Abstract

We demonstrate the use of image support constraints in a noise-reduction algorithm. Previous work has revealed serious limits to the use of support if image noise is wide-sense stationary in the frequency domain; we use simulation and numerical calculations to show these limits are removed for nonstationary noise generated by inverse-filtering adaptive optics image spectra. To quantify the noise reduction, we plot fractional noise removed by the proposed algorithm over a range of support sizes. We repeat this calculation for other noise sources with varying degrees of stationarity.

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References

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  1. C.K. Rushforth, "Signal restoration, functional analysis, and Fredholm integral equations of the first kind," in Image Recovery: Theory and Application, H. Stark, ed. (Academic Press, San Diego, CA, 1987), p. 46
  2. C.L. Matson, "Variance reduction in Fourier spectra and their corresponding images with the use of support constraints," J. Opt. Soc. Am. A 11, p. 97 (1994)
    [CrossRef]
  3. A. Papoulis, "Spectral reprentation of random signals," in Probability, Random Variables, and Stochastic Processes, (McGraw-Hill, New York 1991), p. 418
  4. M.C. Roggemann, E.L. Caudill, D.W. Tyler, M.J. Fox, M.A. Von Bokern, and C.L. Matson, "Compensated speckle imaging: Theory and experimental results," Appl. Opt. 33, 3099 (1994)
    [CrossRef] [PubMed]
  5. M.C. Roggemann, D.W. Tyler, and M.F. Bilmont, "Linear reconstruction of compensated images: theory and experimental results," Appl. Opt. 31, 7429 (1992)
    [CrossRef] [PubMed]
  6. C.L. Matson and M.C. Roggemann, "Noise reduction in adaptive optics imagery with the use of support constraints," Appl. Opt. 34, 767 (1995)
    [CrossRef] [PubMed]
  7. C.L. Matson, "Fourier spectrum extrapolation and enhancement using support constraints," IEEE Trans. Signal Process. 42, 156 (1994)
    [CrossRef]

Other (7)

C.K. Rushforth, "Signal restoration, functional analysis, and Fredholm integral equations of the first kind," in Image Recovery: Theory and Application, H. Stark, ed. (Academic Press, San Diego, CA, 1987), p. 46

C.L. Matson, "Variance reduction in Fourier spectra and their corresponding images with the use of support constraints," J. Opt. Soc. Am. A 11, p. 97 (1994)
[CrossRef]

A. Papoulis, "Spectral reprentation of random signals," in Probability, Random Variables, and Stochastic Processes, (McGraw-Hill, New York 1991), p. 418

M.C. Roggemann, E.L. Caudill, D.W. Tyler, M.J. Fox, M.A. Von Bokern, and C.L. Matson, "Compensated speckle imaging: Theory and experimental results," Appl. Opt. 33, 3099 (1994)
[CrossRef] [PubMed]

M.C. Roggemann, D.W. Tyler, and M.F. Bilmont, "Linear reconstruction of compensated images: theory and experimental results," Appl. Opt. 31, 7429 (1992)
[CrossRef] [PubMed]

C.L. Matson and M.C. Roggemann, "Noise reduction in adaptive optics imagery with the use of support constraints," Appl. Opt. 34, 767 (1995)
[CrossRef] [PubMed]

C.L. Matson, "Fourier spectrum extrapolation and enhancement using support constraints," IEEE Trans. Signal Process. 42, 156 (1994)
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Ensemble noise PSD for the real spectrum of deconvolved image data generated using 21-actuator simulated adaptive optics.

Fig. 2.
Fig. 2.

Fractional noise removed with one step of an interative noise reduction algorithm using support constraints as a function of support diameter.

Fig. 3.
Fig. 3.

Ensemble noise PSD for the real spectrum of image data generated with white Gaussian noise to model the effect of CCD read noise.

Fig. 4.
Fig. 4.

Ensemble noise PSD for the real spectrum of image data generated with white Gaussian noise added to adaptive optics noise.

Fig. 5.
Fig. 5.

Image realization corrupted by white Gaussian (CCD) noise.

Fig. 6.
Fig. 6.

Image realization corrupted by CCD noise and adaptive optics noise.

Fig. 7.
Fig. 7.

Cross-section of long-exposure PSF for ro = 10cm turbulence compensated by a 45-actuator AO system.

Equations (5)

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I c ( u ) = d u I ( v ) W ( u v ) ,
F ( u , u c ) = 1 u u c ,
PSD ( u ) R = < Re { I ( u ) } Re { I ¯ ( u ) } 2 >
PSD ( u ) I = < Im { I ( u ) } Im { I ¯ ( u ) } 2 > ,
F R ( I ) = d u [ PSD ( u ) R ( I ) c ) PSD ( u ) R ( I ) u ] > 0 d u PSD ( u ) R ( I ) u ,

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