Abstract

We use numerical studies to evaluate 13 novel optical remote-sensing geometries for tomographically reconstructing chemical pollutants in air. We simulate the imaging process from data acquisition to reconstruction using a battery of test images. We evaluate the reconstructions generated by each geometry for locating chemical leaks, identifying plumes, and evaluating human chemical exposures. This approach uses three numerical image-quality measures for both static and time-varying concentration maps. Visual evaluation is the most useful method of evaluating the geometries. The numerical measures are not always consistent with one another or with the visual evaluation. This research demonstrates the feasibility of using geometries with only a few detectors for tomographic imaging of air pollutants.

© 1997 Optical Society of America

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References

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  1. R. L. Byer, L. A. Shepp, “Two dimensional remote air-pollution via tomography,” Opt. Lett. 4, 75–77 (1979).
    [CrossRef] [PubMed]
  2. D. C. Wolfe, R. L. Byer, “Model studies of laser absorption computed tomography for remote air pollution measurement,” Appl. Opt. 21, 1165–1177 (1982).
    [CrossRef] [PubMed]
  3. L. Todd, D. Leith, “Remote sensing and computed tomography in industrial hygiene,” Am. Ind. Hyg. Assoc. J. 51, 224–233 (1990).
    [CrossRef]
  4. H. K. Xiao, S. P. Levine, W. F. Herget, J. B. D’arcy, R. Spear, T. Pritchett, “A transportable remote sensing, infrared air monitoring system,” Am. Ind. Hyg. Assoc. J. 52, 449–457 (1991).
    [CrossRef] [PubMed]
  5. W. F. Herget, “Analysis of gaseous air pollutants using a mobile FTIR system,” Am. Lab. 4, 72–78 (1982).
  6. W. B. Grant, R. H. Kagan, W. A. McClenny, “Optical remote measurement of toxic gases,” J. Air Waste Manage. Assoc. 42, 18–30 (1992).
    [CrossRef] [PubMed]
  7. M. Simonds, H. Xiao, S. P. Levine, “Optical remote sensing for air pollutants—review,” Am. Ind. Hyg. Assoc. J. 55, 953–965 (1994).
    [CrossRef] [PubMed]
  8. R. Bhattacharyya, L. A. Todd, “Spatial and temporal visualization of gases and vapours in air using computed tomography: numerical studies,” Ann. Occup. Hyg. 41, 105–122 (1997).
    [PubMed]
  9. L. Todd, G. Ramachandran, “Evaluation of optical source-detector geometry for tomographic reconstruction of chemical concentrations in indoor air,” Am. Ind. Hyg. Assoc. J. 55, 1133–1143 (1994).
    [CrossRef] [PubMed]
  10. L. Todd, G. Ramachandran, “Evaluation of algorithms for tomographic reconstruction of chemical concentrations in indoor air,” Am. Ind. Hyg. Assoc. J. 55, 403–417 (1994).
    [CrossRef] [PubMed]
  11. K. J. Myers, K. M. Hansonm, “Comparison of the algebraic reconstruction technique with the maximum entropy reconstruction technique for a variety of detection tasks,” in Medical Imaging IV: Image Formation, 1231 (Society of Optical Instrumentation Engineers, Newport Beach, Calif., 1990), pp. 176–186.
  12. K. M. Hanson, “Method of evaluating image-recovery algorithms based on task performance,” J. Opt. Soc. Am. A 7, 1294–1304 (1990).
    [CrossRef]
  13. S. R. Hanna, G. A. Briggs, R. P. Hoskar, “Handbook on atmospheric diffusion,” (U.S. Department of Energy, Technical Information Center, Washington, D.C., 1982).
  14. R. A. Brooks, G. Di Chiro, “Theory of image reconstruction in computed tomography,” Radiology 117, 561–572 (1975).
    [PubMed]
  15. B. E. Oppenheim, “Reconstruction tomography from incomplete projections,” in Reconstruction Tomography in Diagnostic Radiology and Nuclear Medicine, M. Ter-Pogossian, ed. (University Park Press, Baltimore, Md., 1977).
  16. B. M. W. Tsui, X. Zhao, E. C. Frey, G. T. Gulberg, “Comparison between ML-EM and WLS-CG algorithms for SPECT image reconstruction,” IEEE Trans. Nucl. Sci. 38, 1766–1772 (1991).
    [CrossRef]
  17. L. A. Shepp, Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imag. MI-1, 113–122 (1982).
    [CrossRef]
  18. G. T. Herman, A. Lent, S. W. Rowland, “ART: mathematics and applications. a report on the mathematical foundations and on the applicability to real data of the algebraic reconstruction techniques,” J. Theor. Biol. 42, 1–32 (1973).
    [CrossRef] [PubMed]
  19. A. Samanta, L. Todd “Mapping air contaminants indoors using a prototype computed tomography system,” Ann. Occup. Hyg. 40, 675–691 (1996).
    [PubMed]

