaro, A. Toledano, C. di Maggio, E. Baldan, E. Bezzon, M. La Grassa, L. Pescarini, I. Polico, A. Proietti, A. Toffoli, and P. C. Muzzio, “Digital breast tomosynthesis versus digital mammography: a clinical performance study,” Eur. Radiol. (2009).
[PubMed]

J. T. Dobbins, “Tomosynthesis: at translational crossroads,” Med. Phys. 36, 1956–1967 (2009).
[PubMed]

A. S. Chawla, J. Y. Lo, J. A. Baker, and E. Samei, “Optimized image acquisition for breast tomosynthesis in projection and reconstruction space,” Med. Phys. 36, 4859–4869 (2009).
[PubMed]

2008 (4)

I. Andersson, D. M. Ikeda, S. Zackrisson, M. Ruschin, T. Svahn, P. Timberg, and A. Tingberg, “Breast tomosynthesis and digital mammography: a comparison of breast cancer visibility and BIRADS classification in a population of cancers with subtle mammographic findings,” Eur. Radiol. 18, 2817–2825 (2008).
[PubMed]

W. F. Good, G. S. Abrams, V. J. Catullo, D. M. Chough, M. A. Ganott, C. M. Hakim, and D. Gur, “Digital breast tomosynthesis: a pilot observer study,” Am. J. Radiology 190, 865–869 (2008).

K. G. Metheany, C. K. Abbey, N. Packard, and J. M. Boone, “Characterizing anatomical variability in breast CT images,” Med. Phys. 35, 4685–4694 (2008).
[PubMed]

C. Zhang, P. R. Bakic, and A. D. A. Maidment, “Development of an anthropomorphic breast software phantom based on region growing algorithm,” Proc. SPIE 6918, 69180V (2008).

2007 (1)

S. P. Poplack, T. D. Tosteson, C. A. Kogel, and H. M. Nagy, “Digital breast tomosyntheis: Initial experiance in 98 women with abnormal digital screening mammography,” Am. J. Radiology 189, 616–623 (2007).

2006 (2)

Y. Zhang, H.-P. Chan, B. Sahiner, J. Wei, M. M. Goodsitt, L. M. Hadjiiiski, J. Ge, and C. Zhou, “A comparative study of limited-angle cone-beam reconstruction methods for breast tomosynthesis,” Med. Phys. 33, 3781–3795 (2006).
[PubMed]

A. Burvall, H. H. Barrett, C. Dainty, and K. J. Myers, “Singular-value decomposition for through-focus imaging systems,” J. Opt. Soc. Am. A 23, 2440–2448 (2006).

2004 (1)

T. Wu, R. H. Moore, E. A. Rafferty, and D. B. Kopans, “A comparison of reconstruction algorithms for breast tomosynthesis,” Med. Phys. 31, 2636–2647 (2004).
[PubMed]

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, R65–R106 (2003).
[PubMed]

2001 (1)

1999 (1)

1998 (1)

1997 (1)

L. T. Niklason, “Digital tomosynthesis in breast imaging,” Radiology 1997, 399–406 (1997).

1993 (1)

H. H. Barrett, J. Yao, J. P. Rolland, and K. J. Myers, “Model observers for assessment of image quality,” Proc. Natl. Acad. Sci. USA 90, 9758–9765 (1993).
[PubMed]

1992 (1)

J. Yao and H. H. Barrett, “Predicting human performance by a channelized Hotelling observer,” Proc. SPIE 1768, 161–168 (1992).

1991 (1)

H. H. Barrett, J. N. Aarsvold, and T. J. Roney, “Null functions and eigenfunctions: tools for the analysis of imaging systems,” Lect. Notes. Comput. Sci. 11, 211–226 (1991).

1979 (1)

Aarsvold, J. N.

H. H. Barrett, J. N. Aarsvold, and T. J. Roney, “Null functions and eigenfunctions: tools for the analysis of imaging systems,” Lect. Notes. Comput. Sci. 11, 211–226 (1991).

Abbey, C. K.

K. G. Metheany, C. K. Abbey, N. Packard, and J. M. Boone, “Characterizing anatomical variability in breast CT images,” Med. Phys. 35, 4685–4694 (2008).
[PubMed]

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, “Statistical texture synthesis of mammographic images with clustered lumpy backgrounds,” Opt. Express 4, 33–43 (1998).

C. K. Abbey and J. M. Boone, “An ideal observer for a model of x-ray imaging in breast parenchymal tissue,” (E.A. Krupinski, Ed.): IWDM 2008, LNCS5116, 393–400 (2008).

Abrams, G. S.

W. F. Good, G. S. Abrams, V. J. Catullo, D. M. Chough, M. A. Ganott, C. M. Hakim, and D. Gur, “Digital breast tomosynthesis: a pilot observer study,” Am. J. Radiology 190, 865–869 (2008).

