Estimation in signal-dependent film-grain noise

Gary K. Froehlich; John F. Walkup; Thomas F. Krile

doi:10.1364/AO.20.003619

Applied Optics
Vol. 20,
Issue 20,
pp. 3619-3626
(1981)
•https://doi.org/10.1364/AO.20.003619

Estimation in signal-dependent film-grain noise

Gary K. Froehlich, John F. Walkup, and Thomas F. Krile

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Gary K. Froehlich, John F. Walkup, and Thomas F. Krile, "Estimation in signal-dependent film-grain noise," Appl. Opt. 20, 3619-3626 (1981)

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Abstract

Optimal estimators are derived for a signal-dependent film-grain noise model, and the effect of signal-dependence on the estimators’s structures is investigated. Due to the mathematical complexity of these optimal estimators, various suboptimal estimators are proposed. Computer simulations are then presented which compare the optimal and suboptimal estimators with regard to mean square estimation error, sensitivity to signal-dependence, and robustness with respect to the a priori signal probability density function.

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Case	$\begin{array}{l} k^{2} σ_{1}^{2} = 0 \\ σ_{2}^{2} = 0.03 \end{array}$	$\begin{array}{l} k^{2} σ_{1}^{2} = 0.01 \\ σ_{2}^{2} = 0.01 \end{array}$	$\begin{array}{l} k^{2} σ_{1}^{2} = 0.03 \\ σ_{2}^{2} = 0 \end{array}$
Noise	0.027	0.014	0.012
MMSE	0.031	0.011	0.011
MAP	0.024	0.014	0.012
ML	0.027	0.014	0.012
WSA	0.163	0.164	0.162
MSIMAP	0.026	0.014	0.012
JS	0.026	0.015	0.012

Case	$\begin{array}{l} k^{2} σ_{1}^{2} = 0 \\ σ_{2}^{2} = 0.03 \end{array}$	$\begin{array}{l} k^{2} σ_{1}^{2} = 0.01 \\ σ_{2}^{2} = 0.01 \end{array}$	$\begin{array}{l} k^{2} σ_{1}^{2} = 0.03 \\ σ_{2}^{2} = 0 \end{array}$
Noise	0.026	0.012	0.011
MMSE	0.024	0.012	0.009
MAP	0.025	0.012	0.010
ML	0.026	0.012	0.011
WSA	0.297	0.290	0.293
MSIMAP	0.025	0.012	0.011
JS	0.025	0.012	0.011

Case	$\begin{array}{l} k^{2} σ_{1}^{2} = 0 \\ σ_{2}^{2} = 0.03 \end{array}$	$\begin{array}{l} k^{2} σ_{1}^{2} = 0.01 \\ σ_{2}^{2} = 0.01 \end{array}$	$\begin{array}{l} k^{2} σ_{1}^{2} = 0.03 \\ σ_{2}^{2} = 0 \end{array}$
Noise	0.038	0.011	0.002
MMSE	0.009	0.007	0.004
MAP	0.015	0.009	0.001
ML	0.038	0.011	0.002
WSA	0.015	0.005	0.001
MSIMAP	0.022	0.009	0.002
JS	0.027	0.007	0.002

Case	$\begin{array}{l} k^{2} σ_{1}^{2} = 0 \\ σ_{2}^{2} = 0.03 \end{array}$	$\begin{array}{l} k^{2} σ_{1}^{2} = 0.01 \\ σ_{2}^{2} = 0.01 \end{array}$	$\begin{array}{l} k^{2} σ_{1}^{2} = 0.03 \\ σ_{2}^{2} = 0 \end{array}$
Noise	0.026	0.014	0.012
MMSE	0.021	0.014	0.014
MAP	0.023	0.014	0.012
ML	0.026	0.014	0.012
WSA	0.021	0.015	0.015
MSIMAP	0.025	0.013	0.012
JS	0.016	0.009	0.012

Case	$\begin{array}{l} k^{2} σ_{1}^{2} = 0 \\ σ_{2}^{2} = 0.03 \end{array}$	$\begin{array}{l} k^{2} σ_{1}^{2} = 0.01 \\ σ_{2}^{2} = 0.01 \end{array}$	$\begin{array}{l} k^{2} σ_{1}^{2} = 0.03 \\ σ_{2}^{2} = 0 \end{array}$
Noise	0.027	0.014	0.012
MMSE	0.031	0.011	0.011
MAP	0.024	0.014	0.012
ML	0.027	0.014	0.012
WSA	0.163	0.164	0.162
MSIMAP	0.026	0.014	0.012
JS	0.026	0.015	0.012

Abstract

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Figures (11)

Tables (4)

Equations (24)

Applied Optics