Abstract

The possibility of retrieving horizontal atmospheric structure from a series of limb images taken aboard a satellite is discussed and a maximum likelihood expectation maximization algorithm is developed. Examples of the retrieval of horizontal structure with this algorithm, for different S/N (signal-to-noise) ratios and different structures, are presented. It is shown that with this algorithm and even in the presence of substantial observational noise, a S/N equal to 10 for a single observation, it is possible to retrieve both horizontal and vertical atmospheric structure.

© 2003 Optical Society of America

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  1. D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
    [CrossRef]
  2. H. Bovensmann, J. P. Burrows, M. Buchwitz, J. Frerick, S. Noël, V. V. Rozanov, K. V. Chance, A. H. P. Goede, “SCIAMACHY—Mission objectives and measurement modes,” J. Atmos. Sci. 56, 127–150 (1999).
    [CrossRef]
  3. S. C. Solomon, P. B. Hays, V. J. Abreu, “Tomographic inversion of satellite photometry,” Appl. Opt. 23, 3409–3414 (1984).
    [CrossRef] [PubMed]
  4. S. C. Solomon, P. B. Hays, V. J. Abreu, “Tomographic inversion of satellite photometry. Part 2”, Appl. Opt. 24, 4134–4140 (1985).
    [CrossRef]
  5. E. Yee, K. V. Paulson, G. G. Shepherd, “Minimum cross-entropy inversion of satellite photometer data,” Appl. Opt. 26, 2106–2110 (1987).
    [CrossRef] [PubMed]
  6. I. C. McDade, N. D. Lloyd, E. J. Llewellyn, “A rocket tomography measurement of the N2+ 3914A emission in an auroral arc,” Planet. Space Sci. 39, 895–906 (1991).
    [CrossRef]
  7. I. C. McDade, E. J. Llewellyn, “Inversion techniques for recovering two-dimensional distributions of auroral emission rates from tomographic rocket photometer measurements,” Can. J. Phys. 69, 1059–1068 (1991).
    [CrossRef]
  8. I. C. McDade, E. J. Llewellyn, “Satellite limb tomography: Methods for recovering structured emission rates in the mesospheric airglow layer,” Can. J. Phys. 71, 552–563 (1993).
    [CrossRef]
  9. S. Frey, S. B. Mende, H. U. Frey, “Satellite limb tomography applied to airglow of the 630 nm emission,” J. Geophys. Res. 106, 21367–21380 (2001).
    [CrossRef]
  10. N. D. Lloyd, E. J. Llewellyn, “Deconvolution of blurred images using photon counting statistics and maximum probability,” Can. J. Phys. 67, 89–94 (1989).
    [CrossRef]
  11. L. A. Shepp, Y. Vardi, “Maximum likelihood reconstruction for positron emission tomography,” IEEE Trans. Med. Imaging MI-1, 113–122 (1982).
    [CrossRef]
  12. Y. Vardi, L. A. Shepp, L. Kaufman, “A statistical model for positron emission tomography,” J. Am. Stat. Assoc. 89, 8–20 (1985).
    [CrossRef]
  13. S. C. Blankespoor, X. Wu, K. Kalki, J. K. Brown, H. R. Tang, C. E. Cann, B. H. Hasewaga, “Attenuation correction of SPECT using x-ray CT on an emission-transmission CT system: Myocardial perfusion assessment,” IEEE Trans. Nucl. Sci. 43, 2263–2274 (1996).
    [CrossRef]
  14. S. Matej, R. M. Lewitt, “Practical considerations for 3-D image reconstruction using spherically symmetric volume elements,” IEEE Trans. Med. Imaging 15, 68–78 (1996).
    [CrossRef] [PubMed]
  15. T-S. Pan, B. M. W. Tsui, C. L. Byrne, “Choice of initial conditions in ML reconstruction of fan-beam transmission with truncated projection data,” IEEE Trans. Med. Imaging 16, 426–438 (1997).
    [CrossRef] [PubMed]
  16. A. Welch, G. T. Gullberg, “Implementation of a model-based non-uniform scatter correction scheme for SPECT,” IEEE Trans. Med. Imaging 16, 717–726 (1997).
    [CrossRef]
  17. A. R. De Pierro, “Multiplicative iterative methods in computed tomography,” in Mathematical Methods in Tomography, G. T. Herman, A. K. Louis, F. Natterer, eds., (Springer-Verlag, Berlin-Heidelberg, 1991) pp. 167–186.
    [CrossRef]
  18. I. Csiszar, G. Tusnady, “Information geometry and alternating minimization procedures,” Statistics Decisions Suppl. No. 1, 205–237 (1984).
  19. A. M. Cormack, “Representation of a function by its line integrals, with some radiological applications,” J. Appl. Phys. 34, 2722–2729 (1963).
    [CrossRef]
  20. A. M. Cormack, “Representation of a function by its line integrals, with some radiological applications. II,” J. Appl. Phys. 35, 2908–2912 (1964).
    [CrossRef]

