Abstract

An iterative method is presented for computed tomography imaging spectrometer (CTIS) image reconstruction in the presence of both photon noise in the image and postdetection Gaussian system noise. The new algorithm, which assumes the transfer matrix of the system has a particular structure, is evaluated experimentally with the result that it is significantly better, for larger problems, than both the multiplicative algebraic reconstruction technique (MART) and the mixed-expectation image-reconstruction technique (MERT) with respect to accuracy and computation time.

© 2007 Optical Society of America

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  1. H. H. Barrett, "Image reconstruction and the solution of inverse problems in medical imaging," in The Formation, Handling, and Evaluation of Medical Images, A. Todd-Pokropek and M. A. Viergever, eds. (Springer-Verlag, 1991), pp. 33-39.
  2. T. R. Miller and J. W. Wallis, "Clinically important characteristics of maximum-likelihood reconstruction," J. Nucl. Med. 33, 1678-1684 (1992).
  3. M. R. Descour, "Non-scanning imaging spectrometry," Ph.D. dissertation (University of Arizona, 1994).
  4. M. R. Descour, B. K. Ford, D. W. Wilson, P. D. Maker, and G. H. Bearman, "High-speed spectral imager for imaging transient fluorescence phenomena," Proc. SPIE 3259, 11-17 (1998).
    [CrossRef]
  5. C. E. Volin, J. P. Garcia, E. L. Dereniak, M. R. Descour, T. Hamilton, and R. McMillan, "Midwave-infrared shapshot imaging spectrometer," Appl. Opt. 40, 4501-4506 (2001).
    [CrossRef]
  6. B. K. Ford and M. R. Descour, "Large-image-format computed tomography imaging spectrometer for fluorescence microscopy," Opt. Express 9, 444-453 (2001).
  7. B. Karacali and W. Snyder, "Automatic target detection using multispectral imaging," presented at the 31st Applied Imagery Pattern Recognition Workshop, 16 October 2002, Washington, DC, p. 55.
  8. E. K. Hege, D. O'Connell, W. Johnson, S. Basty, and E. L. Dereniak, "Hyperspectral imaging for astronomy and space surviellance," Proc. SPIE 5159, 380-391 (2003).
    [CrossRef]
  9. M. R. Descour, T. S. Tkaczyk, B. K. Ford, R. M. Lynch, A. Locke, and E. L. Dereniak, "The computed tomography imaging spectrometer," in The 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2003. LEOS 2003 (IEEE, 2003), pp. 460-461.
    [CrossRef]
  10. W. R. Johnson, D. W. Wilson, W. Fink, M. Humayun, and G. Bearman, "Snapshot hyperspectral imaging in ophthalmology," J. Biomed. Opt. 12, 014036 (2007).
    [CrossRef]
  11. N. Hagen, E. L. Dereniak, and D. T. Sass, "Development of a four-dimensional imaging spectrometer," Proc. SPIE 4816, 381-388 (2002).
    [CrossRef]
  12. J. F. Scholl, E. L. Dereniak, M. R. Descour, C. P. Tebow, and C. E. Volin, "Phase grating design for a dual-band snapshot imaging spectrometer," Appl. Opt. 42, 3745-3748 (2003).
    [CrossRef]
  13. N. Hagen, E. L. Dereniak, and D. T. Sass, "Visible snapshot imaging spectropolarimeter," Proc. SPIE 5888, 277-286 (2005).
  14. N. Hagen and E. L. Dereniak, "Design of an LWIR snapshot imaging spectropolarimeter," Proc. SPIE 6295, 62950E (2006).
    [CrossRef]
  15. R. W. Aumiller, N. Hagen, E. L. Dereniak, S. Robert, and R. McMillan, "New grating designs for a CTIS imaging spectrometer," Proc. SPIE 6565, 62950E (2007).
  16. M. R. Descour, C. E. Volin, T. M. Gleeson, E. L. Dereniak, M. F. Hopkins, D. W. Wilson, and P. D. Maker, "Demonstration of a computed-tomography imaging spectrometer using a computer-generated hologram disperser," Appl. Opt. 36, 3694-3698 (1997).
  17. J. P. Garcia and E. L. Dereniak, "Mixed-expectation image-reconstruction technique," Appl. Opt. 38, 3745-3748 (1999).
  18. M. R. Descour and E. L. Dereniak, "Computed-tomography imaging spectrometer: experimental calibration and reconstruction results," Appl. Opt. 34, 4817-4826 (1995).
  19. W. R. Johnson, E. K. Hege, D. O'Connell, and E. L. Dereniak, "Novel calibration recovery technique for an EM tomographic reconstruction," Opt. Eng. 43, 10-11 (2004).
    [CrossRef]
  20. C. E. Volin, J. P. Garcia, E. L. Dereniak, M. R. Descour, D. T. Sass, and C. G. Simi, "MWIR computed tomography imaging spectrometer: calibration and imaging experiments," Proc. SPIE 3753, 192-202 (1999).
    [CrossRef]
  21. C. E. Volin, "Portable snapshot imaging spectrometer," Ph.D. dissertation (University of Arizona, 2000).
  22. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis (Cambridge U. Press, 1994).
  23. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, "Sherman-Morrison and Woodbury formulas," in Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, 1986), pp. 66-68.
  24. P. J. Davis, Circulant Matrices (Chelsea, 1994).

