Abstract

A fast iterative deconvolution technique that permits the convergence speed of the iterations to be varied is introduced. In this technique, iterations are made to converge as fast as, twice as fast as, and three times (i.e., any integer may be used) as fast as the ordinary methods. The speed of convergence depends on the amount of noise in the data being deconvoluted. This technique is particularly useful for speeding up convergence of the reblurring procedure. The technique converges for all impulse-response function types. The mean-square error versus the deconvolution iteration number for different integral values of the convergence speed of the iterations (1, 5, and 10) is studied for two data sets with and without noise. It is shown that for noisy data sets one has to have control over the convergence speed of the iterations. This technique is also tested with a real data set obtained from an optical multichannel analyzer.

© 1995 Optical Society of America

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  1. P. H. van Cittert, “Zum Einfluss der spaltbreite auf die intensitatsverteilung in spektrallinien,” Z. Phys. 69, 298–308 (1931).
    [CrossRef]
  2. R. N. Bracewell, J. A. Roberts, “Aerial smoothing in radio astronomy,” Aust. J. Phys. 7, 615–640 (1954).
    [CrossRef]
  3. B. R. Frieden, “Image enhancement and restoration,” in Picture Processing and Digital Filtering, T. S. Huang, ed., Vol. 6 of Topics in Applied Physics (Springer-Verlag, Berlin, 1975), pp. 177–248.
    [CrossRef]
  4. N. R. Hill, G. E. Ioup, “Convergence of the van Cittert iterative method of deconvolution,” J. Opt. Soc. Am. 66, 487–489 (1976).
    [CrossRef]
  5. S. Kawata, Y. Ichioka, “Iterative image restoration for linearly degraded images. 1. Basis,” J. Opt. Soc. Am. 70, 762–768 (1980); S. Kawata, Y. Ichioka, “Iterative image restoration for linearly degraded images. II. Reblurring procedure,” J. Opt. Soc. Am. 70, 768–772 (1980).
    [CrossRef]
  6. J. Biemond, R. L. Lagendijk, R. M. Mersereau, “Iterative methods for image deblurring,” Proc. IEEE 78, 856–883 (1990).
    [CrossRef]
  7. P. A. Jansson, Deconvolution with Application in Spectroscopy (Academic, New York, 1984).
  8. L. B. J. La Coste, “Deconvolution by successive approximation,” Geophysics 47, 1724–1730 (1982).
    [CrossRef]
  9. G. E. Ioup, J. W. Ioup, “Iterative deconvolution,” Geophysics 48, 1287–1290 (1983).
    [CrossRef]
  10. C. E. Morris, M. A. Richards, M. H. Hayes, “Iterative deconvolution algorithm with quadratic convergence,” J. Opt. Soc. Am. 4, 200–207 (1987).
    [CrossRef]
  11. A. M. Amini, G. E. Ioup, J. W. Ioup, R. Powe, “Improved deconvolution for low signal-to-noise ratio seismic data,” in Proceedings of the Seventeenth International Symposium on Applied Identification Modeling and Simulation, R. E. Trahan, ed. (International Association of Science and Technology for Development, New Orleans, La., 1987), pp. 116–118.
  12. G. E. Ioup, J. W. Ioup, A. M. Amini, G. H. Rayborn, D. Wang, G. M. Wood, “Enhanced data from analytical instrumentation by deconvolution of periodically sampled signals,” in Proceedings of the Fourth International Conference on Computational Methods and Experimental Measurements, G. M. Carlomango, C. A. Brebbia, eds., Computers and Experiments in Stress Analysis (Springer-Verlag, Berlin, 1989), pp. 449–465.
  13. G. D. Tejwani, D. B. van Dyke, F. E. Bircher, D. J. Chenevert, “Emission spectra of selected SSME elements and materials,” NASA Ref. Publ. 1286 (NASA, Washington, D.C., 1992).
  14. J. D. Morrison, “On the optimum use of ionization efficiency data,” J. Chem. Phys. 39, 200–207 (1963).
    [CrossRef]
  15. G. E. Ioup, B. S. Thomas, “Smoothing and unfolding the data of beam collision experiments,” J. Chem. Phys. 46, 3959–3961 (1967).
    [CrossRef]
  16. P. A. Jansson, “Method for determining the response of a high-resolution infrared spectrometer,” J. Opt. Soc. Am. 60, 184–191 (1970).
    [CrossRef]
  17. G. M. Wood, G. H. Rayborn, J. W. Ioup, G. E. Ioup, B. T. Upchurch, S. J. Howard, “Data enhancement and analysis through mathematical deconvolution of signals from scientific measuring instruments,” in Proceedings of the International Congress on Instrumentation in Aerospace Simulation Facilities (Institute of Electrical and Electronics Engineers, New York, 1981), pp. 25–37.
  18. R. W. Schafer, R. M. Mersereau, M. A. Richards, “Constrained iterative restoration algorithm,” Proc. IEEE 69, 432–450 (1981).
    [CrossRef]
  19. P. A. Jansson, R. H. Hunt, E. K. Plyler, “Resolution enhancement of spectra,” J. Opt. Soc. Am. 60, 596–599 (1970).
    [CrossRef]
  20. H. Ni, A. M. Amini, G. E. Ioup, J. W. Ioup, “Single filter application of always-convergent iterative deconvolution to seismic data,” Bull. Am. Phys. Soc. 33, 669 (1988).
  21. G. E. Ioup, “Always-convergent iterative noise removal and deconvolution,” Bull. Am. Phys. Soc. 26, 1213 (1981).
  22. G. D. Tejwani, D. G. Gardner, D. J. Chenevert, “Approach to SSME health monitoring: materials data base and DTF plume seeding experiments,” in Proceedings of the First Annual Health Monitoring Conference for Space Propulsion Systems, S. J. Rubin, B. K. Walker, eds. (University of Cincinnati, Cincinnati, Ohio, 1989), pp. 14–15.
  23. G. D. Tejwani, “SSME (TTB) and DTFT spectral data quantitative analysis,” NASA CP 3174, in Advanced Earth-to-Orbit Propulsion Technology, R. J. Richmond, S. T. Wu, eds. (NASA, Huntsville, Ala., 1992), Vol. 1, pp. 19–21.
  24. J. W. Ioup, G. E. Ioup, G. H. Rayborn, G. M. Wood, B. T. Upchurch, “Iterative and function-continuation Fourier deconvolution methods for enhancing mass spectrometer resolution,” Int. J. Mass. Spectrom. Ion Phys. 55, 93–109 (1983).
    [CrossRef]