2002 (1)

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

2001 (1)

S. Frey, S. B. Mende, H. U. Frey, “Satellite limb tomography applied to airglow of the 630 nm emission,” J. Geophys. Res. 106, 21367–21380 (2001).
[CrossRef]

1999 (1)

H. Bovensmann, J. P. Burrows, M. Buchwitz, J. Frerick, S. Noël, V. V. Rozanov, K. V. Chance, A. H. P. Goede, “SCIAMACHY—Mission objectives and measurement modes,” J. Atmos. Sci. 56, 127–150 (1999).
[CrossRef]

1997 (2)

T-S. Pan, B. M. W. Tsui, C. L. Byrne, “Choice of initial conditions in ML reconstruction of fan-beam transmission with truncated projection data,” IEEE Trans. Med. Imaging 16, 426–438 (1997).
[CrossRef] [PubMed]

A. Welch, G. T. Gullberg, “Implementation of a model-based non-uniform scatter correction scheme for SPECT,” IEEE Trans. Med. Imaging 16, 717–726 (1997).
[CrossRef]

1996 (2)

S. C. Blankespoor, X. Wu, K. Kalki, J. K. Brown, H. R. Tang, C. E. Cann, B. H. Hasewaga, “Attenuation correction of SPECT using x-ray CT on an emission-transmission CT system: Myocardial perfusion assessment,” IEEE Trans. Nucl. Sci. 43, 2263–2274 (1996).
[CrossRef]

S. Matej, R. M. Lewitt, “Practical considerations for 3-D image reconstruction using spherically symmetric volume elements,” IEEE Trans. Med. Imaging 15, 68–78 (1996).
[CrossRef] [PubMed]

1993 (1)

I. C. McDade, E. J. Llewellyn, “Satellite limb tomography: Methods for recovering structured emission rates in the mesospheric airglow layer,” Can. J. Phys. 71, 552–563 (1993).
[CrossRef]

1991 (2)

I. C. McDade, N. D. Lloyd, E. J. Llewellyn, “A rocket tomography measurement of the N2+ 3914A emission in an auroral arc,” Planet. Space Sci. 39, 895–906 (1991).
[CrossRef]

I. C. McDade, E. J. Llewellyn, “Inversion techniques for recovering two-dimensional distributions of auroral emission rates from tomographic rocket photometer measurements,” Can. J. Phys. 69, 1059–1068 (1991).
[CrossRef]

1989 (1)

N. D. Lloyd, E. J. Llewellyn, “Deconvolution of blurred images using photon counting statistics and maximum probability,” Can. J. Phys. 67, 89–94 (1989).
[CrossRef]

1987 (1)

1985 (2)

S. C. Solomon, P. B. Hays, V. J. Abreu, “Tomographic inversion of satellite photometry. Part 2”, Appl. Opt. 24, 4134–4140 (1985).
[CrossRef]

Y. Vardi, L. A. Shepp, L. Kaufman, “A statistical model for positron emission tomography,” J. Am. Stat. Assoc. 89, 8–20 (1985).
[CrossRef]

1984 (2)

I. Csiszar, G. Tusnady, “Information geometry and alternating minimization procedures,” Statistics Decisions Suppl. No. 1, 205–237 (1984).

S. C. Solomon, P. B. Hays, V. J. Abreu, “Tomographic inversion of satellite photometry,” Appl. Opt. 23, 3409–3414 (1984).
[CrossRef] [PubMed]

1982 (1)

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

1964 (1)

A. M. Cormack, “Representation of a function by its line integrals, with some radiological applications. II,” J. Appl. Phys. 35, 2908–2912 (1964).
[CrossRef]

1963 (1)

A. M. Cormack, “Representation of a function by its line integrals, with some radiological applications,” J. Appl. Phys. 34, 2722–2729 (1963).
[CrossRef]

Abreu, V. J.