1997 (1)

R. Bhattacharyya, L. A. Todd, “Spatial and temporal visualization of gases and vapours in air using computed tomography: numerical studies,” Ann. Occup. Hyg. 41, 105–122 (1997).
[PubMed]

1996 (1)

A. Samanta, L. Todd “Mapping air contaminants indoors using a prototype computed tomography system,” Ann. Occup. Hyg. 40, 675–691 (1996).
[PubMed]

1994 (3)

M. Simonds, H. Xiao, S. P. Levine, “Optical remote sensing for air pollutants—review,” Am. Ind. Hyg. Assoc. J. 55, 953–965 (1994).
[CrossRef] [PubMed]

L. Todd, G. Ramachandran, “Evaluation of optical source-detector geometry for tomographic reconstruction of chemical concentrations in indoor air,” Am. Ind. Hyg. Assoc. J. 55, 1133–1143 (1994).
[CrossRef] [PubMed]

L. Todd, G. Ramachandran, “Evaluation of algorithms for tomographic reconstruction of chemical concentrations in indoor air,” Am. Ind. Hyg. Assoc. J. 55, 403–417 (1994).
[CrossRef] [PubMed]

1992 (1)

W. B. Grant, R. H. Kagan, W. A. McClenny, “Optical remote measurement of toxic gases,” J. Air Waste Manage. Assoc. 42, 18–30 (1992).
[CrossRef] [PubMed]

1991 (2)

B. M. W. Tsui, X. Zhao, E. C. Frey, G. T. Gulberg, “Comparison between ML-EM and WLS-CG algorithms for SPECT image reconstruction,” IEEE Trans. Nucl. Sci. 38, 1766–1772 (1991).
[CrossRef]

H. K. Xiao, S. P. Levine, W. F. Herget, J. B. D’arcy, R. Spear, T. Pritchett, “A transportable remote sensing, infrared air monitoring system,” Am. Ind. Hyg. Assoc. J. 52, 449–457 (1991).
[CrossRef] [PubMed]

1990 (2)

K. M. Hanson, “Method of evaluating image-recovery algorithms based on task performance,” J. Opt. Soc. Am. A 7, 1294–1304 (1990).
[CrossRef]

L. Todd, D. Leith, “Remote sensing and computed tomography in industrial hygiene,” Am. Ind. Hyg. Assoc. J. 51, 224–233 (1990).
[CrossRef]

1982 (3)

L. A. Shepp, Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imag. MI-1, 113–122 (1982).
[CrossRef]

W. F. Herget, “Analysis of gaseous air pollutants using a mobile FTIR system,” Am. Lab. 4, 72–78 (1982).

D. C. Wolfe, R. L. Byer, “Model studies of laser absorption computed tomography for remote air pollution measurement,” Appl. Opt. 21, 1165–1177 (1982).
[CrossRef] [PubMed]

1979 (1)

1975 (1)

R. A. Brooks, G. Di Chiro, “Theory of image reconstruction in computed tomography,” Radiology 117, 561–572 (1975).
[PubMed]

1973 (1)

G. T. Herman, A. Lent, S. W. Rowland, “ART: mathematics and applications. a report on the mathematical foundations and on the applicability to real data of the algebraic reconstruction techniques,” J. Theor. Biol. 42, 1–32 (1973).
[CrossRef] [PubMed]

Bhattacharyya, R.

R. Bhattacharyya, L. A. Todd, “Spatial and temporal visualization of gases and vapours in air using computed tomography: numerical studies,” Ann. Occup. Hyg. 41, 105–122 (1997).
[PubMed]

Briggs, G. A.

S. R. Hanna, G. A. Briggs, R. P. Hoskar, “Handbook on atmospheric diffusion,” (U.S. Department of Energy, Technical Information Center, Washington, D.C., 1982).

