Comparative effects of optical-correlator signal-dependent and signal-independent noise on pattern-recognition performance with the phase-only filter

Jean-Christophe Terrillon

Author Affiliations

Jean-Christophe Terrillon

^{}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.

Bahram Javidi, Amir Fazlollahi, Peter Willett, and Philippe Réfrégier Appl. Opt. 34(20) 3858-3868 (1995)

References

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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).