Auvinen, H.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Baron, P.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Blankespoor, S. C.

S. C. Blankespoor, X. Wu, K. Kalki, J. K. Brown, H. R. Tang, C. E. Cann, B. H. Hasewaga, “Attenuation correction of SPECT using x-ray CT on an emission-transmission CT system: Myocardial perfusion assessment,” IEEE Trans. Nucl. Sci. 43, 2263–2274 (1996).
[CrossRef]

Bovensmann, H.

H. Bovensmann, J. P. Burrows, M. Buchwitz, J. Frerick, S. Noël, V. V. Rozanov, K. V. Chance, A. H. P. Goede, “SCIAMACHY—Mission objectives and measurement modes,” J. Atmos. Sci. 56, 127–150 (1999).
[CrossRef]

Brown, J. K.

S. C. Blankespoor, X. Wu, K. Kalki, J. K. Brown, H. R. Tang, C. E. Cann, B. H. Hasewaga, “Attenuation correction of SPECT using x-ray CT on an emission-transmission CT system: Myocardial perfusion assessment,” IEEE Trans. Nucl. Sci. 43, 2263–2274 (1996).
[CrossRef]

Buchwitz, M.

H. Bovensmann, J. P. Burrows, M. Buchwitz, J. Frerick, S. Noël, V. V. Rozanov, K. V. Chance, A. H. P. Goede, “SCIAMACHY—Mission objectives and measurement modes,” J. Atmos. Sci. 56, 127–150 (1999).
[CrossRef]

Burrows, J. P.

H. Bovensmann, J. P. Burrows, M. Buchwitz, J. Frerick, S. Noël, V. V. Rozanov, K. V. Chance, A. H. P. Goede, “SCIAMACHY—Mission objectives and measurement modes,” J. Atmos. Sci. 56, 127–150 (1999).
[CrossRef]

Byrne, C. L.

T-S. Pan, B. M. W. Tsui, C. L. Byrne, “Choice of initial conditions in ML reconstruction of fan-beam transmission with truncated projection data,” IEEE Trans. Med. Imaging 16, 426–438 (1997).
[CrossRef] [PubMed]

Cann, C. E.

S. C. Blankespoor, X. Wu, K. Kalki, J. K. Brown, H. R. Tang, C. E. Cann, B. H. Hasewaga, “Attenuation correction of SPECT using x-ray CT on an emission-transmission CT system: Myocardial perfusion assessment,” IEEE Trans. Nucl. Sci. 43, 2263–2274 (1996).
[CrossRef]

Chance, K. V.

H. Bovensmann, J. P. Burrows, M. Buchwitz, J. Frerick, S. Noël, V. V. Rozanov, K. V. Chance, A. H. P. Goede, “SCIAMACHY—Mission objectives and measurement modes,” J. Atmos. Sci. 56, 127–150 (1999).
[CrossRef]

Cormack, A. M.

A. M. Cormack, “Representation of a function by its line integrals, with some radiological applications. II,” J. Appl. Phys. 35, 2908–2912 (1964).
[CrossRef]

A. M. Cormack, “Representation of a function by its line integrals, with some radiological applications,” J. Appl. Phys. 34, 2722–2729 (1963).
[CrossRef]

Csiszar, I.

I. Csiszar, G. Tusnady, “Information geometry and alternating minimization procedures,” Statistics Decisions Suppl. No. 1, 205–237 (1984).

de la Nöe, J.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

De Pierro, A. R.

A. R. De Pierro, “Multiplicative iterative methods in computed tomography,” in Mathematical Methods in Tomography, G. T. Herman, A. K. Louis, F. Natterer, eds., (Springer-Verlag, Berlin-Heidelberg, 1991) pp. 167–186.
[CrossRef]

Degenstein, D. A.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Eriksson, P.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Evans, W. F. J.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Frerick, J.