1990 (1)

J. Biemond, R. L. Lagendijk, R. M. Mersereau, “Iterative methods for image deblurring,” Proc. IEEE 78, 856–883 (1990).
[CrossRef]

1988 (1)

H. Ni, A. M. Amini, G. E. Ioup, J. W. Ioup, “Single filter application of always-convergent iterative deconvolution to seismic data,” Bull. Am. Phys. Soc. 33, 669 (1988).

1987 (1)

C. E. Morris, M. A. Richards, M. H. Hayes, “Iterative deconvolution algorithm with quadratic convergence,” J. Opt. Soc. Am. 4, 200–207 (1987).
[CrossRef]

1983 (2)

J. W. Ioup, G. E. Ioup, G. H. Rayborn, G. M. Wood, B. T. Upchurch, “Iterative and function-continuation Fourier deconvolution methods for enhancing mass spectrometer resolution,” Int. J. Mass. Spectrom. Ion Phys. 55, 93–109 (1983).
[CrossRef]

G. E. Ioup, J. W. Ioup, “Iterative deconvolution,” Geophysics 48, 1287–1290 (1983).
[CrossRef]

1982 (1)

L. B. J. La Coste, “Deconvolution by successive approximation,” Geophysics 47, 1724–1730 (1982).
[CrossRef]

1981 (2)

R. W. Schafer, R. M. Mersereau, M. A. Richards, “Constrained iterative restoration algorithm,” Proc. IEEE 69, 432–450 (1981).
[CrossRef]

G. E. Ioup, “Always-convergent iterative noise removal and deconvolution,” Bull. Am. Phys. Soc. 26, 1213 (1981).

1980 (1)