2007 (2)

W. R. Johnson, D. W. Wilson, W. Fink, M. Humayun, and G. Bearman, "Snapshot hyperspectral imaging in ophthalmology," J. Biomed. Opt. 12, 014036 (2007).
[CrossRef]

R. W. Aumiller, N. Hagen, E. L. Dereniak, S. Robert, and R. McMillan, "New grating designs for a CTIS imaging spectrometer," Proc. SPIE 6565, 62950E (2007).

2006 (1)

N. Hagen and E. L. Dereniak, "Design of an LWIR snapshot imaging spectropolarimeter," Proc. SPIE 6295, 62950E (2006).
[CrossRef]

2005 (1)

N. Hagen, E. L. Dereniak, and D. T. Sass, "Visible snapshot imaging spectropolarimeter," Proc. SPIE 5888, 277-286 (2005).

2004 (1)

W. R. Johnson, E. K. Hege, D. O'Connell, and E. L. Dereniak, "Novel calibration recovery technique for an EM tomographic reconstruction," Opt. Eng. 43, 10-11 (2004).
[CrossRef]

2003 (3)

E. K. Hege, D. O'Connell, W. Johnson, S. Basty, and E. L. Dereniak, "Hyperspectral imaging for astronomy and space surviellance," Proc. SPIE 5159, 380-391 (2003).
[CrossRef]

M. R. Descour, T. S. Tkaczyk, B. K. Ford, R. M. Lynch, A. Locke, and E. L. Dereniak, "The computed tomography imaging spectrometer," in The 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2003. LEOS 2003 (IEEE, 2003), pp. 460-461.
[CrossRef]

J. F. Scholl, E. L. Dereniak, M. R. Descour, C. P. Tebow, and C. E. Volin, "Phase grating design for a dual-band snapshot imaging spectrometer," Appl. Opt. 42, 3745-3748 (2003).
[CrossRef]

2002 (2)

N. Hagen, E. L. Dereniak, and D. T. Sass, "Development of a four-dimensional imaging spectrometer," Proc. SPIE 4816, 381-388 (2002).
[CrossRef]

B. Karacali and W. Snyder, "Automatic target detection using multispectral imaging," presented at the 31st Applied Imagery Pattern Recognition Workshop, 16 October 2002, Washington, DC, p. 55.

