Abstract

Uniformly redundant array coded apertures have proven to be useful in the design of collimators for x-ray astronomy. They were initially expected to be equally successful in single-photon emission computed tomography (SPECT). Unfortunately, the SPECT images produced by this collimator contain artifacts, which mask the true picture and can lead to false diagnosis. Monte Carlo simulation has shown that the formation of a composite image will significantly reduce these artifacts. A simulation of a tumor in a compressed breast phantom has produced a composite image, which clearly indicates the presence of a 5 mm × 5 mm × 5 mm tumor with a 6:1 intensity ratio relative to the background tissue.

© 2002 Optical Society of America

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References

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  1. E. E. Fenimore, T. M. Cannon, “Coded aperture with uniformly redundant arrays,” Appl. Opt. 17, 337–347 (1978).
    [CrossRef] [PubMed]
  2. E. E. Fenimore, T. M. Cannon, “Tomographical imaging using uniformly redundant arrays,” Appl. Opt. 18, 1052–1057 (1979).
    [CrossRef] [PubMed]
  3. J. Maublant, M. de Latour, D. Mestas, A. Clemenson, S. Charrier, V. Feillel, G. LeBouedec, P. Kaufmann, J. Dauplat, A. Vegre, “Technetium-99m-sestamibi uptake in breast tumor and associated lymph nodes,” J. Nucl. Med. 37, 922–925 (1996).
    [PubMed]
  4. P. Dunphy, M. McConnell, A. Owens, E. Chupp, D. Forrest, J. Googins, “A balloon-borne coded aperture telescope for low-energy gamma-ray astronomy,” Nucl. Instrum. Methods Phys. Res. A 274, 362–379 (1989).
    [CrossRef]
  5. F. J. MacWilliams, N. J. Sloane, “Pseudo-random sequences and arrays,” Proc. IEEE 64, 1715–1728 (1976).
    [CrossRef]
  6. L. Bomer, M. Antweiler, “Optimizing the aperiodic merit factor of binary arrays,” Signal Process. 30, 1–13 (1993).
    [CrossRef]
  7. H. Wang, C. Scarfone, K. L. Greer, R. E. Coleman, R. J. Jaszczak, “Prone breast tumor imaging using vertical axis-of-rotation (VAOR) SPECT systems: an initial study,” IEEE Trans. Nucl. Sci. 44, 1271–1275 (1997).
    [CrossRef]
  8. M. F. Smith, R. J. Jaszczak, “A rotating parallel hole collimator for high resolution imaging of medium energy radionuclides,” IEEE Trans. Nucl. Sci. 45, 2102–2112 (1998).
    [CrossRef]
  9. W. R. Cook, M. Finger, T. A. Prince, E. C. Stone, “Gamma ray imaging with a rotating hexagonal uniformly redundant array,” IEEE Trans. Nucl. Sci. 31, 771–775 (1984).
    [CrossRef]

1998

M. F. Smith, R. J. Jaszczak, “A rotating parallel hole collimator for high resolution imaging of medium energy radionuclides,” IEEE Trans. Nucl. Sci. 45, 2102–2112 (1998).
[CrossRef]

1997

H. Wang, C. Scarfone, K. L. Greer, R. E. Coleman, R. J. Jaszczak, “Prone breast tumor imaging using vertical axis-of-rotation (VAOR) SPECT systems: an initial study,” IEEE Trans. Nucl. Sci. 44, 1271–1275 (1997).
[CrossRef]

1996

J. Maublant, M. de Latour, D. Mestas, A. Clemenson, S. Charrier, V. Feillel, G. LeBouedec, P. Kaufmann, J. Dauplat, A. Vegre, “Technetium-99m-sestamibi uptake in breast tumor and associated lymph nodes,” J. Nucl. Med. 37, 922–925 (1996).
[PubMed]

1993

L. Bomer, M. Antweiler, “Optimizing the aperiodic merit factor of binary arrays,” Signal Process. 30, 1–13 (1993).
[CrossRef]

1989

P. Dunphy, M. McConnell, A. Owens, E. Chupp, D. Forrest, J. Googins, “A balloon-borne coded aperture telescope for low-energy gamma-ray astronomy,” Nucl. Instrum. Methods Phys. Res. A 274, 362–379 (1989).
[CrossRef]

1984

W. R. Cook, M. Finger, T. A. Prince, E. C. Stone, “Gamma ray imaging with a rotating hexagonal uniformly redundant array,” IEEE Trans. Nucl. Sci. 31, 771–775 (1984).
[CrossRef]

1979

1978

1976

F. J. MacWilliams, N. J. Sloane, “Pseudo-random sequences and arrays,” Proc. IEEE 64, 1715–1728 (1976).
[CrossRef]

Antweiler, M.