S. Kawata, Y. Ichioka, “Iterative image restoration for linearly degraded images. 1. Basis,” J. Opt. Soc. Am. 70, 762–768 (1980); S. Kawata, Y. Ichioka, “Iterative image restoration for linearly degraded images. II. Reblurring procedure,” J. Opt. Soc. Am. 70, 768–772 (1980).
[CrossRef]

1976 (1)

N. R. Hill, G. E. Ioup, “Convergence of the van Cittert iterative method of deconvolution,” J. Opt. Soc. Am. 66, 487–489 (1976).
[CrossRef]

1970 (2)

P. A. Jansson, R. H. Hunt, E. K. Plyler, “Resolution enhancement of spectra,” J. Opt. Soc. Am. 60, 596–599 (1970).
[CrossRef]

P. A. Jansson, “Method for determining the response of a high-resolution infrared spectrometer,” J. Opt. Soc. Am. 60, 184–191 (1970).
[CrossRef]

1967 (1)

G. E. Ioup, B. S. Thomas, “Smoothing and unfolding the data of beam collision experiments,” J. Chem. Phys. 46, 3959–3961 (1967).
[CrossRef]

1963 (1)

J. D. Morrison, “On the optimum use of ionization efficiency data,” J. Chem. Phys. 39, 200–207 (1963).
[CrossRef]

1954 (1)

R. N. Bracewell, J. A. Roberts, “Aerial smoothing in radio astronomy,” Aust. J. Phys. 7, 615–640 (1954).
[CrossRef]

1931 (1)

P. H. van Cittert, “Zum Einfluss der spaltbreite auf die intensitatsverteilung in spektrallinien,” Z. Phys. 69, 298–308 (1931).
[CrossRef]

Amini, A. M.

H. Ni, A. M. Amini, G. E. Ioup, J. W. Ioup, “Single filter application of always-convergent iterative deconvolution to seismic data,” Bull. Am. Phys. Soc. 33, 669 (1988).

A. M. Amini, G. E. Ioup, J. W. Ioup, R. Powe, “Improved deconvolution for low signal-to-noise ratio seismic data,” in Proceedings of the Seventeenth International Symposium on Applied Identification Modeling and Simulation, R. E. Trahan, ed. (International Association of Science and Technology for Development, New Orleans, La., 1987), pp. 116–118.

G. E. Ioup, J. W. Ioup, A. M. Amini, G. H. Rayborn, D. Wang, G. M. Wood, “Enhanced data from analytical instrumentation by deconvolution of periodically sampled signals,” in Proceedings of the Fourth International Conference on Computational Methods and Experimental Measurements, G. M. Carlomango, C. A. Brebbia, eds., Computers and Experiments in Stress Analysis (Springer-Verlag, Berlin, 1989), pp. 449–465.

Biemond, J.

J. Biemond, R. L. Lagendijk, R. M. Mersereau, “Iterative methods for image deblurring,” Proc. IEEE 78, 856–883 (1990).
[CrossRef]

Bircher, F. E.

G. D. Tejwani, D. B. van Dyke, F. E. Bircher, D. J. Chenevert, “Emission spectra of selected SSME elements and materials,” NASA Ref. Publ. 1286 (NASA, Washington, D.C., 1992).

Bracewell, R. N.

R. N. Bracewell, J. A. Roberts, “Aerial smoothing in radio astronomy,” Aust. J. Phys. 7, 615–640 (1954).
[CrossRef]

Chenevert, D. J.

G. D. Tejwani, D. B. van Dyke, F. E. Bircher, D. J. Chenevert, “Emission spectra of selected SSME elements and materials,” NASA Ref. Publ. 1286 (NASA, Washington, D.C., 1992).

G. D. Tejwani, D. G. Gardner, D. J. Chenevert, “Approach to SSME health monitoring: materials data base and DTF plume seeding experiments,” in Proceedings of the First Annual Health Monitoring Conference for Space Propulsion Systems, S. J. Rubin, B. K. Walker, eds. (University of Cincinnati, Cincinnati, Ohio, 1989), pp. 14–15.

Frieden, B. R.