Brooks, R. A.

R. A. Brooks, G. Di Chiro, “Theory of image reconstruction in computed tomography,” Radiology 117, 561–572 (1975).
[PubMed]

Byer, R. L.

D’arcy, J. B.

H. K. Xiao, S. P. Levine, W. F. Herget, J. B. D’arcy, R. Spear, T. Pritchett, “A transportable remote sensing, infrared air monitoring system,” Am. Ind. Hyg. Assoc. J. 52, 449–457 (1991).
[CrossRef] [PubMed]

Di Chiro, G.

R. A. Brooks, G. Di Chiro, “Theory of image reconstruction in computed tomography,” Radiology 117, 561–572 (1975).
[PubMed]

Frey, E. C.

B. M. W. Tsui, X. Zhao, E. C. Frey, G. T. Gulberg, “Comparison between ML-EM and WLS-CG algorithms for SPECT image reconstruction,” IEEE Trans. Nucl. Sci. 38, 1766–1772 (1991).
[CrossRef]

Grant, W. B.

W. B. Grant, R. H. Kagan, W. A. McClenny, “Optical remote measurement of toxic gases,” J. Air Waste Manage. Assoc. 42, 18–30 (1992).
[CrossRef] [PubMed]

Gulberg, G. T.

B. M. W. Tsui, X. Zhao, E. C. Frey, G. T. Gulberg, “Comparison between ML-EM and WLS-CG algorithms for SPECT image reconstruction,” IEEE Trans. Nucl. Sci. 38, 1766–1772 (1991).
[CrossRef]

Hanna, S. R.

S. R. Hanna, G. A. Briggs, R. P. Hoskar, “Handbook on atmospheric diffusion,” (U.S. Department of Energy, Technical Information Center, Washington, D.C., 1982).

Hanson, K. M.

Hansonm, K. M.

K. J. Myers, K. M. Hansonm, “Comparison of the algebraic reconstruction technique with the maximum entropy reconstruction technique for a variety of detection tasks,” in Medical Imaging IV: Image Formation, 1231 (Society of Optical Instrumentation Engineers, Newport Beach, Calif., 1990), pp. 176–186.

Herget, W. F.

H. K. Xiao, S. P. Levine, W. F. Herget, J. B. D’arcy, R. Spear, T. Pritchett, “A transportable remote sensing, infrared air monitoring system,” Am. Ind. Hyg. Assoc. J. 52, 449–457 (1991).
[CrossRef] [PubMed]

W. F. Herget, “Analysis of gaseous air pollutants using a mobile FTIR system,” Am. Lab. 4, 72–78 (1982).

Herman, G. T.

G. T. Herman, A. Lent, S. W. Rowland, “ART: mathematics and applications. a report on the mathematical foundations and on the applicability to real data of the algebraic reconstruction techniques,” J. Theor. Biol. 42, 1–32 (1973).
[CrossRef] [PubMed]

Hoskar, R. P.

S. R. Hanna, G. A. Briggs, R. P. Hoskar, “Handbook on atmospheric diffusion,” (U.S. Department of Energy, Technical Information Center, Washington, D.C., 1982).

Kagan, R. H.

W. B. Grant, R. H. Kagan, W. A. McClenny, “Optical remote measurement of toxic gases,” J. Air Waste Manage. Assoc. 42, 18–30 (1992).
[CrossRef] [PubMed]

Leith, D.

L. Todd, D. Leith, “Remote sensing and computed tomography in industrial hygiene,” Am. Ind. Hyg. Assoc. J. 51, 224–233 (1990).
[CrossRef]

Lent, A.

G. T. Herman, A. Lent, S. W. Rowland, “ART: mathematics and applications. a report on the mathematical foundations and on the applicability to real data of the algebraic reconstruction techniques,” J. Theor. Biol. 42, 1–32 (1973).
[CrossRef] [PubMed]

Levine, S. P.

M. Simonds, H. Xiao, S. P. Levine, “Optical remote sensing for air pollutants—review,” Am. Ind. Hyg. Assoc. J. 55, 953–965 (1994).
[CrossRef] [PubMed]

H. K. Xiao, S. P. Levine, W. F. Herget, J. B. D’arcy, R. Spear, T. Pritchett, “A transportable remote sensing, infrared air monitoring system,” Am. Ind. Hyg. Assoc. J. 52, 449–457 (1991).
[CrossRef] [PubMed]

McClenny, W. A.