Andersson, I.

I. Andersson, D. M. Ikeda, S. Zackrisson, M. Ruschin, T. Svahn, P. Timberg, and A. Tingberg, “Breast tomosynthesis and digital mammography: a comparison of breast cancer visibility and BIRADS classification in a population of cancers with subtle mammographic findings,” Eur. Radiol. 18, 2817–2825 (2008).
[PubMed]

Arendt, J. W.

Baker, J. A.

A. S. Chawla, J. Y. Lo, J. A. Baker, and E. Samei, “Optimized image acquisition for breast tomosynthesis in projection and reconstruction space,” Med. Phys. 36, 4859–4869 (2009).
[PubMed]

Bakic, P. R.

C. Zhang, P. R. Bakic, and A. D. A. Maidment, “Development of an anthropomorphic breast software phantom based on region growing algorithm,” Proc. SPIE 6918, 69180V (2008).

Baldan, E.

G. Gennaro, A. Toledano, C. di Maggio, E. Baldan, E. Bezzon, M. La Grassa, L. Pescarini, I. Polico, A. Proietti, A. Toffoli, and P. C. Muzzio, “Digital breast tomosynthesis versus digital mammography: a clinical performance study,” Eur. Radiol. (2009).
[PubMed]

Barrett, H. H.

A. Burvall, H. H. Barrett, C. Dainty, and K. J. Myers, “Singular-value decomposition for through-focus imaging systems,” J. Opt. Soc. Am. A 23, 2440–2448 (2006).

H. H. Barrett, J. Yao, J. P. Rolland, and K. J. Myers, “Model observers for assessment of image quality,” Proc. Natl. Acad. Sci. USA 90, 9758–9765 (1993).
[PubMed]

J. Yao and H. H. Barrett, “Predicting human performance by a channelized Hotelling observer,” Proc. SPIE 1768, 161–168 (1992).

H. H. Barrett, J. N. Aarsvold, and T. J. Roney, “Null functions and eigenfunctions: tools for the analysis of imaging systems,” Lect. Notes. Comput. Sci. 11, 211–226 (1991).

M. Y. Chiu, H. H. Barrett, R. G. Simpson, C. Chou, J. W. Arendt, and G. R. Gindi, “Three-dimensional radio-graphic imaging with a restricted view angle,” J. Opt. Soc. Am. 69, 1323–1333 (1979).

H. H. Barrett and K. J. Myers, Foundations of Image Science (John Wiley, Hoboken, New Jersey, 2004).

Bertero, M.

M. Bertero and P. Boccacci, Inverse Problems in Imaging (Institute of Physics Publishing, Bristol, UK, 1998)

Bezzon, E.

G. Gennaro, A. Toledano, C. di Maggio, E. Baldan, E. Bezzon, M. La Grassa, L. Pescarini, I. Polico, A. Proietti, A. Toffoli, and P. C. Muzzio, “Digital breast tomosynthesis versus digital mammography: a clinical performance study,” Eur. Radiol. (2009).
[PubMed]

Boccacci, P.

M. Bertero and P. Boccacci, Inverse Problems in Imaging (Institute of Physics Publishing, Bristol, UK, 1998)

Bochud, F. O.

Boone, J. M.

K. G. Metheany, C. K. Abbey, N. Packard, and J. M. Boone, “Characterizing anatomical variability in breast CT images,” Med. Phys. 35, 4685–4694 (2008).
[PubMed]

C. K. Abbey and J. M. Boone, “An ideal observer for a model of x-ray imaging in breast parenchymal tissue,” (E.A. Krupinski, Ed.): IWDM 2008, LNCS5116, 393–400 (2008).

Burgess, A. E.

Burvall, A.

Catullo, V. J.

W. F. Good, G. S. Abrams, V. J. Catullo, D. M. Chough, M. A. Ganott, C. M. Hakim, and D. Gur, “Digital breast tomosynthesis: a pilot observer study,” Am. J. Radiology 190, 865–869 (2008).

Chan, H.-P.

Y. Zhang, H.-P. Chan, B. Sahiner, J. Wei, M. M. Goodsitt, L. M. Hadjiiiski, J. Ge, and C. Zhou, “A comparative study of limited-angle cone-beam reconstruction methods for breast tomosynthesis,” Med. Phys. 33, 3781–3795 (2006).
[PubMed]

Chawla, A. S.

A. S. Chawla, J. Y. Lo, J. A. Baker, and E. Samei, “Optimized image acquisition for breast tomosynthesis in projection and reconstruction space,” Med. Phys. 36, 4859–4869 (2009).
[PubMed]

Chiu, M. Y.

Chou, C.

Chough, D. M.