B. R. Frieden, “Image enhancement and restoration,” in Picture Processing and Digital Filtering, T. S. Huang, ed., Vol. 6 of Topics in Applied Physics (Springer-Verlag, Berlin, 1975), pp. 177–248.
[CrossRef]

Gardner, D. G.

G. D. Tejwani, D. G. Gardner, D. J. Chenevert, “Approach to SSME health monitoring: materials data base and DTF plume seeding experiments,” in Proceedings of the First Annual Health Monitoring Conference for Space Propulsion Systems, S. J. Rubin, B. K. Walker, eds. (University of Cincinnati, Cincinnati, Ohio, 1989), pp. 14–15.

Hayes, M. H.

C. E. Morris, M. A. Richards, M. H. Hayes, “Iterative deconvolution algorithm with quadratic convergence,” J. Opt. Soc. Am. 4, 200–207 (1987).
[CrossRef]

Hill, N. R.

N. R. Hill, G. E. Ioup, “Convergence of the van Cittert iterative method of deconvolution,” J. Opt. Soc. Am. 66, 487–489 (1976).
[CrossRef]

Howard, S. J.

G. M. Wood, G. H. Rayborn, J. W. Ioup, G. E. Ioup, B. T. Upchurch, S. J. Howard, “Data enhancement and analysis through mathematical deconvolution of signals from scientific measuring instruments,” in Proceedings of the International Congress on Instrumentation in Aerospace Simulation Facilities (Institute of Electrical and Electronics Engineers, New York, 1981), pp. 25–37.

Hunt, R. H.

Ichioka, Y.

S. Kawata, Y. Ichioka, “Iterative image restoration for linearly degraded images. 1. Basis,” J. Opt. Soc. Am. 70, 762–768 (1980); S. Kawata, Y. Ichioka, “Iterative image restoration for linearly degraded images. II. Reblurring procedure,” J. Opt. Soc. Am. 70, 768–772 (1980).
[CrossRef]

Ioup, G. E.

H. Ni, A. M. Amini, G. E. Ioup, J. W. Ioup, “Single filter application of always-convergent iterative deconvolution to seismic data,” Bull. Am. Phys. Soc. 33, 669 (1988).

J. W. Ioup, G. E. Ioup, G. H. Rayborn, G. M. Wood, B. T. Upchurch, “Iterative and function-continuation Fourier deconvolution methods for enhancing mass spectrometer resolution,” Int. J. Mass. Spectrom. Ion Phys. 55, 93–109 (1983).
[CrossRef]

G. E. Ioup, J. W. Ioup, “Iterative deconvolution,” Geophysics 48, 1287–1290 (1983).
[CrossRef]

G. E. Ioup, “Always-convergent iterative noise removal and deconvolution,” Bull. Am. Phys. Soc. 26, 1213 (1981).

N. R. Hill, G. E. Ioup, “Convergence of the van Cittert iterative method of deconvolution,” J. Opt. Soc. Am. 66, 487–489 (1976).
[CrossRef]

G. E. Ioup, B. S. Thomas, “Smoothing and unfolding the data of beam collision experiments,” J. Chem. Phys. 46, 3959–3961 (1967).
[CrossRef]

G. E. Ioup, J. W. Ioup, A. M. Amini, G. H. Rayborn, D. Wang, G. M. Wood, “Enhanced data from analytical instrumentation by deconvolution of periodically sampled signals,” in Proceedings of the Fourth International Conference on Computational Methods and Experimental Measurements, G. M. Carlomango, C. A. Brebbia, eds., Computers and Experiments in Stress Analysis (Springer-Verlag, Berlin, 1989), pp. 449–465.

A. M. Amini, G. E. Ioup, J. W. Ioup, R. Powe, “Improved deconvolution for low signal-to-noise ratio seismic data,” in Proceedings of the Seventeenth International Symposium on Applied Identification Modeling and Simulation, R. E. Trahan, ed. (International Association of Science and Technology for Development, New Orleans, La., 1987), pp. 116–118.

G. M. Wood, G. H. Rayborn, J. W. Ioup, G. E. Ioup, B. T. Upchurch, S. J. Howard, “Data enhancement and analysis through mathematical deconvolution of signals from scientific measuring instruments,” in Proceedings of the International Congress on Instrumentation in Aerospace Simulation Facilities (Institute of Electrical and Electronics Engineers, New York, 1981), pp. 25–37.