W. B. Grant, R. H. Kagan, W. A. McClenny, “Optical remote measurement of toxic gases,” J. Air Waste Manage. Assoc. 42, 18–30 (1992).
[CrossRef] [PubMed]

Myers, K. J.

K. J. Myers, K. M. Hansonm, “Comparison of the algebraic reconstruction technique with the maximum entropy reconstruction technique for a variety of detection tasks,” in Medical Imaging IV: Image Formation, 1231 (Society of Optical Instrumentation Engineers, Newport Beach, Calif., 1990), pp. 176–186.

Oppenheim, B. E.

B. E. Oppenheim, “Reconstruction tomography from incomplete projections,” in Reconstruction Tomography in Diagnostic Radiology and Nuclear Medicine, M. Ter-Pogossian, ed. (University Park Press, Baltimore, Md., 1977).

Pritchett, T.

H. K. Xiao, S. P. Levine, W. F. Herget, J. B. D’arcy, R. Spear, T. Pritchett, “A transportable remote sensing, infrared air monitoring system,” Am. Ind. Hyg. Assoc. J. 52, 449–457 (1991).
[CrossRef] [PubMed]

Ramachandran, G.

L. Todd, G. Ramachandran, “Evaluation of algorithms for tomographic reconstruction of chemical concentrations in indoor air,” Am. Ind. Hyg. Assoc. J. 55, 403–417 (1994).
[CrossRef] [PubMed]

L. Todd, G. Ramachandran, “Evaluation of optical source-detector geometry for tomographic reconstruction of chemical concentrations in indoor air,” Am. Ind. Hyg. Assoc. J. 55, 1133–1143 (1994).
[CrossRef] [PubMed]

Rowland, S. W.

G. T. Herman, A. Lent, S. W. Rowland, “ART: mathematics and applications. a report on the mathematical foundations and on the applicability to real data of the algebraic reconstruction techniques,” J. Theor. Biol. 42, 1–32 (1973).
[CrossRef] [PubMed]

Samanta, A.

A. Samanta, L. Todd “Mapping air contaminants indoors using a prototype computed tomography system,” Ann. Occup. Hyg. 40, 675–691 (1996).
[PubMed]

Shepp, L. A.

L. A. Shepp, Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imag. MI-1, 113–122 (1982).
[CrossRef]

R. L. Byer, L. A. Shepp, “Two dimensional remote air-pollution via tomography,” Opt. Lett. 4, 75–77 (1979).
[CrossRef] [PubMed]

Simonds, M.

M. Simonds, H. Xiao, S. P. Levine, “Optical remote sensing for air pollutants—review,” Am. Ind. Hyg. Assoc. J. 55, 953–965 (1994).
[CrossRef] [PubMed]

Spear, R.

H. K. Xiao, S. P. Levine, W. F. Herget, J. B. D’arcy, R. Spear, T. Pritchett, “A transportable remote sensing, infrared air monitoring system,” Am. Ind. Hyg. Assoc. J. 52, 449–457 (1991).
[CrossRef] [PubMed]

Todd, L.

A. Samanta, L. Todd “Mapping air contaminants indoors using a prototype computed tomography system,” Ann. Occup. Hyg. 40, 675–691 (1996).
[PubMed]

L. Todd, G. Ramachandran, “Evaluation of algorithms for tomographic reconstruction of chemical concentrations in indoor air,” Am. Ind. Hyg. Assoc. J. 55, 403–417 (1994).
[CrossRef] [PubMed]

L. Todd, G. Ramachandran, “Evaluation of optical source-detector geometry for tomographic reconstruction of chemical concentrations in indoor air,” Am. Ind. Hyg. Assoc. J. 55, 1133–1143 (1994).
[CrossRef] [PubMed]

L. Todd, D. Leith, “Remote sensing and computed tomography in industrial hygiene,” Am. Ind. Hyg. Assoc. J. 51, 224–233 (1990).
[CrossRef]

Todd, L. A.

R. Bhattacharyya, L. A. Todd, “Spatial and temporal visualization of gases and vapours in air using computed tomography: numerical studies,” Ann. Occup. Hyg. 41, 105–122 (1997).
[PubMed]

Tsui, B. M. W.