L. Bomer, M. Antweiler, “Optimizing the aperiodic merit factor of binary arrays,” Signal Process. 30, 1–13 (1993).
[CrossRef]

Bomer, L.

L. Bomer, M. Antweiler, “Optimizing the aperiodic merit factor of binary arrays,” Signal Process. 30, 1–13 (1993).
[CrossRef]

Cannon, T. M.

Charrier, S.

J. Maublant, M. de Latour, D. Mestas, A. Clemenson, S. Charrier, V. Feillel, G. LeBouedec, P. Kaufmann, J. Dauplat, A. Vegre, “Technetium-99m-sestamibi uptake in breast tumor and associated lymph nodes,” J. Nucl. Med. 37, 922–925 (1996).
[PubMed]

Chupp, E.

P. Dunphy, M. McConnell, A. Owens, E. Chupp, D. Forrest, J. Googins, “A balloon-borne coded aperture telescope for low-energy gamma-ray astronomy,” Nucl. Instrum. Methods Phys. Res. A 274, 362–379 (1989).
[CrossRef]

Clemenson, A.

J. Maublant, M. de Latour, D. Mestas, A. Clemenson, S. Charrier, V. Feillel, G. LeBouedec, P. Kaufmann, J. Dauplat, A. Vegre, “Technetium-99m-sestamibi uptake in breast tumor and associated lymph nodes,” J. Nucl. Med. 37, 922–925 (1996).
[PubMed]

Coleman, R. E.

H. Wang, C. Scarfone, K. L. Greer, R. E. Coleman, R. J. Jaszczak, “Prone breast tumor imaging using vertical axis-of-rotation (VAOR) SPECT systems: an initial study,” IEEE Trans. Nucl. Sci. 44, 1271–1275 (1997).
[CrossRef]

Cook, W. R.

W. R. Cook, M. Finger, T. A. Prince, E. C. Stone, “Gamma ray imaging with a rotating hexagonal uniformly redundant array,” IEEE Trans. Nucl. Sci. 31, 771–775 (1984).
[CrossRef]

Dauplat, J.

J. Maublant, M. de Latour, D. Mestas, A. Clemenson, S. Charrier, V. Feillel, G. LeBouedec, P. Kaufmann, J. Dauplat, A. Vegre, “Technetium-99m-sestamibi uptake in breast tumor and associated lymph nodes,” J. Nucl. Med. 37, 922–925 (1996).
[PubMed]

Dunphy, P.

P. Dunphy, M. McConnell, A. Owens, E. Chupp, D. Forrest, J. Googins, “A balloon-borne coded aperture telescope for low-energy gamma-ray astronomy,” Nucl. Instrum. Methods Phys. Res. A 274, 362–379 (1989).
[CrossRef]

Feillel, V.

J. Maublant, M. de Latour, D. Mestas, A. Clemenson, S. Charrier, V. Feillel, G. LeBouedec, P. Kaufmann, J. Dauplat, A. Vegre, “Technetium-99m-sestamibi uptake in breast tumor and associated lymph nodes,” J. Nucl. Med. 37, 922–925 (1996).
[PubMed]

Fenimore, E. E.

Finger, M.

W. R. Cook, M. Finger, T. A. Prince, E. C. Stone, “Gamma ray imaging with a rotating hexagonal uniformly redundant array,” IEEE Trans. Nucl. Sci. 31, 771–775 (1984).
[CrossRef]

Forrest, D.

P. Dunphy, M. McConnell, A. Owens, E. Chupp, D. Forrest, J. Googins, “A balloon-borne coded aperture telescope for low-energy gamma-ray astronomy,” Nucl. Instrum. Methods Phys. Res. A 274, 362–379 (1989).
[CrossRef]

Googins, J.

P. Dunphy, M. McConnell, A. Owens, E. Chupp, D. Forrest, J. Googins, “A balloon-borne coded aperture telescope for low-energy gamma-ray astronomy,” Nucl. Instrum. Methods Phys. Res. A 274, 362–379 (1989).
[CrossRef]

Greer, K. L.

H. Wang, C. Scarfone, K. L. Greer, R. E. Coleman, R. J. Jaszczak, “Prone breast tumor imaging using vertical axis-of-rotation (VAOR) SPECT systems: an initial study,” IEEE Trans. Nucl. Sci. 44, 1271–1275 (1997).
[CrossRef]

Jaszczak, R. J.

M. F. Smith, R. J. Jaszczak, “A rotating parallel hole collimator for high resolution imaging of medium energy radionuclides,” IEEE Trans. Nucl. Sci. 45, 2102–2112 (1998).
[CrossRef]

H. Wang, C. Scarfone, K. L. Greer, R. E. Coleman, R. J. Jaszczak, “Prone breast tumor imaging using vertical axis-of-rotation (VAOR) SPECT systems: an initial study,” IEEE Trans. Nucl. Sci. 44, 1271–1275 (1997).
[CrossRef]

Kaufmann, P.