Ioup, J. W.

H. Ni, A. M. Amini, G. E. Ioup, J. W. Ioup, “Single filter application of always-convergent iterative deconvolution to seismic data,” Bull. Am. Phys. Soc. 33, 669 (1988).

J. W. Ioup, G. E. Ioup, G. H. Rayborn, G. M. Wood, B. T. Upchurch, “Iterative and function-continuation Fourier deconvolution methods for enhancing mass spectrometer resolution,” Int. J. Mass. Spectrom. Ion Phys. 55, 93–109 (1983).
[CrossRef]

G. E. Ioup, J. W. Ioup, “Iterative deconvolution,” Geophysics 48, 1287–1290 (1983).
[CrossRef]

A. M. Amini, G. E. Ioup, J. W. Ioup, R. Powe, “Improved deconvolution for low signal-to-noise ratio seismic data,” in Proceedings of the Seventeenth International Symposium on Applied Identification Modeling and Simulation, R. E. Trahan, ed. (International Association of Science and Technology for Development, New Orleans, La., 1987), pp. 116–118.

G. E. Ioup, J. W. Ioup, A. M. Amini, G. H. Rayborn, D. Wang, G. M. Wood, “Enhanced data from analytical instrumentation by deconvolution of periodically sampled signals,” in Proceedings of the Fourth International Conference on Computational Methods and Experimental Measurements, G. M. Carlomango, C. A. Brebbia, eds., Computers and Experiments in Stress Analysis (Springer-Verlag, Berlin, 1989), pp. 449–465.

G. M. Wood, G. H. Rayborn, J. W. Ioup, G. E. Ioup, B. T. Upchurch, S. J. Howard, “Data enhancement and analysis through mathematical deconvolution of signals from scientific measuring instruments,” in Proceedings of the International Congress on Instrumentation in Aerospace Simulation Facilities (Institute of Electrical and Electronics Engineers, New York, 1981), pp. 25–37.

Jansson, P. A.

P. A. Jansson, “Method for determining the response of a high-resolution infrared spectrometer,” J. Opt. Soc. Am. 60, 184–191 (1970).
[CrossRef]

P. A. Jansson, R. H. Hunt, E. K. Plyler, “Resolution enhancement of spectra,” J. Opt. Soc. Am. 60, 596–599 (1970).
[CrossRef]

P. A. Jansson, Deconvolution with Application in Spectroscopy (Academic, New York, 1984).

Kawata, S.

S. Kawata, Y. Ichioka, “Iterative image restoration for linearly degraded images. 1. Basis,” J. Opt. Soc. Am. 70, 762–768 (1980); S. Kawata, Y. Ichioka, “Iterative image restoration for linearly degraded images. II. Reblurring procedure,” J. Opt. Soc. Am. 70, 768–772 (1980).
[CrossRef]

La Coste, L. B. J.

L. B. J. La Coste, “Deconvolution by successive approximation,” Geophysics 47, 1724–1730 (1982).
[CrossRef]

Lagendijk, R. L.

J. Biemond, R. L. Lagendijk, R. M. Mersereau, “Iterative methods for image deblurring,” Proc. IEEE 78, 856–883 (1990).
[CrossRef]

Mersereau, R. M.

J. Biemond, R. L. Lagendijk, R. M. Mersereau, “Iterative methods for image deblurring,” Proc. IEEE 78, 856–883 (1990).
[CrossRef]

R. W. Schafer, R. M. Mersereau, M. A. Richards, “Constrained iterative restoration algorithm,” Proc. IEEE 69, 432–450 (1981).
[CrossRef]

Morris, C. E.

C. E. Morris, M. A. Richards, M. H. Hayes, “Iterative deconvolution algorithm with quadratic convergence,” J. Opt. Soc. Am. 4, 200–207 (1987).
[CrossRef]

Morrison, J. D.

J. D. Morrison, “On the optimum use of ionization efficiency data,” J. Chem. Phys. 39, 200–207 (1963).
[CrossRef]

Ni, H.