H. Bovensmann, J. P. Burrows, M. Buchwitz, J. Frerick, S. Noël, V. V. Rozanov, K. V. Chance, A. H. P. Goede, “SCIAMACHY—Mission objectives and measurement modes,” J. Atmos. Sci. 56, 127–150 (1999).
[CrossRef]

Frey, H. U.

S. Frey, S. B. Mende, H. U. Frey, “Satellite limb tomography applied to airglow of the 630 nm emission,” J. Geophys. Res. 106, 21367–21380 (2001).
[CrossRef]

Frey, S.

S. Frey, S. B. Mende, H. U. Frey, “Satellite limb tomography applied to airglow of the 630 nm emission,” J. Geophys. Res. 106, 21367–21380 (2001).
[CrossRef]

Frisk, U.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Gattinger, R. L.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Goede, A. H. P.

H. Bovensmann, J. P. Burrows, M. Buchwitz, J. Frerick, S. Noël, V. V. Rozanov, K. V. Chance, A. H. P. Goede, “SCIAMACHY—Mission objectives and measurement modes,” J. Atmos. Sci. 56, 127–150 (1999).
[CrossRef]

Gullberg, G. T.

A. Welch, G. T. Gullberg, “Implementation of a model-based non-uniform scatter correction scheme for SPECT,” IEEE Trans. Med. Imaging 16, 717–726 (1997).
[CrossRef]

Haley, C. S.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Hasewaga, B. H.

S. C. Blankespoor, X. Wu, K. Kalki, J. K. Brown, H. R. Tang, C. E. Cann, B. H. Hasewaga, “Attenuation correction of SPECT using x-ray CT on an emission-transmission CT system: Myocardial perfusion assessment,” IEEE Trans. Nucl. Sci. 43, 2263–2274 (1996).
[CrossRef]

Hauchcorne, A.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Hays, P. B.

Jiménez, C.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Jonsson, A.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Kalki, K.

S. C. Blankespoor, X. Wu, K. Kalki, J. K. Brown, H. R. Tang, C. E. Cann, B. H. Hasewaga, “Attenuation correction of SPECT using x-ray CT on an emission-transmission CT system: Myocardial perfusion assessment,” IEEE Trans. Nucl. Sci. 43, 2263–2274 (1996).
[CrossRef]

Kaufman, L.

Y. Vardi, L. A. Shepp, L. Kaufman, “A statistical model for positron emission tomography,” J. Am. Stat. Assoc. 89, 8–20 (1985).
[CrossRef]

Kyrölä, E.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Leppelmeier, G. W.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Lewitt, R. M.

S. Matej, R. M. Lewitt, “Practical considerations for 3-D image reconstruction using spherically symmetric volume elements,” IEEE Trans. Med. Imaging 15, 68–78 (1996).
[CrossRef] [PubMed]

Llewellyn, E. J.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

I. C. McDade, E. J. Llewellyn, “Satellite limb tomography: Methods for recovering structured emission rates in the mesospheric airglow layer,” Can. J. Phys. 71, 552–563 (1993).
[CrossRef]

I. C. McDade, N. D. Lloyd, E. J. Llewellyn, “A rocket tomography measurement of the N2+ 3914A emission in an auroral arc,” Planet. Space Sci. 39, 895–906 (1991).
[CrossRef]

I. C. McDade, E. J. Llewellyn, “Inversion techniques for recovering two-dimensional distributions of auroral emission rates from tomographic rocket photometer measurements,” Can. J. Phys. 69, 1059–1068 (1991).
[CrossRef]

N. D. Lloyd, E. J. Llewellyn, “Deconvolution of blurred images using photon counting statistics and maximum probability,” Can. J. Phys. 67, 89–94 (1989).
[CrossRef]

Lloyd, N. D.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

I. C. McDade, N. D. Lloyd, E. J. Llewellyn, “A rocket tomography measurement of the N2+ 3914A emission in an auroral arc,” Planet. Space Sci. 39, 895–906 (1991).
[CrossRef]

N. D. Lloyd, E. J. Llewellyn, “Deconvolution of blurred images using photon counting statistics and maximum probability,” Can. J. Phys. 67, 89–94 (1989).
[CrossRef]

Matej, S.