B. M. W. Tsui, X. Zhao, E. C. Frey, G. T. Gulberg, “Comparison between ML-EM and WLS-CG algorithms for SPECT image reconstruction,” IEEE Trans. Nucl. Sci. 38, 1766–1772 (1991).
[CrossRef]

Vardi, Y.

L. A. Shepp, Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imag. MI-1, 113–122 (1982).
[CrossRef]

Wolfe, D. C.

Xiao, H.

M. Simonds, H. Xiao, S. P. Levine, “Optical remote sensing for air pollutants—review,” Am. Ind. Hyg. Assoc. J. 55, 953–965 (1994).
[CrossRef] [PubMed]

Xiao, H. K.

H. K. Xiao, S. P. Levine, W. F. Herget, J. B. D’arcy, R. Spear, T. Pritchett, “A transportable remote sensing, infrared air monitoring system,” Am. Ind. Hyg. Assoc. J. 52, 449–457 (1991).
[CrossRef] [PubMed]

Zhao, X.

B. M. W. Tsui, X. Zhao, E. C. Frey, G. T. Gulberg, “Comparison between ML-EM and WLS-CG algorithms for SPECT image reconstruction,” IEEE Trans. Nucl. Sci. 38, 1766–1772 (1991).
[CrossRef]

Am. Ind. Hyg. Assoc. J. (5)

L. Todd, D. Leith, “Remote sensing and computed tomography in industrial hygiene,” Am. Ind. Hyg. Assoc. J. 51, 224–233 (1990).
[CrossRef]

H. K. Xiao, S. P. Levine, W. F. Herget, J. B. D’arcy, R. Spear, T. Pritchett, “A transportable remote sensing, infrared air monitoring system,” Am. Ind. Hyg. Assoc. J. 52, 449–457 (1991).
[CrossRef] [PubMed]

L. Todd, G. Ramachandran, “Evaluation of optical source-detector geometry for tomographic reconstruction of chemical concentrations in indoor air,” Am. Ind. Hyg. Assoc. J. 55, 1133–1143 (1994).
[CrossRef] [PubMed]

L. Todd, G. Ramachandran, “Evaluation of algorithms for tomographic reconstruction of chemical concentrations in indoor air,” Am. Ind. Hyg. Assoc. J. 55, 403–417 (1994).
[CrossRef] [PubMed]

M. Simonds, H. Xiao, S. P. Levine, “Optical remote sensing for air pollutants—review,” Am. Ind. Hyg. Assoc. J. 55, 953–965 (1994).
[CrossRef] [PubMed]

Am. Lab. (1)

W. F. Herget, “Analysis of gaseous air pollutants using a mobile FTIR system,” Am. Lab. 4, 72–78 (1982).

Ann. Occup. Hyg. (2)

R. Bhattacharyya, L. A. Todd, “Spatial and temporal visualization of gases and vapours in air using computed tomography: numerical studies,” Ann. Occup. Hyg. 41, 105–122 (1997).
[PubMed]

A. Samanta, L. Todd “Mapping air contaminants indoors using a prototype computed tomography system,” Ann. Occup. Hyg. 40, 675–691 (1996).
[PubMed]

Appl. Opt. (1)

IEEE Trans. Med. Imag. (1)

L. A. Shepp, Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imag. MI-1, 113–122 (1982).
[CrossRef]

IEEE Trans. Nucl. Sci. (1)

B. M. W. Tsui, X. Zhao, E. C. Frey, G. T. Gulberg, “Comparison between ML-EM and WLS-CG algorithms for SPECT image reconstruction,” IEEE Trans. Nucl. Sci. 38, 1766–1772 (1991).
[CrossRef]

J. Air Waste Manage. Assoc. (1)

W. B. Grant, R. H. Kagan, W. A. McClenny, “Optical remote measurement of toxic gases,” J. Air Waste Manage. Assoc. 42, 18–30 (1992).
[CrossRef] [PubMed]

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

J. Theor. Biol. (1)

G. T. Herman, A. Lent, S. W. Rowland, “ART: mathematics and applications. a report on the mathematical foundations and on the applicability to real data of the algebraic reconstruction techniques,” J. Theor. Biol. 42, 1–32 (1973).
[CrossRef] [PubMed]

Opt. Lett. (1)

Radiology (1)

R. A. Brooks, G. Di Chiro, “Theory of image reconstruction in computed tomography,” Radiology 117, 561–572 (1975).
[PubMed]

Other (3)

B. E. Oppenheim, “Reconstruction tomography from incomplete projections,” in Reconstruction Tomography in Diagnostic Radiology and Nuclear Medicine, M. Ter-Pogossian, ed. (University Park Press, Baltimore, Md., 1977).