2001 (2)

2000 (1)

C. E. Volin, "Portable snapshot imaging spectrometer," Ph.D. dissertation (University of Arizona, 2000).

1999 (2)

C. E. Volin, J. P. Garcia, E. L. Dereniak, M. R. Descour, D. T. Sass, and C. G. Simi, "MWIR computed tomography imaging spectrometer: calibration and imaging experiments," Proc. SPIE 3753, 192-202 (1999).
[CrossRef]

J. P. Garcia and E. L. Dereniak, "Mixed-expectation image-reconstruction technique," Appl. Opt. 38, 3745-3748 (1999).

1998 (1)

M. R. Descour, B. K. Ford, D. W. Wilson, P. D. Maker, and G. H. Bearman, "High-speed spectral imager for imaging transient fluorescence phenomena," Proc. SPIE 3259, 11-17 (1998).
[CrossRef]

1997 (1)

1995 (1)

1994 (3)

M. R. Descour, "Non-scanning imaging spectrometry," Ph.D. dissertation (University of Arizona, 1994).

R. A. Horn and C. R. Johnson, Topics in Matrix Analysis (Cambridge U. Press, 1994).

P. J. Davis, Circulant Matrices (Chelsea, 1994).

1992 (1)

T. R. Miller and J. W. Wallis, "Clinically important characteristics of maximum-likelihood reconstruction," J. Nucl. Med. 33, 1678-1684 (1992).

1991 (1)

H. H. Barrett, "Image reconstruction and the solution of inverse problems in medical imaging," in The Formation, Handling, and Evaluation of Medical Images, A. Todd-Pokropek and M. A. Viergever, eds. (Springer-Verlag, 1991), pp. 33-39.

1986 (1)

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, "Sherman-Morrison and Woodbury formulas," in Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, 1986), pp. 66-68.

Aumiller, R. W.

R. W. Aumiller, N. Hagen, E. L. Dereniak, S. Robert, and R. McMillan, "New grating designs for a CTIS imaging spectrometer," Proc. SPIE 6565, 62950E (2007).

Barrett, H. H.

H. H. Barrett, "Image reconstruction and the solution of inverse problems in medical imaging," in The Formation, Handling, and Evaluation of Medical Images, A. Todd-Pokropek and M. A. Viergever, eds. (Springer-Verlag, 1991), pp. 33-39.

Basty, S.

E. K. Hege, D. O'Connell, W. Johnson, S. Basty, and E. L. Dereniak, "Hyperspectral imaging for astronomy and space surviellance," Proc. SPIE 5159, 380-391 (2003).
[CrossRef]

Bearman, G.

W. R. Johnson, D. W. Wilson, W. Fink, M. Humayun, and G. Bearman, "Snapshot hyperspectral imaging in ophthalmology," J. Biomed. Opt. 12, 014036 (2007).
[CrossRef]

Bearman, G. H.

M. R. Descour, B. K. Ford, D. W. Wilson, P. D. Maker, and G. H. Bearman, "High-speed spectral imager for imaging transient fluorescence phenomena," Proc. SPIE 3259, 11-17 (1998).
[CrossRef]

Davis, P. J.

P. J. Davis, Circulant Matrices (Chelsea, 1994).

Dereniak, E. L.

R. W. Aumiller, N. Hagen, E. L. Dereniak, S. Robert, and R. McMillan, "New grating designs for a CTIS imaging spectrometer," Proc. SPIE 6565, 62950E (2007).

N. Hagen and E. L. Dereniak, "Design of an LWIR snapshot imaging spectropolarimeter," Proc. SPIE 6295, 62950E (2006).
[CrossRef]

N. Hagen, E. L. Dereniak, and D. T. Sass, "Visible snapshot imaging spectropolarimeter," Proc. SPIE 5888, 277-286 (2005).

