^{}The author is a fellow of the Science and Technology Agency of Japan with the Kansai Advanced Research Center, Communications Research Laboratory, Ministry of Posts and Telecommunications, 588-2 Iwaoka, Iwaoka-cho, Nishi-ku, Kobe 651-24, Japan.

Jean-Christophe Terrillon, "Comparative effects of optical-correlator signal-dependent and signal-independent noise on pattern-recognition performance with the phase-only filter," Appl. Opt. 34, 7561-7564 (1995)

The comparative effects of optical-correlator signal-dependent and additive signal-independent noise on correlation-filter performance are analyzed by three different performance measures. For an identical value of the signal-to-noise ratio imposed on each type of noise in a binary input image, computer simulations performed with the phase-only filter show (i) that additive Gaussian signal-independent noise yields a much larger correlation-performance degradation than signal-dependent noise and (ii) that the different types of signal-dependent noise lead to similar correlation results because of similar effects on the input image that are inherent to the nature of the noise.

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S is the original image signal; R is the noisy image. N is a Gaussian noise with zero mean and variance
${\mathrm{\sigma}}_{N}^{2}$ (except for film-grain SDN, where
${\mathrm{\sigma}}_{N}^{2}=1.0$). N_{sp} is a random variable with a Gamma probability-density function of order M with unit mean and variance 1/M. P_{λ}(λS) is a stochastic Poisson process with a mean and a variance both equal to λS. k is a real constant, and p and λ are both real parameters. σ_{R} is the standard deviation of R, and SNR_{in} is the signal-to-noise ratio (SNR) measured pointwise in the input image.

Table 2

Correlation Results of the POF of the Capital Letter I Degraded with Additive Gaussian SIN and with Four Different Types of SDN for an Identical Value of the SNR Measured in the Input Image, SNR_{in} = 1.0a

Input Image

Correlation, POF

Noise Source

〈MSD〉

SNR

P_{FA}

〈I_{p}〉_{n}

Additive SIN

64936.0

38.36

0.1916

1.1150

Speckle

6436.6

77.15

0.0030

1.0143

Film grain

6425.8

81.33

0.0079

1.0158

Poisson

6421.2

80.64

0.0070

1.0130

Speckle + SIN

35705.4

47.85

0.0780

1.0598

With a signal S = S_{0} = 255, σ_{N} = 255.0 for additive SIN, M = 1 for speckle SDN, p = 0.5 and k = 15.97 for film-grain SDN, λ = 3.9 × 10^{−3} for Poisson SDN, and M = 2 and σ_{N} = 180.31 for the combination of speckle SDN and of additive SIN. In each simulation, the statistics are calculated over 10^{4} noise realizations of the input image and of the correlation. 〈I_{p}〉 is normalized with respect to I_{P}(I_{p} = 1,553,627 units of intensity).

Tables (2)

Table 1

Models and Associated Statistical Parameters Describing Additive Signal-Independent Noise and Four Different Signal-Dependent Noise Sourcesa

S is the original image signal; R is the noisy image. N is a Gaussian noise with zero mean and variance
${\mathrm{\sigma}}_{N}^{2}$ (except for film-grain SDN, where
${\mathrm{\sigma}}_{N}^{2}=1.0$). N_{sp} is a random variable with a Gamma probability-density function of order M with unit mean and variance 1/M. P_{λ}(λS) is a stochastic Poisson process with a mean and a variance both equal to λS. k is a real constant, and p and λ are both real parameters. σ_{R} is the standard deviation of R, and SNR_{in} is the signal-to-noise ratio (SNR) measured pointwise in the input image.

Table 2

Correlation Results of the POF of the Capital Letter I Degraded with Additive Gaussian SIN and with Four Different Types of SDN for an Identical Value of the SNR Measured in the Input Image, SNR_{in} = 1.0a

Input Image

Correlation, POF

Noise Source

〈MSD〉

SNR

P_{FA}

〈I_{p}〉_{n}

Additive SIN

64936.0

38.36

0.1916

1.1150

Speckle

6436.6

77.15

0.0030

1.0143

Film grain

6425.8

81.33

0.0079

1.0158

Poisson

6421.2

80.64

0.0070

1.0130

Speckle + SIN

35705.4

47.85

0.0780

1.0598

With a signal S = S_{0} = 255, σ_{N} = 255.0 for additive SIN, M = 1 for speckle SDN, p = 0.5 and k = 15.97 for film-grain SDN, λ = 3.9 × 10^{−3} for Poisson SDN, and M = 2 and σ_{N} = 180.31 for the combination of speckle SDN and of additive SIN. In each simulation, the statistics are calculated over 10^{4} noise realizations of the input image and of the correlation. 〈I_{p}〉 is normalized with respect to I_{P}(I_{p} = 1,553,627 units of intensity).