K. J. Myers, K. M. Hansonm, “Comparison of the algebraic reconstruction technique with the maximum entropy reconstruction technique for a variety of detection tasks,” in Medical Imaging IV: Image Formation, 1231 (Society of Optical Instrumentation Engineers, Newport Beach, Calif., 1990), pp. 176–186.

S. R. Hanna, G. A. Briggs, R. P. Hoskar, “Handbook on atmospheric diffusion,” (U.S. Department of Energy, Technical Information Center, Washington, D.C., 1982).

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Figures (9)

Fig. 1
Fig. 1

Each geometry is illustrated by a pair of diagrams. The first diagram of each pair shows a few rays, and the second diagram shows the overall pattern of the rays. A solid box indicates a mirror, and a stippled box indicates a retroreflector. Single-detector geometries: (a) 1sRef, (b) 1sRefE, (c) 1sRef4Cor (d) 1sRef4CorE, and (e) 1sRef4Sid. Two-detector geometries: (f) 2sCor, (g) 2sCorRef, (h) 2sSid, and (i) 2sSidRef. Three-detector geometries: (j) 3sCor and (k) 3sSid. Four-detector geometries: (l) 4sCor and (m) 4sSid.

Fig. 2
Fig. 2

Static original and reconstructed test maps with six peaks. (a) Original map. Reconstructed maps: (b) 1sRef, (c) 1sRefE, (d) 1sRef4Cor, (e) 1sRef4Sid, (f) 1sRef4CorE, (g) 2sCor, (h) 2sCorRef, (i) 2sSid, (j) 2sSidRef, (k) 3sCor, (l) 3sSid, (m) 4sCor, and (n) 4sSid.

Fig. 3
Fig. 3

Static original and reconstructed test maps with five peaks. (a) Original map. Reconstructed maps: (b) 1sRef, (c) 1sRefE, (d) 1sRef4Cor, (e) 1sRef4Sid, (f) 1sRef4CorE, (g) 2sCor, (h) 2sCorRef, (i) 2sSid, (j) 2sSidRef, (k) 3sCor, (l) 3sSid, (m) 4sCor, and (n) 4sSid.

Fig. 4
Fig. 4

Variation of average nearness values for multiple-source time-series test maps with geometry.

Fig. 5
Fig. 5

Variation of average nearness values for moving-source time-series test maps with geometry.

Fig. 6
Fig. 6

Two columns of original and reconstructed multiple-source time-series maps. A: Original maps. Reconstructed maps: B, 1sRef; C, 1sRefE; D, 2sSidRef; E, 3sSid; and F, 4sCor.

Fig. 7
Fig. 7

Original and reconstructed moving-source time-series maps: column 1, 1.25 h; column 2, 1.75 h; column 3, 2.5 h. A: Original maps. Reconstructed maps: B, 1sRef; C, 1sRefE; D, 2sSidRef; E, 3sSid; and F, 4sCor.

Fig. 8
Fig. 8

Original and multiple-source time-series maps reconstructed by geometries with the same overall scan times. (a) Original map. Reconstructed maps: (b) 1sRef, (c) 1sRefE, (d) 2sSidRef, (e) 3sSid, and (f) 4sCor.

Fig. 9
Fig. 9

Original and moving-source time-series maps reconstructed by geometries with the same overall scan times: column 1, 1.25 h; column 2, 3 h. A: Original maps. Reconstructed maps: B, 1sRef; C, 1sRefE; D, 2sSidRef; E, 3sSid; and F, 4sCor.

Tables (2)

Tables Icon

Table 1 Nearness and Peak Error Results for Static-Test Maps

Tables Icon

Table 2 Peak Exposure Errors for Time-Series Maps

Equations (4)

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

lnLC=Σ-Σtijcj+pi lnΣtijcj-lnpi,
peak exposure error=time space cj*-time spacecjtime space cj*×100,
peak location error=x-x*2+y-y*2,1/2
nearness=j=1N2cj*-cj2j=1N2cj*-cavg*21/2,

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