W. R. Johnson, E. K. Hege, D. O'Connell, and E. L. Dereniak, "Novel calibration recovery technique for an EM tomographic reconstruction," Opt. Eng. 43, 10-11 (2004).
[CrossRef]

E. K. Hege, D. O'Connell, W. Johnson, S. Basty, and E. L. Dereniak, "Hyperspectral imaging for astronomy and space surviellance," Proc. SPIE 5159, 380-391 (2003).
[CrossRef]

M. R. Descour, T. S. Tkaczyk, B. K. Ford, R. M. Lynch, A. Locke, and E. L. Dereniak, "The computed tomography imaging spectrometer," in The 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2003. LEOS 2003 (IEEE, 2003), pp. 460-461.
[CrossRef]

J. F. Scholl, E. L. Dereniak, M. R. Descour, C. P. Tebow, and C. E. Volin, "Phase grating design for a dual-band snapshot imaging spectrometer," Appl. Opt. 42, 3745-3748 (2003).
[CrossRef]

N. Hagen, E. L. Dereniak, and D. T. Sass, "Development of a four-dimensional imaging spectrometer," Proc. SPIE 4816, 381-388 (2002).
[CrossRef]

C. E. Volin, J. P. Garcia, E. L. Dereniak, M. R. Descour, T. Hamilton, and R. McMillan, "Midwave-infrared shapshot imaging spectrometer," Appl. Opt. 40, 4501-4506 (2001).
[CrossRef]

C. E. Volin, J. P. Garcia, E. L. Dereniak, M. R. Descour, D. T. Sass, and C. G. Simi, "MWIR computed tomography imaging spectrometer: calibration and imaging experiments," Proc. SPIE 3753, 192-202 (1999).
[CrossRef]

J. P. Garcia and E. L. Dereniak, "Mixed-expectation image-reconstruction technique," Appl. Opt. 38, 3745-3748 (1999).

M. R. Descour, C. E. Volin, T. M. Gleeson, E. L. Dereniak, M. F. Hopkins, D. W. Wilson, and P. D. Maker, "Demonstration of a computed-tomography imaging spectrometer using a computer-generated hologram disperser," Appl. Opt. 36, 3694-3698 (1997).

M. R. Descour and E. L. Dereniak, "Computed-tomography imaging spectrometer: experimental calibration and reconstruction results," Appl. Opt. 34, 4817-4826 (1995).

Descour, M. R.

M. R. Descour, T. S. Tkaczyk, B. K. Ford, R. M. Lynch, A. Locke, and E. L. Dereniak, "The computed tomography imaging spectrometer," in The 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2003. LEOS 2003 (IEEE, 2003), pp. 460-461.
[CrossRef]

J. F. Scholl, E. L. Dereniak, M. R. Descour, C. P. Tebow, and C. E. Volin, "Phase grating design for a dual-band snapshot imaging spectrometer," Appl. Opt. 42, 3745-3748 (2003).
[CrossRef]

B. K. Ford and M. R. Descour, "Large-image-format computed tomography imaging spectrometer for fluorescence microscopy," Opt. Express 9, 444-453 (2001).

C. E. Volin, J. P. Garcia, E. L. Dereniak, M. R. Descour, T. Hamilton, and R. McMillan, "Midwave-infrared shapshot imaging spectrometer," Appl. Opt. 40, 4501-4506 (2001).
[CrossRef]

C. E. Volin, J. P. Garcia, E. L. Dereniak, M. R. Descour, D. T. Sass, and C. G. Simi, "MWIR computed tomography imaging spectrometer: calibration and imaging experiments," Proc. SPIE 3753, 192-202 (1999).
[CrossRef]

M. R. Descour, B. K. Ford, D. W. Wilson, P. D. Maker, and G. H. Bearman, "High-speed spectral imager for imaging transient fluorescence phenomena," Proc. SPIE 3259, 11-17 (1998).
[CrossRef]

M. R. Descour, C. E. Volin, T. M. Gleeson, E. L. Dereniak, M. F. Hopkins, D. W. Wilson, and P. D. Maker, "Demonstration of a computed-tomography imaging spectrometer using a computer-generated hologram disperser," Appl. Opt. 36, 3694-3698 (1997).

M. R. Descour and E. L. Dereniak, "Computed-tomography imaging spectrometer: experimental calibration and reconstruction results," Appl. Opt. 34, 4817-4826 (1995).