S. Matej, R. M. Lewitt, “Practical considerations for 3-D image reconstruction using spherically symmetric volume elements,” IEEE Trans. Med. Imaging 15, 68–78 (1996).
[CrossRef] [PubMed]

McConnell, J. C.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

McDade, I. C.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

I. C. McDade, E. J. Llewellyn, “Satellite limb tomography: Methods for recovering structured emission rates in the mesospheric airglow layer,” Can. J. Phys. 71, 552–563 (1993).
[CrossRef]

I. C. McDade, E. J. Llewellyn, “Inversion techniques for recovering two-dimensional distributions of auroral emission rates from tomographic rocket photometer measurements,” Can. J. Phys. 69, 1059–1068 (1991).
[CrossRef]

I. C. McDade, N. D. Lloyd, E. J. Llewellyn, “A rocket tomography measurement of the N2+ 3914A emission in an auroral arc,” Planet. Space Sci. 39, 895–906 (1991).
[CrossRef]

Megie, G.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Mende, S. B.

S. Frey, S. B. Mende, H. U. Frey, “Satellite limb tomography applied to airglow of the 630 nm emission,” J. Geophys. Res. 106, 21367–21380 (2001).
[CrossRef]

Merino, F.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Murtagh, D. P.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Noël, S.

H. Bovensmann, J. P. Burrows, M. Buchwitz, J. Frerick, S. Noël, V. V. Rozanov, K. V. Chance, A. H. P. Goede, “SCIAMACHY—Mission objectives and measurement modes,” J. Atmos. Sci. 56, 127–150 (1999).
[CrossRef]

Oikarinen, L.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Pan, T-S.

T-S. Pan, B. M. W. Tsui, C. L. Byrne, “Choice of initial conditions in ML reconstruction of fan-beam transmission with truncated projection data,” IEEE Trans. Med. Imaging 16, 426–438 (1997).
[CrossRef] [PubMed]

Pardo, J. R.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Paulson, K. V.

Ricaud, P.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Richardson, E. H.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Ridal, M.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Rozanov, V. V.

H. Bovensmann, J. P. Burrows, M. Buchwitz, J. Frerick, S. Noël, V. V. Rozanov, K. V. Chance, A. H. P. Goede, “SCIAMACHY—Mission objectives and measurement modes,” J. Atmos. Sci. 56, 127–150 (1999).
[CrossRef]

Shepherd, G. G.

Shepp, L. A.

Y. Vardi, L. A. Shepp, L. Kaufman, “A statistical model for positron emission tomography,” J. Am. Stat. Assoc. 89, 8–20 (1985).
[CrossRef]

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

Sioris, C.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Solheim, B. H.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Solomon, S. C.

Stegman, J.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Strong, K.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Tang, H. R.

S. C. Blankespoor, X. Wu, K. Kalki, J. K. Brown, H. R. Tang, C. E. Cann, B. H. Hasewaga, “Attenuation correction of SPECT using x-ray CT on an emission-transmission CT system: Myocardial perfusion assessment,” IEEE Trans. Nucl. Sci. 43, 2263–2274 (1996).
[CrossRef]

Tsui, B. M. W.

T-S. Pan, B. M. W. Tsui, C. L. Byrne, “Choice of initial conditions in ML reconstruction of fan-beam transmission with truncated projection data,” IEEE Trans. Med. Imaging 16, 426–438 (1997).
[CrossRef] [PubMed]

Tusnady, G.

I. Csiszar, G. Tusnady, “Information geometry and alternating minimization procedures,” Statistics Decisions Suppl. No. 1, 205–237 (1984).

Vardi, Y.

Y. Vardi, L. A. Shepp, L. Kaufman, “A statistical model for positron emission tomography,” J. Am. Stat. Assoc. 89, 8–20 (1985).
[CrossRef]

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

von Savigny, C.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Welch, A.

A. Welch, G. T. Gullberg, “Implementation of a model-based non-uniform scatter correction scheme for SPECT,” IEEE Trans. Med. Imaging 16, 717–726 (1997).
[CrossRef]

Witt, G.

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

Wu, X.

S. C. Blankespoor, X. Wu, K. Kalki, J. K. Brown, H. R. Tang, C. E. Cann, B. H. Hasewaga, “Attenuation correction of SPECT using x-ray CT on an emission-transmission CT system: Myocardial perfusion assessment,” IEEE Trans. Nucl. Sci. 43, 2263–2274 (1996).
[CrossRef]

Yee, E.