H. Ni, A. M. Amini, G. E. Ioup, J. W. Ioup, “Single filter application of always-convergent iterative deconvolution to seismic data,” Bull. Am. Phys. Soc. 33, 669 (1988).

Plyler, E. K.

Powe, R.

A. M. Amini, G. E. Ioup, J. W. Ioup, R. Powe, “Improved deconvolution for low signal-to-noise ratio seismic data,” in Proceedings of the Seventeenth International Symposium on Applied Identification Modeling and Simulation, R. E. Trahan, ed. (International Association of Science and Technology for Development, New Orleans, La., 1987), pp. 116–118.

Rayborn, G. H.

J. W. Ioup, G. E. Ioup, G. H. Rayborn, G. M. Wood, B. T. Upchurch, “Iterative and function-continuation Fourier deconvolution methods for enhancing mass spectrometer resolution,” Int. J. Mass. Spectrom. Ion Phys. 55, 93–109 (1983).
[CrossRef]

G. M. Wood, G. H. Rayborn, J. W. Ioup, G. E. Ioup, B. T. Upchurch, S. J. Howard, “Data enhancement and analysis through mathematical deconvolution of signals from scientific measuring instruments,” in Proceedings of the International Congress on Instrumentation in Aerospace Simulation Facilities (Institute of Electrical and Electronics Engineers, New York, 1981), pp. 25–37.

G. E. Ioup, J. W. Ioup, A. M. Amini, G. H. Rayborn, D. Wang, G. M. Wood, “Enhanced data from analytical instrumentation by deconvolution of periodically sampled signals,” in Proceedings of the Fourth International Conference on Computational Methods and Experimental Measurements, G. M. Carlomango, C. A. Brebbia, eds., Computers and Experiments in Stress Analysis (Springer-Verlag, Berlin, 1989), pp. 449–465.

Richards, M. A.

C. E. Morris, M. A. Richards, M. H. Hayes, “Iterative deconvolution algorithm with quadratic convergence,” J. Opt. Soc. Am. 4, 200–207 (1987).
[CrossRef]

R. W. Schafer, R. M. Mersereau, M. A. Richards, “Constrained iterative restoration algorithm,” Proc. IEEE 69, 432–450 (1981).
[CrossRef]

Roberts, J. A.

R. N. Bracewell, J. A. Roberts, “Aerial smoothing in radio astronomy,” Aust. J. Phys. 7, 615–640 (1954).
[CrossRef]

Schafer, R. W.

R. W. Schafer, R. M. Mersereau, M. A. Richards, “Constrained iterative restoration algorithm,” Proc. IEEE 69, 432–450 (1981).
[CrossRef]

Tejwani, G. D.

G. D. Tejwani, D. G. Gardner, D. J. Chenevert, “Approach to SSME health monitoring: materials data base and DTF plume seeding experiments,” in Proceedings of the First Annual Health Monitoring Conference for Space Propulsion Systems, S. J. Rubin, B. K. Walker, eds. (University of Cincinnati, Cincinnati, Ohio, 1989), pp. 14–15.

G. D. Tejwani, “SSME (TTB) and DTFT spectral data quantitative analysis,” NASA CP 3174, in Advanced Earth-to-Orbit Propulsion Technology, R. J. Richmond, S. T. Wu, eds. (NASA, Huntsville, Ala., 1992), Vol. 1, pp. 19–21.

G. D. Tejwani, D. B. van Dyke, F. E. Bircher, D. J. Chenevert, “Emission spectra of selected SSME elements and materials,” NASA Ref. Publ. 1286 (NASA, Washington, D.C., 1992).

Thomas, B. S.

G. E. Ioup, B. S. Thomas, “Smoothing and unfolding the data of beam collision experiments,” J. Chem. Phys. 46, 3959–3961 (1967).
[CrossRef]

Upchurch, B. T.