W. F. Good, G. S. Abrams, V. J. Catullo, D. M. Chough, M. A. Ganott, C. M. Hakim, and D. Gur, “Digital breast tomosynthesis: a pilot observer study,” Am. J. Radiology 190, 865–869 (2008).

Dainty, C.

di Maggio, C.

G. Gennaro, A. Toledano, C. di Maggio, E. Baldan, E. Bezzon, M. La Grassa, L. Pescarini, I. Polico, A. Proietti, A. Toffoli, and P. C. Muzzio, “Digital breast tomosynthesis versus digital mammography: a clinical performance study,” Eur. Radiol. (2009).
[PubMed]

Dobbins, J. T.

J. T. Dobbins, “Tomosynthesis: at translational crossroads,” Med. Phys. 36, 1956–1967 (2009).
[PubMed]

J. T. Dobbins and D. J. Godfrey, “Digital x-ray tomosynthesis: current state of the art and clinical potential,” Phys. Med. Biol. 48, R65–R106 (2003).
[PubMed]

Eckstein, M. P.

Ganott, M. A.

W. F. Good, G. S. Abrams, V. J. Catullo, D. M. Chough, M. A. Ganott, C. M. Hakim, and D. Gur, “Digital breast tomosynthesis: a pilot observer study,” Am. J. Radiology 190, 865–869 (2008).

Ge, J.

Y. Zhang, H.-P. Chan, B. Sahiner, J. Wei, M. M. Goodsitt, L. M. Hadjiiiski, J. Ge, and C. Zhou, “A comparative study of limited-angle cone-beam reconstruction methods for breast tomosynthesis,” Med. Phys. 33, 3781–3795 (2006).
[PubMed]

Gennaro, G.

G. Gennaro, A. Toledano, C. di Maggio, E. Baldan, E. Bezzon, M. La Grassa, L. Pescarini, I. Polico, A. Proietti, A. Toffoli, and P. C. Muzzio, “Digital breast tomosynthesis versus digital mammography: a clinical performance study,” Eur. Radiol. (2009).
[PubMed]

Gindi, G. R.

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, R65–R106 (2003).
[PubMed]

Good, W. F.

W. F. Good, G. S. Abrams, V. J. Catullo, D. M. Chough, M. A. Ganott, C. M. Hakim, and D. Gur, “Digital breast tomosynthesis: a pilot observer study,” Am. J. Radiology 190, 865–869 (2008).

Goodsitt, M. M.

Y. Zhang, H.-P. Chan, B. Sahiner, J. Wei, M. M. Goodsitt, L. M. Hadjiiiski, J. Ge, and C. Zhou, “A comparative study of limited-angle cone-beam reconstruction methods for breast tomosynthesis,” Med. Phys. 33, 3781–3795 (2006).
[PubMed]

Gur, D.

W. F. Good, G. S. Abrams, V. J. Catullo, D. M. Chough, M. A. Ganott, C. M. Hakim, and D. Gur, “Digital breast tomosynthesis: a pilot observer study,” Am. J. Radiology 190, 865–869 (2008).

Hadjiiiski, L. M.

Y. Zhang, H.-P. Chan, B. Sahiner, J. Wei, M. M. Goodsitt, L. M. Hadjiiiski, J. Ge, and C. Zhou, “A comparative study of limited-angle cone-beam reconstruction methods for breast tomosynthesis,” Med. Phys. 33, 3781–3795 (2006).
[PubMed]

Hakim, C. M.

W. F. Good, G. S. Abrams, V. J. Catullo, D. M. Chough, M. A. Ganott, C. M. Hakim, and D. Gur, “Digital breast tomosynthesis: a pilot observer study,” Am. J. Radiology 190, 865–869 (2008).

Ikeda, D. M.

I. Andersson, D. M. Ikeda, S. Zackrisson, M. Ruschin, T. Svahn, P. Timberg, and A. Tingberg, “Breast tomosynthesis and digital mammography: a comparison of breast cancer visibility and BIRADS classification in a population of cancers with subtle mammographic findings,” Eur. Radiol. 18, 2817–2825 (2008).
[PubMed]

Kogel, C. A.

S. P. Poplack, T. D. Tosteson, C. A. Kogel, and H. M. Nagy, “Digital breast tomosyntheis: Initial experiance in 98 women with abnormal digital screening mammography,” Am. J. Radiology 189, 616–623 (2007).

Kopans, D. B.

T. Wu, R. H. Moore, E. A. Rafferty, and D. B. Kopans, “A comparison of reconstruction algorithms for breast tomosynthesis,” Med. Phys. 31, 2636–2647 (2004).
[PubMed]

La Grassa, M.