M. R. Descour, "Non-scanning imaging spectrometry," Ph.D. dissertation (University of Arizona, 1994).

Fink, W.

W. R. Johnson, D. W. Wilson, W. Fink, M. Humayun, and G. Bearman, "Snapshot hyperspectral imaging in ophthalmology," J. Biomed. Opt. 12, 014036 (2007).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, "Sherman-Morrison and Woodbury formulas," in Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, 1986), pp. 66-68.

Ford, B. K.

M. R. Descour, T. S. Tkaczyk, B. K. Ford, R. M. Lynch, A. Locke, and E. L. Dereniak, "The computed tomography imaging spectrometer," in The 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2003. LEOS 2003 (IEEE, 2003), pp. 460-461.
[CrossRef]

B. K. Ford and M. R. Descour, "Large-image-format computed tomography imaging spectrometer for fluorescence microscopy," Opt. Express 9, 444-453 (2001).

M. R. Descour, B. K. Ford, D. W. Wilson, P. D. Maker, and G. H. Bearman, "High-speed spectral imager for imaging transient fluorescence phenomena," Proc. SPIE 3259, 11-17 (1998).
[CrossRef]

Garcia, J. P.

C. E. Volin, J. P. Garcia, E. L. Dereniak, M. R. Descour, T. Hamilton, and R. McMillan, "Midwave-infrared shapshot imaging spectrometer," Appl. Opt. 40, 4501-4506 (2001).
[CrossRef]

J. P. Garcia and E. L. Dereniak, "Mixed-expectation image-reconstruction technique," Appl. Opt. 38, 3745-3748 (1999).

C. E. Volin, J. P. Garcia, E. L. Dereniak, M. R. Descour, D. T. Sass, and C. G. Simi, "MWIR computed tomography imaging spectrometer: calibration and imaging experiments," Proc. SPIE 3753, 192-202 (1999).
[CrossRef]

Gleeson, T. M.

Hagen, N.

R. W. Aumiller, N. Hagen, E. L. Dereniak, S. Robert, and R. McMillan, "New grating designs for a CTIS imaging spectrometer," Proc. SPIE 6565, 62950E (2007).

N. Hagen and E. L. Dereniak, "Design of an LWIR snapshot imaging spectropolarimeter," Proc. SPIE 6295, 62950E (2006).
[CrossRef]

N. Hagen, E. L. Dereniak, and D. T. Sass, "Visible snapshot imaging spectropolarimeter," Proc. SPIE 5888, 277-286 (2005).

N. Hagen, E. L. Dereniak, and D. T. Sass, "Development of a four-dimensional imaging spectrometer," Proc. SPIE 4816, 381-388 (2002).
[CrossRef]

Hamilton, T.

Hege, E. K.

W. R. Johnson, E. K. Hege, D. O'Connell, and E. L. Dereniak, "Novel calibration recovery technique for an EM tomographic reconstruction," Opt. Eng. 43, 10-11 (2004).
[CrossRef]

E. K. Hege, D. O'Connell, W. Johnson, S. Basty, and E. L. Dereniak, "Hyperspectral imaging for astronomy and space surviellance," Proc. SPIE 5159, 380-391 (2003).
[CrossRef]

Hopkins, M. F.

Horn, R. A.

R. A. Horn and C. R. Johnson, Topics in Matrix Analysis (Cambridge U. Press, 1994).

Humayun, M.

W. R. Johnson, D. W. Wilson, W. Fink, M. Humayun, and G. Bearman, "Snapshot hyperspectral imaging in ophthalmology," J. Biomed. Opt. 12, 014036 (2007).
[CrossRef]

Johnson, C. R.

R. A. Horn and C. R. Johnson, Topics in Matrix Analysis (Cambridge U. Press, 1994).

Johnson, W.

E. K. Hege, D. O'Connell, W. Johnson, S. Basty, and E. L. Dereniak, "Hyperspectral imaging for astronomy and space surviellance," Proc. SPIE 5159, 380-391 (2003).
[CrossRef]

Johnson, W. R.