J. W. Ioup, G. E. Ioup, G. H. Rayborn, G. M. Wood, B. T. Upchurch, “Iterative and function-continuation Fourier deconvolution methods for enhancing mass spectrometer resolution,” Int. J. Mass. Spectrom. Ion Phys. 55, 93–109 (1983).
[CrossRef]

G. M. Wood, G. H. Rayborn, J. W. Ioup, G. E. Ioup, B. T. Upchurch, S. J. Howard, “Data enhancement and analysis through mathematical deconvolution of signals from scientific measuring instruments,” in Proceedings of the International Congress on Instrumentation in Aerospace Simulation Facilities (Institute of Electrical and Electronics Engineers, New York, 1981), pp. 25–37.

van Cittert, P. H.

P. H. van Cittert, “Zum Einfluss der spaltbreite auf die intensitatsverteilung in spektrallinien,” Z. Phys. 69, 298–308 (1931).
[CrossRef]

van Dyke, D. B.

G. D. Tejwani, D. B. van Dyke, F. E. Bircher, D. J. Chenevert, “Emission spectra of selected SSME elements and materials,” NASA Ref. Publ. 1286 (NASA, Washington, D.C., 1992).

Wang, D.

G. E. Ioup, J. W. Ioup, A. M. Amini, G. H. Rayborn, D. Wang, G. M. Wood, “Enhanced data from analytical instrumentation by deconvolution of periodically sampled signals,” in Proceedings of the Fourth International Conference on Computational Methods and Experimental Measurements, G. M. Carlomango, C. A. Brebbia, eds., Computers and Experiments in Stress Analysis (Springer-Verlag, Berlin, 1989), pp. 449–465.

Wood, G. M.

J. W. Ioup, G. E. Ioup, G. H. Rayborn, G. M. Wood, B. T. Upchurch, “Iterative and function-continuation Fourier deconvolution methods for enhancing mass spectrometer resolution,” Int. J. Mass. Spectrom. Ion Phys. 55, 93–109 (1983).
[CrossRef]

G. M. Wood, G. H. Rayborn, J. W. Ioup, G. E. Ioup, B. T. Upchurch, S. J. Howard, “Data enhancement and analysis through mathematical deconvolution of signals from scientific measuring instruments,” in Proceedings of the International Congress on Instrumentation in Aerospace Simulation Facilities (Institute of Electrical and Electronics Engineers, New York, 1981), pp. 25–37.

G. E. Ioup, J. W. Ioup, A. M. Amini, G. H. Rayborn, D. Wang, G. M. Wood, “Enhanced data from analytical instrumentation by deconvolution of periodically sampled signals,” in Proceedings of the Fourth International Conference on Computational Methods and Experimental Measurements, G. M. Carlomango, C. A. Brebbia, eds., Computers and Experiments in Stress Analysis (Springer-Verlag, Berlin, 1989), pp. 449–465.

Aust. J. Phys. (1)

R. N. Bracewell, J. A. Roberts, “Aerial smoothing in radio astronomy,” Aust. J. Phys. 7, 615–640 (1954).
[CrossRef]

Bull. Am. Phys. Soc. (1)

G. E. Ioup, “Always-convergent iterative noise removal and deconvolution,” Bull. Am. Phys. Soc. 26, 1213 (1981).

Bull. Am. Phys. Soc. (1)

H. Ni, A. M. Amini, G. E. Ioup, J. W. Ioup, “Single filter application of always-convergent iterative deconvolution to seismic data,” Bull. Am. Phys. Soc. 33, 669 (1988).

Geophysics (2)

L. B. J. La Coste, “Deconvolution by successive approximation,” Geophysics 47, 1724–1730 (1982).
[CrossRef]

G. E. Ioup, J. W. Ioup, “Iterative deconvolution,” Geophysics 48, 1287–1290 (1983).
[CrossRef]

Int. J. Mass. Spectrom. Ion Phys. (1)

J. W. Ioup, G. E. Ioup, G. H. Rayborn, G. M. Wood, B. T. Upchurch, “Iterative and function-continuation Fourier deconvolution methods for enhancing mass spectrometer resolution,” Int. J. Mass. Spectrom. Ion Phys. 55, 93–109 (1983).
[CrossRef]

J. Opt. Soc. Am. (1)

P. A. Jansson, “Method for determining the response of a high-resolution infrared spectrometer,” J. Opt. Soc. Am. 60, 184–191 (1970).
[CrossRef]