G. Gennaro, A. Toledano, C. di Maggio, E. Baldan, E. Bezzon, M. La Grassa, L. Pescarini, I. Polico, A. Proietti, A. Toffoli, and P. C. Muzzio, “Digital breast tomosynthesis versus digital mammography: a clinical performance study,” Eur. Radiol. (2009).
[PubMed]

Lanczos, C.

C. Lanczos, Linear differential operators (Van Nostrand, London, 1961).

Liseno, A.

Lo, J. Y.

A. S. Chawla, J. Y. Lo, J. A. Baker, and E. Samei, “Optimized image acquisition for breast tomosynthesis in projection and reconstruction space,” Med. Phys. 36, 4859–4869 (2009).
[PubMed]

Maidment, A. D. A.

C. Zhang, P. R. Bakic, and A. D. A. Maidment, “Development of an anthropomorphic breast software phantom based on region growing algorithm,” Proc. SPIE 6918, 69180V (2008).

Manzhirov, A. V.

A. D. Polianin and A. V. Manzhirov, Handbook of integral equations (CRC Press, Florida, 1998) chapter 11.2.

Metheany, K. G.

K. G. Metheany, C. K. Abbey, N. Packard, and J. M. Boone, “Characterizing anatomical variability in breast CT images,” Med. Phys. 35, 4685–4694 (2008).
[PubMed]

Moore, R. H.

T. Wu, R. H. Moore, E. A. Rafferty, and D. B. Kopans, “A comparison of reconstruction algorithms for breast tomosynthesis,” Med. Phys. 31, 2636–2647 (2004).
[PubMed]

Muzzio, P. C.

G. Gennaro, A. Toledano, C. di Maggio, E. Baldan, E. Bezzon, M. La Grassa, L. Pescarini, I. Polico, A. Proietti, A. Toffoli, and P. C. Muzzio, “Digital breast tomosynthesis versus digital mammography: a clinical performance study,” Eur. Radiol. (2009).
[PubMed]

Myers, K. J.

S. Park, J. M. Witten, and K. J. Myers, “Singular vectors of a linear imaging system as efficient channels for the bayesian ideal observer,” IEEE Trans. Med. Imaging 28, 657–668 (2009).
[PubMed]

A. Burvall, H. H. Barrett, C. Dainty, and K. J. Myers, “Singular-value decomposition for through-focus imaging systems,” J. Opt. Soc. Am. A 23, 2440–2448 (2006).

H. H. Barrett, J. Yao, J. P. Rolland, and K. J. Myers, “Model observers for assessment of image quality,” Proc. Natl. Acad. Sci. USA 90, 9758–9765 (1993).
[PubMed]

H. H. Barrett and K. J. Myers, Foundations of Image Science (John Wiley, Hoboken, New Jersey, 2004).

Nagy, H. M.

S. P. Poplack, T. D. Tosteson, C. A. Kogel, and H. M. Nagy, “Digital breast tomosyntheis: Initial experiance in 98 women with abnormal digital screening mammography,” Am. J. Radiology 189, 616–623 (2007).

Niklason, L. T.

L. T. Niklason, “Digital tomosynthesis in breast imaging,” Radiology 1997, 399–406 (1997).

Nishikawa, R. M.

I. Reiser and R. M. Nishikawa, “Task-based assessment of breast tomosynthesis: Effects of acquisition parameters and quantum noise,” Med. Phys. 37, 1591–1600 (2010).
[PubMed]

Packard, N.

K. G. Metheany, C. K. Abbey, N. Packard, and J. M. Boone, “Characterizing anatomical variability in breast CT images,” Med. Phys. 35, 4685–4694 (2008).
[PubMed]

Park, S.

S. Park, J. M. Witten, and K. J. Myers, “Singular vectors of a linear imaging system as efficient channels for the bayesian ideal observer,” IEEE Trans. Med. Imaging 28, 657–668 (2009).
[PubMed]

Pescarini, L.

G. Gennaro, A. Toledano, C. di Maggio, E. Baldan, E. Bezzon, M. La Grassa, L. Pescarini, I. Polico, A. Proietti, A. Toffoli, and P. C. Muzzio, “Digital breast tomosynthesis versus digital mammography: a clinical performance study,” Eur. Radiol. (2009).
[PubMed]

Pierri, R.

Polianin, A. D.

A. D. Polianin and A. V. Manzhirov, Handbook of integral equations (CRC Press, Florida, 1998) chapter 11.2.

Polico, I.

G. Gennaro, A. Toledano, C. di Maggio, E. Baldan, E. Bezzon, M. La Grassa, L. Pescarini, I. Polico, A. Proietti, A. Toffoli, and P. C. Muzzio, “Digital breast tomosynthesis versus digital mammography: a clinical performance study,” Eur. Radiol. (2009).
[PubMed]

Poplack, S. P.