W. R. Johnson, D. W. Wilson, W. Fink, M. Humayun, and G. Bearman, "Snapshot hyperspectral imaging in ophthalmology," J. Biomed. Opt. 12, 014036 (2007).
[CrossRef]

W. R. Johnson, E. K. Hege, D. O'Connell, and E. L. Dereniak, "Novel calibration recovery technique for an EM tomographic reconstruction," Opt. Eng. 43, 10-11 (2004).
[CrossRef]

Karacali, B.

B. Karacali and W. Snyder, "Automatic target detection using multispectral imaging," presented at the 31st Applied Imagery Pattern Recognition Workshop, 16 October 2002, Washington, DC, p. 55.

Locke, A.

M. R. Descour, T. S. Tkaczyk, B. K. Ford, R. M. Lynch, A. Locke, and E. L. Dereniak, "The computed tomography imaging spectrometer," in The 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2003. LEOS 2003 (IEEE, 2003), pp. 460-461.
[CrossRef]

Lynch, R. M.

M. R. Descour, T. S. Tkaczyk, B. K. Ford, R. M. Lynch, A. Locke, and E. L. Dereniak, "The computed tomography imaging spectrometer," in The 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2003. LEOS 2003 (IEEE, 2003), pp. 460-461.
[CrossRef]

Maker, P. D.

M. R. Descour, B. K. Ford, D. W. Wilson, P. D. Maker, and G. H. Bearman, "High-speed spectral imager for imaging transient fluorescence phenomena," Proc. SPIE 3259, 11-17 (1998).
[CrossRef]

M. R. Descour, C. E. Volin, T. M. Gleeson, E. L. Dereniak, M. F. Hopkins, D. W. Wilson, and P. D. Maker, "Demonstration of a computed-tomography imaging spectrometer using a computer-generated hologram disperser," Appl. Opt. 36, 3694-3698 (1997).

McMillan, R.

R. W. Aumiller, N. Hagen, E. L. Dereniak, S. Robert, and R. McMillan, "New grating designs for a CTIS imaging spectrometer," Proc. SPIE 6565, 62950E (2007).

C. E. Volin, J. P. Garcia, E. L. Dereniak, M. R. Descour, T. Hamilton, and R. McMillan, "Midwave-infrared shapshot imaging spectrometer," Appl. Opt. 40, 4501-4506 (2001).
[CrossRef]

Miller, T. R.

T. R. Miller and J. W. Wallis, "Clinically important characteristics of maximum-likelihood reconstruction," J. Nucl. Med. 33, 1678-1684 (1992).

O'Connell, D.

W. R. Johnson, E. K. Hege, D. O'Connell, and E. L. Dereniak, "Novel calibration recovery technique for an EM tomographic reconstruction," Opt. Eng. 43, 10-11 (2004).
[CrossRef]

E. K. Hege, D. O'Connell, W. Johnson, S. Basty, and E. L. Dereniak, "Hyperspectral imaging for astronomy and space surviellance," Proc. SPIE 5159, 380-391 (2003).
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, "Sherman-Morrison and Woodbury formulas," in Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, 1986), pp. 66-68.

Robert, S.

R. W. Aumiller, N. Hagen, E. L. Dereniak, S. Robert, and R. McMillan, "New grating designs for a CTIS imaging spectrometer," Proc. SPIE 6565, 62950E (2007).

Sass, D. T.

N. Hagen, E. L. Dereniak, and D. T. Sass, "Visible snapshot imaging spectropolarimeter," Proc. SPIE 5888, 277-286 (2005).

N. Hagen, E. L. Dereniak, and D. T. Sass, "Development of a four-dimensional imaging spectrometer," Proc. SPIE 4816, 381-388 (2002).
[CrossRef]

C. E. Volin, J. P. Garcia, E. L. Dereniak, M. R. Descour, D. T. Sass, and C. G. Simi, "MWIR computed tomography imaging spectrometer: calibration and imaging experiments," Proc. SPIE 3753, 192-202 (1999).
[CrossRef]

Scholl, J. F.

