Abstract

We describe how to transfer the characteristic functional of an object model through a noisy, discrete imaging system to arrive at the characteristic function of the images. Our method can also incorporate linear post-processing of the images.

© 2002 Optical Society of America

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References

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  1. H. H. Barrett, �??Objective assessment of image quality: E.ects of quantum noise and object variability,�?? J. Opt. Soc. Am. A 7, 1266�??1278 (1990).
    [CrossRef] [PubMed]
  2. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1991).
  3. H. H. Barrett, C. Abbey, B. Gallas, and M. Eckstein, �??Stabilized estimates of Hotelling-observer detection performance in patient-structured noise,�?? in SPIE Medical Imaging: Image Perception, ed. H. L. Kundel, Proc. SPIE 3340, 27�??43 (1998).
    [CrossRef]

J. Opt. Soc. Am. A (1)

Proc. SPIE (1)

H. H. Barrett, C. Abbey, B. Gallas, and M. Eckstein, �??Stabilized estimates of Hotelling-observer detection performance in patient-structured noise,�?? in SPIE Medical Imaging: Image Perception, ed. H. L. Kundel, Proc. SPIE 3340, 27�??43 (1998).
[CrossRef]

Other (1)

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1991).

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Equations (23)

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g = H f + n ,
g ¯ = H f .
Ψ f ( ξ ) = exp ( 2 πi ξ f ) f
Ψ g ¯ ( ρ ) = exp ( 2 πi ρ g ¯ ) g ¯
Ψ g ¯ ( ρ ) = exp ( 2 πi ρ H f ) f
= exp ( 2 πi ( H ρ ) f ) f .
Ψ g ¯ ( ρ ) = Ψ f ( H ρ ) .
Ψ n ( ρ ) = exp ( 2 π 2 ρ ) .
Ψ g ( ρ ) = Ψ f ( H ρ ) Ψ n ( ρ ) .
pr ( g g ¯ ) = m = 1 M exp ( g ¯ m ) g ¯ m g m g m ! ,
pr ( g ) = pr ( g g ¯ ) pr ( g ¯ ) d g ¯
= pr ( g ¯ ) m = 1 M exp ( g ¯ m ) g ¯ m g m g m ! d g . ¯
Ψ g ( ρ ) = exp ( 2 πi ρ g ) g
= g exp ( 2 πi m = 1 M ρ m g m ) pr ( g )
= g exp ( 2 πi m = 1 M ρ m g m ) d g ¯ pr ( g ¯ ) m = 1 M exp ( g ¯ m ) g ¯ m g m g m ! ,
g = g 1 = 0 g 2 = 0 g M = 0 .
Ψ g ( ρ ) = d g ¯ pr ( g ¯ ) g m = 1 M exp ( g ¯ m 2 πi ρ m g m ) g ¯ m g m g m !
= d g ¯ pr ( g ¯ ) m = 1 M exp ( g ¯ m ) g m = 0 ( exp ( ln ( g ¯ m 2 πi ρ m ) ) ) g m g m !
Ψ g ( ρ ) = d g ¯ pr ( g ¯ ) m = 1 M exp ( g ¯ m + e ln ( g ¯ m ) 2 πi ρ m ) ,
= d g ¯ pr ( g ¯ ) m = 1 M exp ( g ¯ m + g ¯ m e 2 πi ρ m ) ,
[ Γ ( ρ ) ] m = 1 + exp ( 2 πi ρ m ) 2 πi .
Ψ g ( ρ ) = Ψ g ¯ ( Γ ( ρ ) ) = Ψ f ( H Γ ( ρ ) ) .
Ψ v ( ω ) = Ψ f ( H Γ ( T ω ω ) ) ,

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