S. P. Poplack, T. D. Tosteson, C. A. Kogel, and H. M. Nagy, “Digital breast tomosyntheis: Initial experiance in 98 women with abnormal digital screening mammography,” Am. J. Radiology 189, 616–623 (2007).

Proietti, A.

G. Gennaro, A. Toledano, C. di Maggio, E. Baldan, E. Bezzon, M. La Grassa, L. Pescarini, I. Polico, A. Proietti, A. Toffoli, and P. C. Muzzio, “Digital breast tomosynthesis versus digital mammography: a clinical performance study,” Eur. Radiol. (2009).
[PubMed]

Rafferty, E. A.

T. Wu, R. H. Moore, E. A. Rafferty, and D. B. Kopans, “A comparison of reconstruction algorithms for breast tomosynthesis,” Med. Phys. 31, 2636–2647 (2004).
[PubMed]

Reiser, I.

I. Reiser and R. M. Nishikawa, “Task-based assessment of breast tomosynthesis: Effects of acquisition parameters and quantum noise,” Med. Phys. 37, 1591–1600 (2010).
[PubMed]

Rolland, J. P.

H. H. Barrett, J. Yao, J. P. Rolland, and K. J. Myers, “Model observers for assessment of image quality,” Proc. Natl. Acad. Sci. USA 90, 9758–9765 (1993).
[PubMed]

Roney, T. J.

H. H. Barrett, J. N. Aarsvold, and T. J. Roney, “Null functions and eigenfunctions: tools for the analysis of imaging systems,” Lect. Notes. Comput. Sci. 11, 211–226 (1991).

Ruschin, M.

I. Andersson, D. M. Ikeda, S. Zackrisson, M. Ruschin, T. Svahn, P. Timberg, and A. Tingberg, “Breast tomosynthesis and digital mammography: a comparison of breast cancer visibility and BIRADS classification in a population of cancers with subtle mammographic findings,” Eur. Radiol. 18, 2817–2825 (2008).
[PubMed]

Sahiner, B.

Y. Zhang, H.-P. Chan, B. Sahiner, J. Wei, M. M. Goodsitt, L. M. Hadjiiiski, J. Ge, and C. Zhou, “A comparative study of limited-angle cone-beam reconstruction methods for breast tomosynthesis,” Med. Phys. 33, 3781–3795 (2006).
[PubMed]

Samei, E.

A. S. Chawla, J. Y. Lo, J. A. Baker, and E. Samei, “Optimized image acquisition for breast tomosynthesis in projection and reconstruction space,” Med. Phys. 36, 4859–4869 (2009).
[PubMed]

Simpson, R. G.

Soldovieri, F.

Solimene, R.

Svahn, T.

I. Andersson, D. M. Ikeda, S. Zackrisson, M. Ruschin, T. Svahn, P. Timberg, and A. Tingberg, “Breast tomosynthesis and digital mammography: a comparison of breast cancer visibility and BIRADS classification in a population of cancers with subtle mammographic findings,” Eur. Radiol. 18, 2817–2825 (2008).
[PubMed]

Timberg, P.

I. Andersson, D. M. Ikeda, S. Zackrisson, M. Ruschin, T. Svahn, P. Timberg, and A. Tingberg, “Breast tomosynthesis and digital mammography: a comparison of breast cancer visibility and BIRADS classification in a population of cancers with subtle mammographic findings,” Eur. Radiol. 18, 2817–2825 (2008).
[PubMed]

Tingberg, A.

I. Andersson, D. M. Ikeda, S. Zackrisson, M. Ruschin, T. Svahn, P. Timberg, and A. Tingberg, “Breast tomosynthesis and digital mammography: a comparison of breast cancer visibility and BIRADS classification in a population of cancers with subtle mammographic findings,” Eur. Radiol. 18, 2817–2825 (2008).
[PubMed]

Toffoli, A.

G. Gennaro, A. Toledano, C. di Maggio, E. Baldan, E. Bezzon, M. La Grassa, L. Pescarini, I. Polico, A. Proietti, A. Toffoli, and P. C. Muzzio, “Digital breast tomosynthesis versus digital mammography: a clinical performance study,” Eur. Radiol. (2009).
[PubMed]

Toledano, A.

G. Gennaro, A. Toledano, C. di Maggio, E. Baldan, E. Bezzon, M. La Grassa, L. Pescarini, I. Polico, A. Proietti, A. Toffoli, and P. C. Muzzio, “Digital breast tomosynthesis versus digital mammography: a clinical performance study,” Eur. Radiol. (2009).
[PubMed]

Tosteson, T. D.

S. P. Poplack, T. D. Tosteson, C. A. Kogel, and H. M. Nagy, “Digital breast tomosyntheis: Initial experiance in 98 women with abnormal digital screening mammography,” Am. J. Radiology 189, 616–623 (2007).

Wei, J.

