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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Models and Associated Statistical Parameters Describing Additive Signal-Independent Noise and Four Different Signal-Dependent Noise Sourcesa
Noise Source
Models
σR
SNRin
Additive SIN
RSIN = S + N
σN
S/σN
Speckle
Rsp = SNsp
Film grain
Rfg = S + kSpN
kSp
S1−p/k
Poisson
Speckle + SIN
Rsp+SIN = SNsp + N
S is the original image signal; R is the noisy image. N is a Gaussian noise with zero mean and variance
(except for film-grain SDN, where
). Nsp is a random variable with a Gamma probability-density function of order M with unit mean and variance 1/M. Pλ(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. σR is the standard deviation of R, and SNRin 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, SNRin = 1.0a
Input Image
Correlation, POF
Noise Source
〈MSD〉
SNR
PFA
〈Ip〉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 = S0 = 255, σN = 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 σN = 180.31 for the combination of speckle SDN and of additive SIN. In each simulation, the statistics are calculated over 104 noise realizations of the input image and of the correlation. 〈Ip〉 is normalized with respect to IP(Ip = 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
Noise Source
Models
σR
SNRin
Additive SIN
RSIN = S + N
σN
S/σN
Speckle
Rsp = SNsp
Film grain
Rfg = S + kSpN
kSp
S1−p/k
Poisson
Speckle + SIN
Rsp+SIN = SNsp + N
S is the original image signal; R is the noisy image. N is a Gaussian noise with zero mean and variance
(except for film-grain SDN, where
). Nsp is a random variable with a Gamma probability-density function of order M with unit mean and variance 1/M. Pλ(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. σR is the standard deviation of R, and SNRin 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, SNRin = 1.0a
Input Image
Correlation, POF
Noise Source
〈MSD〉
SNR
PFA
〈Ip〉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 = S0 = 255, σN = 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 σN = 180.31 for the combination of speckle SDN and of additive SIN. In each simulation, the statistics are calculated over 104 noise realizations of the input image and of the correlation. 〈Ip〉 is normalized with respect to IP(Ip = 1,553,627 units of intensity).