Simi, C. G.

C. E. Volin, J. P. Garcia, E. L. Dereniak, M. R. Descour, D. T. Sass, and C. G. Simi, "MWIR computed tomography imaging spectrometer: calibration and imaging experiments," Proc. SPIE 3753, 192-202 (1999).
[CrossRef]

Snyder, W.

B. Karacali and W. Snyder, "Automatic target detection using multispectral imaging," presented at the 31st Applied Imagery Pattern Recognition Workshop, 16 October 2002, Washington, DC, p. 55.

Tebow, C. P.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, "Sherman-Morrison and Woodbury formulas," in Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, 1986), pp. 66-68.

Tkaczyk, T. S.

M. R. Descour, T. S. Tkaczyk, B. K. Ford, R. M. Lynch, A. Locke, and E. L. Dereniak, "The computed tomography imaging spectrometer," in The 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2003. LEOS 2003 (IEEE, 2003), pp. 460-461.
[CrossRef]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, "Sherman-Morrison and Woodbury formulas," in Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, 1986), pp. 66-68.

Volin, C. E.

Wallis, J. W.

T. R. Miller and J. W. Wallis, "Clinically important characteristics of maximum-likelihood reconstruction," J. Nucl. Med. 33, 1678-1684 (1992).

Wilson, D. W.

W. R. Johnson, D. W. Wilson, W. Fink, M. Humayun, and G. Bearman, "Snapshot hyperspectral imaging in ophthalmology," J. Biomed. Opt. 12, 014036 (2007).
[CrossRef]

M. R. Descour, B. K. Ford, D. W. Wilson, P. D. Maker, and G. H. Bearman, "High-speed spectral imager for imaging transient fluorescence phenomena," Proc. SPIE 3259, 11-17 (1998).
[CrossRef]

M. R. Descour, C. E. Volin, T. M. Gleeson, E. L. Dereniak, M. F. Hopkins, D. W. Wilson, and P. D. Maker, "Demonstration of a computed-tomography imaging spectrometer using a computer-generated hologram disperser," Appl. Opt. 36, 3694-3698 (1997).

Appl. Opt. (5)

J. Biomed. Opt. (1)

W. R. Johnson, D. W. Wilson, W. Fink, M. Humayun, and G. Bearman, "Snapshot hyperspectral imaging in ophthalmology," J. Biomed. Opt. 12, 014036 (2007).
[CrossRef]

J. Nucl. Med. (1)

T. R. Miller and J. W. Wallis, "Clinically important characteristics of maximum-likelihood reconstruction," J. Nucl. Med. 33, 1678-1684 (1992).

Opt. Eng. (1)

W. R. Johnson, E. K. Hege, D. O'Connell, and E. L. Dereniak, "Novel calibration recovery technique for an EM tomographic reconstruction," Opt. Eng. 43, 10-11 (2004).
[CrossRef]

Opt. Express (1)

Proc. SPIE (7)

C. E. Volin, J. P. Garcia, E. L. Dereniak, M. R. Descour, D. T. Sass, and C. G. Simi, "MWIR computed tomography imaging spectrometer: calibration and imaging experiments," Proc. SPIE 3753, 192-202 (1999).
[CrossRef]

M. R. Descour, B. K. Ford, D. W. Wilson, P. D. Maker, and G. H. Bearman, "High-speed spectral imager for imaging transient fluorescence phenomena," Proc. SPIE 3259, 11-17 (1998).
[CrossRef]

N. Hagen, E. L. Dereniak, and D. T. Sass, "Development of a four-dimensional imaging spectrometer," Proc. SPIE 4816, 381-388 (2002).
[CrossRef]

N. Hagen, E. L. Dereniak, and D. T. Sass, "Visible snapshot imaging spectropolarimeter," Proc. SPIE 5888, 277-286 (2005).