Y. Zhang, H.-P. Chan, B. Sahiner, J. Wei, M. M. Goodsitt, L. M. Hadjiiiski, J. Ge, and C. Zhou, “A comparative study of limited-angle cone-beam reconstruction methods for breast tomosynthesis,” Med. Phys. 33, 3781–3795 (2006).
[PubMed]

Witten, J. M.

S. Park, J. M. Witten, and K. J. Myers, “Singular vectors of a linear imaging system as efficient channels for the bayesian ideal observer,” IEEE Trans. Med. Imaging 28, 657–668 (2009).
[PubMed]

Wu, T.

T. Wu, R. H. Moore, E. A. Rafferty, and D. B. Kopans, “A comparison of reconstruction algorithms for breast tomosynthesis,” Med. Phys. 31, 2636–2647 (2004).
[PubMed]

Yao, J.

H. H. Barrett, J. Yao, J. P. Rolland, and K. J. Myers, “Model observers for assessment of image quality,” Proc. Natl. Acad. Sci. USA 90, 9758–9765 (1993).
[PubMed]

J. Yao and H. H. Barrett, “Predicting human performance by a channelized Hotelling observer,” Proc. SPIE 1768, 161–168 (1992).

Zackrisson, S.

I. Andersson, D. M. Ikeda, S. Zackrisson, M. Ruschin, T. Svahn, P. Timberg, and A. Tingberg, “Breast tomosynthesis and digital mammography: a comparison of breast cancer visibility and BIRADS classification in a population of cancers with subtle mammographic findings,” Eur. Radiol. 18, 2817–2825 (2008).
[PubMed]

Zhang, C.

C. Zhang, P. R. Bakic, and A. D. A. Maidment, “Development of an anthropomorphic breast software phantom based on region growing algorithm,” Proc. SPIE 6918, 69180V (2008).

Zhang, Y.

Y. Zhang, H.-P. Chan, B. Sahiner, J. Wei, M. M. Goodsitt, L. M. Hadjiiiski, J. Ge, and C. Zhou, “A comparative study of limited-angle cone-beam reconstruction methods for breast tomosynthesis,” Med. Phys. 33, 3781–3795 (2006).
[PubMed]

Zhou, C.

Y. Zhang, H.-P. Chan, B. Sahiner, J. Wei, M. M. Goodsitt, L. M. Hadjiiiski, J. Ge, and C. Zhou, “A comparative study of limited-angle cone-beam reconstruction methods for breast tomosynthesis,” Med. Phys. 33, 3781–3795 (2006).
[PubMed]

Am. J. Radiology (2)

W. F. Good, G. S. Abrams, V. J. Catullo, D. M. Chough, M. A. Ganott, C. M. Hakim, and D. Gur, “Digital breast tomosynthesis: a pilot observer study,” Am. J. Radiology 190, 865–869 (2008).

S. P. Poplack, T. D. Tosteson, C. A. Kogel, and H. M. Nagy, “Digital breast tomosyntheis: Initial experiance in 98 women with abnormal digital screening mammography,” Am. J. Radiology 189, 616–623 (2007).

Eur. Radiol. (2)

G. Gennaro, A. Toledano, C. di Maggio, E. Baldan, E. Bezzon, M. La Grassa, L. Pescarini, I. Polico, A. Proietti, A. Toffoli, and P. C. Muzzio, “Digital breast tomosynthesis versus digital mammography: a clinical performance study,” Eur. Radiol. (2009).
[PubMed]

I. Andersson, D. M. Ikeda, S. Zackrisson, M. Ruschin, T. Svahn, P. Timberg, and A. Tingberg, “Breast tomosynthesis and digital mammography: a comparison of breast cancer visibility and BIRADS classification in a population of cancers with subtle mammographic findings,” Eur. Radiol. 18, 2817–2825 (2008).
[PubMed]

IEEE Trans. Med. Imaging (1)

S. Park, J. M. Witten, and K. J. Myers, “Singular vectors of a linear imaging system as efficient channels for the bayesian ideal observer,” IEEE Trans. Med. Imaging 28, 657–668 (2009).
[PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Lect. Notes. Comput. Sci. (1)

H. H. Barrett, J. N. Aarsvold, and T. J. Roney, “Null functions and eigenfunctions: tools for the analysis of imaging systems,” Lect. Notes. Comput. Sci. 11, 211–226 (1991).

