Abstract

We analyze the behavior of regularized linear filters designed for overlapping noise in the presence of images distorted by nonoverlapping noise. In particular we show that there necessarily exist non-null values of the target’s illumination that result in the failure of regularized linear filters. The characteristics of those values are analyzed and discussed relative to the correlation length of the background noise.

© 1995 Optical Society of America

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References

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A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Scene with the target and additive uniform noise, (b) scene with the target and nonoverlapping uniform noise, (c) correlation of image (a) with an OT filter, (d) correlation of image (b) with the same OT filter. Note that (c) and (d) are plots of the maximum of each line of the modulus square of the correlation plane.

Fig. 2
Fig. 2

Top: impulse response of the OT filter used in our simulations; the image is 256 × 256 pixels. Bottom: cross section of the 128th line of the upper image.

Fig. 3
Fig. 3

Square root of 〈δa 2 non 〉 computed from Eq. (3) and the standard deviation of anon measured from 500 noise realizations. These two values are plotted versus the correlation length of the noise expressed in pixels. Inset: the upper curve plots 10 ( δ C b , h 2 / i h i + t i 2 ) 1 / 2 computed from Eq. (4); the lower curve plots the average length of the forbidden interval measured from 100 noise realizations. These two values are plotted versus the correlation length of the noise expressed in pixels. Note the parallel variations of the curve.

Equations (4)

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s i = a t i + b i ( 1 - w i ) ,
a non = i h i - b i i h i + t i ,             a add = - i h i b i i h i + t i .
δ a non 2 = i h ^ v - 2 S v i h i + t i 2 ,
δ C b , h 2 = v h ^ v 2 S v = v t ^ v 2 S v B v 2 .

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