Appl. Opt. (3)

Can. J. Phys. (4)

D. P. Murtagh, U. Frisk, F. Merino, M. Ridal, A. Jonsson, J. Stegman, G. Witt, P. Eriksson, C. Jiménez, G. Megie, J. de la Nöe, P. Ricaud, P. Baron, J. R. Pardo, A. Hauchcorne, E. J. Llewellyn, D. A. Degenstein, R. L. Gattinger, N. D. Lloyd, W. F. J. Evans, I. C. McDade, C. S. Haley, C. Sioris, C. von Savigny, B. H. Solheim, J. C. McConnell, K. Strong, E. H. Richardson, G. W. Leppelmeier, E. Kyrölä, H. Auvinen, L. Oikarinen, “An overview of the Odin Atmospheric Mission,” Can. J. Phys. 80, 309–319 (2002).
[CrossRef]

I. C. McDade, E. J. Llewellyn, “Inversion techniques for recovering two-dimensional distributions of auroral emission rates from tomographic rocket photometer measurements,” Can. J. Phys. 69, 1059–1068 (1991).
[CrossRef]

I. C. McDade, E. J. Llewellyn, “Satellite limb tomography: Methods for recovering structured emission rates in the mesospheric airglow layer,” Can. J. Phys. 71, 552–563 (1993).
[CrossRef]

N. D. Lloyd, E. J. Llewellyn, “Deconvolution of blurred images using photon counting statistics and maximum probability,” Can. J. Phys. 67, 89–94 (1989).
[CrossRef]

IEEE Trans. Med. Imaging (4)

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

S. Matej, R. M. Lewitt, “Practical considerations for 3-D image reconstruction using spherically symmetric volume elements,” IEEE Trans. Med. Imaging 15, 68–78 (1996).
[CrossRef] [PubMed]

T-S. Pan, B. M. W. Tsui, C. L. Byrne, “Choice of initial conditions in ML reconstruction of fan-beam transmission with truncated projection data,” IEEE Trans. Med. Imaging 16, 426–438 (1997).
[CrossRef] [PubMed]

A. Welch, G. T. Gullberg, “Implementation of a model-based non-uniform scatter correction scheme for SPECT,” IEEE Trans. Med. Imaging 16, 717–726 (1997).
[CrossRef]

IEEE Trans. Nucl. Sci. (1)

S. C. Blankespoor, X. Wu, K. Kalki, J. K. Brown, H. R. Tang, C. E. Cann, B. H. Hasewaga, “Attenuation correction of SPECT using x-ray CT on an emission-transmission CT system: Myocardial perfusion assessment,” IEEE Trans. Nucl. Sci. 43, 2263–2274 (1996).
[CrossRef]

J. Am. Stat. Assoc. (1)

Y. Vardi, L. A. Shepp, L. Kaufman, “A statistical model for positron emission tomography,” J. Am. Stat. Assoc. 89, 8–20 (1985).
[CrossRef]

J. Appl. Phys. (2)

A. M. Cormack, “Representation of a function by its line integrals, with some radiological applications,” J. Appl. Phys. 34, 2722–2729 (1963).
[CrossRef]

A. M. Cormack, “Representation of a function by its line integrals, with some radiological applications. II,” J. Appl. Phys. 35, 2908–2912 (1964).
[CrossRef]

J. Atmos. Sci. (1)

H. Bovensmann, J. P. Burrows, M. Buchwitz, J. Frerick, S. Noël, V. V. Rozanov, K. V. Chance, A. H. P. Goede, “SCIAMACHY—Mission objectives and measurement modes,” J. Atmos. Sci. 56, 127–150 (1999).
[CrossRef]

J. Geophys. Res. (1)

S. Frey, S. B. Mende, H. U. Frey, “Satellite limb tomography applied to airglow of the 630 nm emission,” J. Geophys. Res. 106, 21367–21380 (2001).
[CrossRef]

Planet. Space Sci. (1)

I. C. McDade, N. D. Lloyd, E. J. Llewellyn, “A rocket tomography measurement of the N2+ 3914A emission in an auroral arc,” Planet. Space Sci. 39, 895–906 (1991).
[CrossRef]

Statistics Decisions (1)

I. Csiszar, G. Tusnady, “Information geometry and alternating minimization procedures,” Statistics Decisions Suppl. No. 1, 205–237 (1984).