Med. Phys. (6)

J. T. Dobbins, “Tomosynthesis: at translational crossroads,” Med. Phys. 36, 1956–1967 (2009).
[PubMed]

A. S. Chawla, J. Y. Lo, J. A. Baker, and E. Samei, “Optimized image acquisition for breast tomosynthesis in projection and reconstruction space,” Med. Phys. 36, 4859–4869 (2009).
[PubMed]

T. Wu, R. H. Moore, E. A. Rafferty, and D. B. Kopans, “A comparison of reconstruction algorithms for breast tomosynthesis,” Med. Phys. 31, 2636–2647 (2004).
[PubMed]

Y. Zhang, H.-P. Chan, B. Sahiner, J. Wei, M. M. Goodsitt, L. M. Hadjiiiski, J. Ge, and C. Zhou, “A comparative study of limited-angle cone-beam reconstruction methods for breast tomosynthesis,” Med. Phys. 33, 3781–3795 (2006).
[PubMed]

I. Reiser and R. M. Nishikawa, “Task-based assessment of breast tomosynthesis: Effects of acquisition parameters and quantum noise,” Med. Phys. 37, 1591–1600 (2010).
[PubMed]

K. G. Metheany, C. K. Abbey, N. Packard, and J. M. Boone, “Characterizing anatomical variability in breast CT images,” Med. Phys. 35, 4685–4694 (2008).
[PubMed]

Opt. Express (1)

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, R65–R106 (2003).
[PubMed]

Proc. Natl. Acad. Sci. USA (1)

H. H. Barrett, J. Yao, J. P. Rolland, and K. J. Myers, “Model observers for assessment of image quality,” Proc. Natl. Acad. Sci. USA 90, 9758–9765 (1993).
[PubMed]

Proc. SPIE (2)

C. Zhang, P. R. Bakic, and A. D. A. Maidment, “Development of an anthropomorphic breast software phantom based on region growing algorithm,” Proc. SPIE 6918, 69180V (2008).

J. Yao and H. H. Barrett, “Predicting human performance by a channelized Hotelling observer,” Proc. SPIE 1768, 161–168 (1992).

Radiology (1)

L. T. Niklason, “Digital tomosynthesis in breast imaging,” Radiology 1997, 399–406 (1997).

Other (5)

H. H. Barrett and K. J. Myers, Foundations of Image Science (John Wiley, Hoboken, New Jersey, 2004).

M. Bertero and P. Boccacci, Inverse Problems in Imaging (Institute of Physics Publishing, Bristol, UK, 1998)

A. D. Polianin and A. V. Manzhirov, Handbook of integral equations (CRC Press, Florida, 1998) chapter 11.2.

C. Lanczos, Linear differential operators (Van Nostrand, London, 1961).

C. K. Abbey and J. M. Boone, “An ideal observer for a model of x-ray imaging in breast parenchymal tissue,” (E.A. Krupinski, Ed.): IWDM 2008, LNCS5116, 393–400 (2008).

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Figures (8)

Fig. 1
Fig. 1

Geometry of the considered tomographic system. The different source positions are χm , and the screen is placed along the z axis.

Fig. 2
Fig. 2

The change of variables moves the source plane to minus infinity. Rays originating from two source positions, one on-axis and one off-axis, are shown. The object in this figure is distorted compared to the object in Fig. 1, but the image is not.

Fig. 3
Fig. 3

Eigenvalues μρx,j for j ranging from 1 to 11.

Fig. 4
Fig. 4

Absolute values of the singular functions (a) U 1(ρx,z̃), (b) U 2(ρx,z̃), (c) U 6(ρx,z̃), and (d) U 11(ρx,z̃).

Fig. 5
Fig. 5

Example object f ̃(, ), including a designer nodule and a 3D clustered lumpy background. (a) Section through the object at = −60mm, or z = −50mm. (b) Section through the object at = = 0. Both sections go through the center of the designer nodule.

Fig. 6
Fig. 6

Measurement component of the object in Fig. 5. (a) Section through the measurement component at = −60mm, or z = −50mm. (b) Section through the measurement component at = y = 0. Both sections go through the center of the designer nodule.

Fig. 7
Fig. 7

(a) Image or projection of the measurement component in Fig. 6. (b) Image or projection of the object in Fig. 5. Both are calculated through direct numerical propagation of the object and measurement component respectively, for the source placed on the z-axis.

Fig. 8
Fig. 8

Difference between the projection of the measurement component (see Fig. 7(a)) and the projection of the object (see Fig. 7(b)). The maximum absolute value is around 3 × 10−6 compared to the maximum of the projections, which is around 2 × 10−4. This gives an error of roughly 1%.