J. Maublant, M. de Latour, D. Mestas, A. Clemenson, S. Charrier, V. Feillel, G. LeBouedec, P. Kaufmann, J. Dauplat, A. Vegre, “Technetium-99m-sestamibi uptake in breast tumor and associated lymph nodes,” J. Nucl. Med. 37, 922–925 (1996).
[PubMed]

Latour, M. de

J. Maublant, M. de Latour, D. Mestas, A. Clemenson, S. Charrier, V. Feillel, G. LeBouedec, P. Kaufmann, J. Dauplat, A. Vegre, “Technetium-99m-sestamibi uptake in breast tumor and associated lymph nodes,” J. Nucl. Med. 37, 922–925 (1996).
[PubMed]

LeBouedec, G.

J. Maublant, M. de Latour, D. Mestas, A. Clemenson, S. Charrier, V. Feillel, G. LeBouedec, P. Kaufmann, J. Dauplat, A. Vegre, “Technetium-99m-sestamibi uptake in breast tumor and associated lymph nodes,” J. Nucl. Med. 37, 922–925 (1996).
[PubMed]

MacWilliams, F. J.

F. J. MacWilliams, N. J. Sloane, “Pseudo-random sequences and arrays,” Proc. IEEE 64, 1715–1728 (1976).
[CrossRef]

Maublant, J.

J. Maublant, M. de Latour, D. Mestas, A. Clemenson, S. Charrier, V. Feillel, G. LeBouedec, P. Kaufmann, J. Dauplat, A. Vegre, “Technetium-99m-sestamibi uptake in breast tumor and associated lymph nodes,” J. Nucl. Med. 37, 922–925 (1996).
[PubMed]

McConnell, M.

P. Dunphy, M. McConnell, A. Owens, E. Chupp, D. Forrest, J. Googins, “A balloon-borne coded aperture telescope for low-energy gamma-ray astronomy,” Nucl. Instrum. Methods Phys. Res. A 274, 362–379 (1989).
[CrossRef]

Mestas, D.

J. Maublant, M. de Latour, D. Mestas, A. Clemenson, S. Charrier, V. Feillel, G. LeBouedec, P. Kaufmann, J. Dauplat, A. Vegre, “Technetium-99m-sestamibi uptake in breast tumor and associated lymph nodes,” J. Nucl. Med. 37, 922–925 (1996).
[PubMed]

Owens, A.

P. Dunphy, M. McConnell, A. Owens, E. Chupp, D. Forrest, J. Googins, “A balloon-borne coded aperture telescope for low-energy gamma-ray astronomy,” Nucl. Instrum. Methods Phys. Res. A 274, 362–379 (1989).
[CrossRef]

Prince, T. A.

W. R. Cook, M. Finger, T. A. Prince, E. C. Stone, “Gamma ray imaging with a rotating hexagonal uniformly redundant array,” IEEE Trans. Nucl. Sci. 31, 771–775 (1984).
[CrossRef]

Scarfone, C.

H. Wang, C. Scarfone, K. L. Greer, R. E. Coleman, R. J. Jaszczak, “Prone breast tumor imaging using vertical axis-of-rotation (VAOR) SPECT systems: an initial study,” IEEE Trans. Nucl. Sci. 44, 1271–1275 (1997).
[CrossRef]

Sloane, N. J.

F. J. MacWilliams, N. J. Sloane, “Pseudo-random sequences and arrays,” Proc. IEEE 64, 1715–1728 (1976).
[CrossRef]

Smith, M. F.

M. F. Smith, R. J. Jaszczak, “A rotating parallel hole collimator for high resolution imaging of medium energy radionuclides,” IEEE Trans. Nucl. Sci. 45, 2102–2112 (1998).
[CrossRef]

Stone, E. C.

W. R. Cook, M. Finger, T. A. Prince, E. C. Stone, “Gamma ray imaging with a rotating hexagonal uniformly redundant array,” IEEE Trans. Nucl. Sci. 31, 771–775 (1984).
[CrossRef]

Vegre, A.

J. Maublant, M. de Latour, D. Mestas, A. Clemenson, S. Charrier, V. Feillel, G. LeBouedec, P. Kaufmann, J. Dauplat, A. Vegre, “Technetium-99m-sestamibi uptake in breast tumor and associated lymph nodes,” J. Nucl. Med. 37, 922–925 (1996).
[PubMed]

Wang, H.