Other (1)

A. R. De Pierro, “Multiplicative iterative methods in computed tomography,” in Mathematical Methods in Tomography, G. T. Herman, A. K. Louis, F. Natterer, eds., (Springer-Verlag, Berlin-Heidelberg, 1991) pp. 167–186.
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Geometry of the model drawn to scale. The circles on the outer shell indicate the satellite, the lines coming from the satellite represent the complete field-of-view of the optical instrument, the dark ring represents the lowest 100 km of atmosphere, and the shaded region represents the solid Earth.

Fig. 2
Fig. 2

Two-dimensional volume-emission-rate grid geometry in a coordinate system that is defined by the position of the ascending node. A sample line of sight, P asc, is shown. This figure is not drawn to scale.

Fig. 3
Fig. 3

(a) Sample two-dimensional input volume-emission-rate grid. Grid covers only a partial orbit and corresponds to the 2400 images, taken every half second, that are shown in (b).

Fig. 4
Fig. 4

Structured and unstructured profiles compared in cross-section.

Fig. 5
Fig. 5

Example of the retrieved volume-emission-rate profiles that are analyzed throughout this work. The retrieval indicates the desired structure in the interior of the grid, while at the angular extremes, the retrieval is inaccurate due to undersampling of the grid cells. The input grid and the observations are those shown in Fig. 3.

Fig. 6
Fig. 6

Cross-sections taken from the input and retrieved grids shown in Figs. 3(a) and 5, respectively. The structure is well identified and the edge effect is clearly visible in the radial shell cross-section plot.

Fig. 7
Fig. 7

Histograms of the percent difference calculations for two different retrievals. Both histograms are approximately Gaussian and centered near 0%. The histogram (b) that corresponds to the lower imaging rate and higher noise level is considerably wider.

Fig. 8
Fig. 8

Standard deviations of the percent-error histograms for 32 retrievals done with different imaging rates and various noise levels. This figure illustrates the noise reduction capabilities of the tomographic algorithm. The standard deviation decreases, independent of the noise level, as the imaging rate increases.

Fig. 9
Fig. 9

Pixel cross-sections or measurements from a single tangent altitude. These measurements indicate that the perturbations due to the structure imposed on the input volume-emission-rate profiles become more blurred through the line-of-sight integration as the scale size of that structure decreases.

Fig. 10
Fig. 10

Radial shell cross-section comparisons of the input and retrieved volume-emission-rates for angular structure (from top to bottom) of 0.5°, 1°, 2°, and 3°. The 1° and larger structures are fully resolved. These simulations are for the highest imaging rate, 2400 images (a), and the lowest imaging rate, 400 images (b).

Fig. 11
Fig. 11

Pixel cross-sections, or measurements, from a single tangent altitude that contain two percent Gaussian random noise. The perturbations are due to the structure imposed on the input volume-emission-rate profiles and are barely visible even for the larger scale structures.

Fig. 12
Fig. 12

Radial shell cross-section comparisons of the input and retrieved volume-emission rates for an angular structure of 1° and four different noise rates. These simulations are for the highest imaging rate, 2400 images (a), and the lowest imaging rate, 400 images (b). The signal to noise in the measurements for each of the two plots increases, from top to bottom, from 5:1, 10:1, 20:1, to 50:1.

Fig. 13
Fig. 13

Radial shell cross-section comparisons of the input and retrieved volume emission rates for angular structure of 3° and four different noise rates. The raw retrievals in (a) have been smoothed (b) with a very simple three-element wide boxcar filter. These simulations are for the highest imaging rate of 2400 images.

Equations (9)

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Pij=Bi+niAijTjj AijTj-1,
Tj=i Piji Aij,
Vjn=iOi+niLijVjn-1j LijVjn-1-1i Lij,
Vjn=Vjn-1iOij LijVjn-1Liji Lij.
Vjn=Vjn-1iOiOiestn-1 βij.
Vj0=iOij Lij βij.
xjk+1=xjkibijaijxjkaijiaij=xjkibijaijxjk βij,
M=1-Amin+eβr-rminH×e-γ-γ022σ2 coskrrcoskγγ,
Amax=Amin+eβHH.

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