Equations (39)

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I m ( r d ) = A cos θ | r 1 r 0 | 2 exp [ 0 | r 1 r 0 | d l f ( r 1 r 1 r 0 | r 1 r 0 | l ) ] ,
log ( I m ( r d ) | r 1 r 0 | 2 A cos θ ) = | r 1 r 0 | s 0 s d z f ( r 0 + ( r 0 r 1 ) z s ) .
log [ 1 A s ( | r d r m | 2 + s 2 ) 3 / 2 I m ( r d ) ] = 0 s d z f ( r d + ( r d r m ) z s , z )
g m ( r d ) = s ( s 2 + | r d r m | 2 ) 1 / 2 log [ 1 A s ( s 2 + | r d r m | 2 ) 3 / 2 I m ( r d ) ] .
g m ( r d ) = [ H f ] m ( r d ) = z 1 z 2 d z d 2 r b f ( r , z ) f ( r , z ) h m ( r , r d , z ) ,
[ H g ] ( r , z ) = m = 1 M d 2 r d b g ( r d ) g m ( r d ) h m ( r , r d , z ) ,
h m ( r , r d , z ) = δ ( r r d ( r d r m ) z s ) .
r = ( x , y ) = ( s s + z x , s s + z y ) , z = s s + z z
r = ( x , y ) = ( s s z x , s s z y ) , z = s s z z .
h m ( r r d , z ) = ( s z s ) 2 δ ( r r d + z s r m ) ,
| ( x , y , z ) ( x , y , z ) | = s 4 ( s z ) 4
g m ( r d ) = [ H f ] m ( r d ) = z 1 z 2 d z d 2 r s 4 ( s z ) 4 b f ( r , z ) f ( r , z ) h m ( r r d , z ) ,
[ H g ] ( r , z ) = m = 1 M d 2 r d b g ( r d ) g m ( r d ) h m ( r r d , z ) ,
f 1 ( r , z ) , f 2 ( r , z ) obj = d 2 r z 1 z 2 d z b f ( r , z ) f 1 ( r , z ) f 2 ( r , z ) s 4 ( s z ) 4
g 1 ( r d ) , g 2 ( r d ) im = m = 1 M d 2 r d b g ( r d ) g 1 m ( r d ) g 2 m ( r d ) .
H f , g im = f , H g obj .
[ H , H g ] m ( r d ) = m = 1 M d 2 r d b g ( r d ) g m ( r d ) k m m ( r d , r d )
k m m ( r d , r d ) = z 1 z 2 d z d 2 r b f ( r , z ) s 4 ( s z ) 4 h m ( r r d , z ) h m ( r r d , z ) .
[ H H f ] ( r , z ) = z 1 z 2 d z d 2 r b f ( z , r ) f ( z , r ) p ( r , r , z , z )
p ( r , r , z , z ) = s 4 ( s z ) 4 m = 1 M d 2 r d b g ( r d ) h m ( r r d , z ) h m ( r r d , z ) .
k m m ( r d r d ) = z 1 z 2 d z δ ( r d r d z s ( r m r m ) ) .
v ρ , j ( r d ) = V j ( ρ ) exp ( 2 π i ρ r d )
K ( ρ ) V j ( ρ ) = μ ρ , j V j ( ρ )
k m m = d 2 r d k m m ( r d ) exp ( 2 π i ρ r d ) .
k m m = z 1 z 2 d z exp ( 2 π i ρ ( r m r m ) z s ) ,
K m m = z 2 z 1
K m m = i s 2 π ρ ( r m r m ) { exp [ 2 π i ρ ( r m r m ) z 2 s ] exp [ 2 π i ρ ( r m r m ) z 1 s ] }
p ( r r , z , z ) = ( s z s z ) 2 m 1 M δ ( r r + r m z z s ) ,
z 1 z 2 d z ( s z s z ) 2 U j ( ρ , z ) m = 1 M exp ( 2 π i ρ r m ( z z ) 1 s ) = μ ρ , j U j ( ρ , z )
u j , ρ ( r , z ) = U j ( ρ , z ) exp ( 2 π i ρ r ) .
U ^ j ( ρ , z ) = z 1 z 2 d z U ^ ( ρ , z ) m = 1 M exp ( 2 π i z s ρ r m ) exp ( 2 π i z s ρ r m ) .
[ H v ρ , j ] = μ ρ , j u ρ , j ( r , z ) .
u ρ , j ( r , z ) = exp ( 2 π i ρ r ) U j ( ρ , z )
U j ( ρ , z ) = 1 μ ρ , j ( s z s ) 2 m = 1 M [ V j ( ρ ) ] m exp ( 2 π i z s ρ r m ) .
g m ( r d ) = A rect ( 2 | r d | R ) ( 1 | r d | 2 R 2 ) v
f ( r ) = A 3 4 R rect ( 2 | r | R ) ( 1 | r | 2 R 2 ) ,
g ( r d ) = k = 1 K n = 1 N k b ( 1 a k n ( r d r k r k n ) , R θ k n )
f meas ( r , z ) = d 2 ρ j = 1 M A j ( ρ ) U j ( ρ , z ) exp 2 π i ρ r ,
A j ( ρ ) = z 1 z 2 d z F ( ρ , z ) U j ( ρ , z ) s 4 ( s z ) 4

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