H. Wang, C. Scarfone, K. L. Greer, R. E. Coleman, R. J. Jaszczak, “Prone breast tumor imaging using vertical axis-of-rotation (VAOR) SPECT systems: an initial study,” IEEE Trans. Nucl. Sci. 44, 1271–1275 (1997).
[CrossRef]

Appl. Opt.

IEEE Trans. Nucl. Sci.

H. Wang, C. Scarfone, K. L. Greer, R. E. Coleman, R. J. Jaszczak, “Prone breast tumor imaging using vertical axis-of-rotation (VAOR) SPECT systems: an initial study,” IEEE Trans. Nucl. Sci. 44, 1271–1275 (1997).
[CrossRef]

M. F. Smith, R. J. Jaszczak, “A rotating parallel hole collimator for high resolution imaging of medium energy radionuclides,” IEEE Trans. Nucl. Sci. 45, 2102–2112 (1998).
[CrossRef]

W. R. Cook, M. Finger, T. A. Prince, E. C. Stone, “Gamma ray imaging with a rotating hexagonal uniformly redundant array,” IEEE Trans. Nucl. Sci. 31, 771–775 (1984).
[CrossRef]

J. Nucl. Med.

J. Maublant, M. de Latour, D. Mestas, A. Clemenson, S. Charrier, V. Feillel, G. LeBouedec, P. Kaufmann, J. Dauplat, A. Vegre, “Technetium-99m-sestamibi uptake in breast tumor and associated lymph nodes,” J. Nucl. Med. 37, 922–925 (1996).
[PubMed]

Nucl. Instrum. Methods Phys. Res. A

P. Dunphy, M. McConnell, A. Owens, E. Chupp, D. Forrest, J. Googins, “A balloon-borne coded aperture telescope for low-energy gamma-ray astronomy,” Nucl. Instrum. Methods Phys. Res. A 274, 362–379 (1989).
[CrossRef]

Proc. IEEE

F. J. MacWilliams, N. J. Sloane, “Pseudo-random sequences and arrays,” Proc. IEEE 64, 1715–1728 (1976).
[CrossRef]

Signal Process.

L. Bomer, M. Antweiler, “Optimizing the aperiodic merit factor of binary arrays,” Signal Process. 30, 1–13 (1993).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

(a) Overlap of picture array and postprocessing array for an on-axis point source. (b) Overlap of picture array and postprocessing array for an off-axis point source. The shaded area in the picture represents the truncated portion of the aperture array A used in the correlation. (c) Overlap of picture array and postprocessing array for an on-axis out-of-focus point source.

Fig. 2
Fig. 2

Imaging system modeled in Monte Carlo simulation.

Fig. 3
Fig. 3

(a) Reconstructed image and profile of 10 mm × 10 mm × 10 mm source centered in a background. The ratio of source-to-background intensity is 10:1. (b) Reconstructed image and profile of 10 mm × 10 mm × 10 mm source without background. (c) Reconstructed image and profile of 10 mm × 10 mm × 10 mm source in a background, obtained by composite picture reconstruction. The source-to-background ratio is 10:1.

Fig. 4
Fig. 4

Profile of reconstructed image of the 10 mm × 10 mm × 10 mm source with a source-to-background ratio of 6:1. The composite reconstruction was used. Source was placed (a) at the center of the front imaging plane, (b) at the center of the central imaging plane, (c) at the far right side of the central imaging plane, (d) at the corner of the central imaging plane.

Fig. 5
Fig. 5

Profile of reconstructed image of the 5 mm × 5 mm × 5 mm source with a source-to-background ratio of 6:1. The composite reconstruction was used. Aperture pixel size was 1 mm × 1 mm. Source was placed (a) at the center of the front imaging plane, (b) at the center of the central imaging plane.

Fig. 6
Fig. 6

Cross-sectional view of an imaging system with multiple apertures.

Fig. 7
Fig. 7

Reconstructed image of the (a) 10 mm × 10 mm × 10 mm and (b) 5 mm × 5 mm × 5 mm tumor located at the center of the phantom. The reconstruction procedure was performed for various depths.

Tables (1)

Tables Icon

Table 1 Quantitative Parameters of the Imaging Systems

Equations (15)

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

P=O  A+N,
O=RP  G,
ROα, β, γ=O-α,-β, γ.
O=RP  G=RO  A  G+R  N  G=RO  A  G+RN  G.
O=RO+RN  G,
Oi, j=kl Pk, lGk+i, l+j.
O+=P  G+.
G-=-1G+.
O-=P-  G-=O  A-  G-.
O=O  A+  G++O  A-  G-.
O=O  G+  G+.
ρi=1nj=0n-1 ajai+j,  i=0, ±1, ±2,.
ρ0=1, ρi=-1/n for 1i2m-2.
R0=rs+1/2,Ri=0 for 1i2m-2.
R0=rs,Ri=-1 for 1i2m-2.

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