N. Hagen and E. L. Dereniak, "Design of an LWIR snapshot imaging spectropolarimeter," Proc. SPIE 6295, 62950E (2006).
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R. W. Aumiller, N. Hagen, E. L. Dereniak, S. Robert, and R. McMillan, "New grating designs for a CTIS imaging spectrometer," Proc. SPIE 6565, 62950E (2007).

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The 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2003. LEOS 2003 (1)

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Figures (5)

Fig. 1
Fig. 1

Initial field of view image f: closeup of mosquito.

Fig. 2
Fig. 2

CTIS focal plane image g (corresponding to f).

Fig. 3
Fig. 3

Average pixel error versus iteration.

Fig. 4
Fig. 4

(a) Vose–Horton (3 iterations; 457 s); (b) MART (3000 iterations; 45700 s); (c) Vose–Horton (4 iterations, noise level σ s = 2 ; 470   s ); (d) MERT (210 iterations, noise level σ s = 2 ; 4700   s ).

Fig. 5
Fig. 5

Average pixel error versus iteration (noise level σ s = 2 ).

Equations (41)

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g = H f + n 1 + n 2 ,
x = H f .
Prob ( g f ) = k exp { ( g k x k ) 2 / ( 2 x k + 2 σ s 2 ) } / 2 π ( x k + σ s 2 ) ,
0 = ( x k + σ s 2 ) 2 ( g k x k ) ( x k + σ s 2 ) ( g k x k ) 2 ( x k + σ s 2 ) 2 .
x k = ( 1 + 2 σ s 2 ) 2 + 4 ( g k ( g k + 2 σ s 2 ) σ s 2 ) ( 1 + 2 σ s 2 ) 2 .
g k ( g k + 2 σ s 2 ) σ s 2 0 ,
g k σ s 4 + σ s 2 σ s 2 .
x = H f
H = ( H 0 | | H w 1 ) ,
H k = ( T k , 0 | | T k , α 1 ) ,
T k , = R g T k , 0 ,
( R g ) i , j = [ g = i j mod n ] .
C i , j = c i j mod n ,
F i , j = 1 n e 2 π 1 i j / n .
Q = ( I a 0 ) ,
E = ( I α Q 0 ) ,
H f = ( H 0 | | H w 1 ) ( f 0 f w 1 ) = H k f k = C k E f k ,
Η = ( C 0 | | C w 1 ) .
x = H f = Η ( I w E ) f .
h = Η T x = Η T Η y ,
y = ( I w E ) f ,
f = ( I w E T ) y ,
y = ( I w E ) ( I w E T ) y .
h = ( μ I + Η T Η ) y ,
( A + U C V ) 1 = A 1 A 1 U ( C 1 + V A 1 U ) 1 V A 1 ,
y = ( μ 1 I μ 2 Η T ( I + μ 1 C k C k T ) 1 Η ) h
I + μ 1 C k C k T
y = M h = ( μ 1 I P P T ) h ,
M Η T Η = μ P P T ,
P = μ 1 Η T ( I + μ 1 C k C k T ) 1 / 2 .
Z = diag ( ( I w E ) 1 m ) ,
y 0 = Z M h y i + 1 = y i + Z M Η T Η v i , v 0 = Z M h v i + 1 = Z M Η T Η v i .
y = lim i y i = Z M h + μ Z P P T i = 0 { μ ( Z P ) ( Z P ) T } i v 0 = Z ( I + μ P P T { I μ ( Z P ) ( Z P ) T } 1 Z ) M h .
y = Z ( I + μ P P T Z { I + P ( μ 1 I P T Z P ) 1 P T Z } ) M h .
( μ 1 I P T Z P ) 1 v
v = ( μ 1 I P T Z P ) u .
f 0 = ( I w E T ) y ,
f 0 , , f i
η i f i
x H η i f i = H f .
f k + 1 = f k H T g + μ 1 H T H f k + μ 1 ,

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