J. Chem. Phys. (1)

G. E. Ioup, B. S. Thomas, “Smoothing and unfolding the data of beam collision experiments,” J. Chem. Phys. 46, 3959–3961 (1967).
[CrossRef]

J. Chem. Phys. (1)

J. D. Morrison, “On the optimum use of ionization efficiency data,” J. Chem. Phys. 39, 200–207 (1963).
[CrossRef]

J. Opt. Soc. Am. (2)

N. R. Hill, G. E. Ioup, “Convergence of the van Cittert iterative method of deconvolution,” J. Opt. Soc. Am. 66, 487–489 (1976).
[CrossRef]

S. Kawata, Y. Ichioka, “Iterative image restoration for linearly degraded images. 1. Basis,” J. Opt. Soc. Am. 70, 762–768 (1980); S. Kawata, Y. Ichioka, “Iterative image restoration for linearly degraded images. II. Reblurring procedure,” J. Opt. Soc. Am. 70, 768–772 (1980).
[CrossRef]

J. Opt. Soc. Am. (1)

C. E. Morris, M. A. Richards, M. H. Hayes, “Iterative deconvolution algorithm with quadratic convergence,” J. Opt. Soc. Am. 4, 200–207 (1987).
[CrossRef]

J. Opt. Soc. Am. (1)

Proc. IEEE (2)

J. Biemond, R. L. Lagendijk, R. M. Mersereau, “Iterative methods for image deblurring,” Proc. IEEE 78, 856–883 (1990).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Magnitude versus index number for (a) the 24 points input function, f, and (b) the convolution of (a) with a wide symmetrical Gaussian.

Fig. 2
Fig. 2

MSE versus iteration number with the VCSIT for deconvolution of (a) Fig. 1(b) and (b) Fig. 1(b) plus a small amount of Gaussian-distributed noise.

Fig. 3
Fig. 3

Intensity versus index number for the measured optical multichannel analyzer output corresponding to the 349.34-nm emission line of the element nickel: (a) display of the original data, (b) the same data smoothed by the FT interpolation technique.

Fig. 4
Fig. 4

Intensity versus index number for deconvolution of Fig. 3(b) with 10 iterations of (a) the VCSIT [Eq. (12)] with S = 1 and (b) with 10 iterations of the reblurring procedure [Eq. (6)].

Equations (20)

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h ( x ) = f ( u ) g ( x - u ) d u = f * g ,
F ( υ ) = - f ( x ) exp ( - i 2 π υ x ) d x ,
F n = F n - 1 + ( H - G F n - 1 ) , n = 1 , 2 , 3 , , ,
F n = [ 1 + ( 1 - G ) + ( 1 - G ) 2 + ( 1 - G ) 3 + ] H .
F n = [ 1 - ( 1 - G ) n + 1 ] ( H / G ) .
F n = F n - 1 + ( H r - F n - 1 G r ) , n = 1 , 2 , 3 , , ,
G r = G G - = G 2 , H r = H G - , F 0 = H r ,
F k = ( 2 F k - 1 - G k - 1 F k - 1 ) , n = 1 , 2 , 3 , , ,
G k = 2 G k - 1 - G k - 1 2 , k = 1 , 2 , 3 , , , F 0 = H , G 0 = G .
F k = F k - 1 V k = V 1 V 2 V 3 V k H ,
V k = ( 2 - G k - 1 ) , k = 1 , 2 , 3 , , .
F k = [ 1 - ( 1 - G ) 2 k ] ( H / G ) .
F k = H s + F k - 1 G s , k = 1 , 2 , 3 , , ,
H s = H ( 1 - G s ) / G , F 0 = H s ,
G s = ( 1 - R ) S .
F n = F n - 1 + ( H a - F n - 1 G a ) , n = 1 , 2 , 3 , , ,
H a = ( H G a / G ) = H exp ( - i θ ) , G a = ( G r ) 1 / 2 , F 0 = H a ,
F k = ( 1 + G s + G s 2 + G s 3 + + G s k ) H s .
F k = ( 1 - G s k + 1 1 - G s ) H s .
F k = [ 1 - ( 1 - G ) s ( k + 1 ) ] ( H / G ) ,

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