Abstract

In previous work, we introduced a dynamic range compression-based technique for image correction using nonlinear deconvolution; the impulse response of the distortion function and the distorted image are jointly transformed to pump a clean reference beam in a photorefractive two-beam coupling arrangement. The Fourier transform of the pumped reference beam contains the deconvolved image and its conjugate. Here we extend our work to spectrally variable dynamic range compression. This approach allows the retrieval of distorted signals embedded in a very high noise environment and does not require one to work with a very high beam ratio as in our previous work. Resolution recovery of blurred noisy images is demonstrated for several different types of image blur.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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2006

2004

J. Khoury, P. D. Gianino, and C. L. Woods, "Companding nonlinear correlators," Proc. SPIE 5362, 160-177 (2004).
[CrossRef]

B. Haji-Saeed, D. Pyburn, R. Leon, S. K. Sengupta, W. Goodhue, M. Testorf, J. Kierstead, J. Khoury, and C. L. Woods, "Real-time holographic deconvolution for one-way image transmission through distorting media," Opt. Eng. 43, 1862-1866 (2004).
[CrossRef]

1998

M. S. Alam, "Deblurring using fringe-adjusted joint transform correlation," Opt. Eng. 37, 556-564 (1998).
[CrossRef]

M. S. Alam, "Image enhancement using joint transform correlation," in Optical Pattern Recognition IX; D. P. Casasent, T.-H. Chao, eds., Proc. SPIE 3386, 190-201 (1998).
[CrossRef]

J. Khoury, G. Asimellis, P. D. Gianino, and C. L. Woods, "Nonlinear compansive noise reduction in joint transform correlator," Opt. Eng. 37, 66-74 (1998).
[CrossRef]

1996

1995

1994

1992

1991

1966

Appl. Opt.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Eng.

M. S. Alam, "Deblurring using fringe-adjusted joint transform correlation," Opt. Eng. 37, 556-564 (1998).
[CrossRef]

B. Haji-Saeed, D. Pyburn, R. Leon, S. K. Sengupta, W. Goodhue, M. Testorf, J. Kierstead, J. Khoury, and C. L. Woods, "Real-time holographic deconvolution for one-way image transmission through distorting media," Opt. Eng. 43, 1862-1866 (2004).
[CrossRef]

J. Khoury, G. Asimellis, P. D. Gianino, and C. L. Woods, "Nonlinear compansive noise reduction in joint transform correlator," Opt. Eng. 37, 66-74 (1998).
[CrossRef]

Opt. Lett.

Proc. SPIE

M. S. Alam, "Image enhancement using joint transform correlation," in Optical Pattern Recognition IX; D. P. Casasent, T.-H. Chao, eds., Proc. SPIE 3386, 190-201 (1998).
[CrossRef]

J. Khoury, P. D. Gianino, and C. L. Woods, "Companding nonlinear correlators," Proc. SPIE 5362, 160-177 (2004).
[CrossRef]

Other

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signal and Noise (McGraw-Hill, 1958).

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice-Hall, 2002).

M. Schwartz, W. Bennet, and S. Stein, Communication Systems and Techniques (McGraw-Hill, 1966), Chap. 4, pp. 213-216; Chap. 6, p. 247.

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Figures (5)

Fig. 1
Fig. 1

Schematic illustrating spectrally variable nonlinear deconvolution via photorefractive two-beam coupling.

Fig. 2
Fig. 2

Input–output nonlinear transfer function of photorefractive two-beam coupling.

Fig. 3
Fig. 3

Computer simulation of image deconvolution via two-beam coupling in the linear range. A, Joint image of the input and the point source. B, Output joint image, which consists of a distorted noisy input and the impulse response of the distortion medium (atmospheric turbulence). C, Corrected image in the linear range.

Fig. 4
Fig. 4

Computer simulation for nonlinear deconvolution for spectrally variable and invariant. A, Blurred image and the aberration impulse response function; B, corrected image and its complex conjugate using spectrally invariant method with beam ratio m = 1 ; C, corrected image and its complex conjugate using spectrally invariant method with beam ratio m = 10 5 ; D, corrected image and its complex conjugate using spectrally variable method with beam ratio m = 1 .

Fig. 5
Fig. 5

Computer simulation of the first-order ( k = 1 ) nonlinear deconvolution for spectrally variable and invariant via two beam coupling. A, Distorted image with additive low-frequency noise using the motion distortion function; B, corrected versions of image using constant dynamic range compression with beam ratio m = 1 ; C, corrected image with same constant dynamic range compression method with m = 10 5 ; D, corresponding corrected images using spectrally variable dynamic range compression method for m = 1 . A’, Distorted image with additive low-frequency noise using the atmospheric turbulence distortion function; B’, corrected versions of image using constant dynamic range compression with beam ratio m = 1 ; C’, corrected image with same constant dynamic range compression method with m = 10 5 ; D’, corresponding corrected images using spectrally variable dynamic range compression method for m = 1 . A”, Distorted image with additive low-frequency noise using the misfocusing distortion function; B”, corrected versions of image using constant dynamic range compression with beam ratio m = 1 ; C”, corrected image with same constant dynamic range compression method with m = 10 5 ; D”, corresponding corrected images using spectrally variable dynamic range compression method for m = 1 .

Equations (6)

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A 3 = | A 2 | 2 | H ( v x , v y ) + H ( v x , v y ) F ( v x , v y ) | 2 A 1 I ( v x , v y ) | A 2 | 2 | H ( v x , v y ) + H ( v x , v y ) F ( v x , v y ) | 2 + | A 1 | 2 I ( v x , v y ) ,
= m I ( v x , v y ) | H ( v x , v y ) + H ( v x , v y ) F ( v x , v y ) | 2 A 1 m I ( v x , v y ) | H ( v x , v y ) + H ( v x , v y ) F ( v x , v y ) | 2 + 1 ,
A 3 = m | H ( v x , v y ) + H ( v x , v y ) F ( v x , v y ) | 2 A 1 I ( v x , v y ) = m ( | H ( v x , v y ) | 2 + | H ( v x , v y ) F ( v x , v y ) | 2 + F ( v x , v y ) H ( v x , v y ) H * ( v x , v y ) + F * ( v x , v y ) H ( v x , v y ) H * ( v x , v y ) ) A 1 I ( v x , v y ) .
A 3 = m | H ( v x , v y ) + H ( v x , v y ) F ( v x , v y ) | 2 A 1 I ( v x , v y ) = m ( 1 + | F ( v x , v y ) | 2 + F ( v x , v y ) + F * ( v x , v y ) ) A 1 I ( v x , v y ) .
A 3 = H k ( v x , v y ) cos [ 2 k y 0 v y + k ϕ F ] ,
H k ( v x , v y ) = 1 { [ 1 + m ( | H ( v x , v y ) | | H ( v x , v y ) F ( v x , v y ) | ) 2 ] [ 1 + m ( | H ( v x , v y ) | + | H ( v x , v y ) F ( v x , v y ) | ) 2 ] } 1 / 2 × ( 2 m H ( v x , v y ) H * ( v x , v y ) F ( v x , v y ) 1 + m ( | ( v x , v y ) | 2 + | H ( v x , v y ) | 2 | F ( v x , v y ) | 2 ) + { [ 1 + m ( | H ( v x , v y ) | | H ( v x , v y ) F ( v x , v y ) | ) 2 ] [ 1 + m ( | H ( v x , v y ) | + | H ( v x , v y ) F ( v x , v y ) | ) 2 ] } 1 / 2 ) k .

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