Transcript Practical Poissonian-Gaussian Noise Modeling and Fitting for Single

Practical Poissonian-Gaussian Noise
Modeling and Fitting for SingleImage Raw-Data
Reporter:
沈廷翰
陳奇業
Poissonian-Gaussian Modeling
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: the pixel position in the domain X
: the recorded signal
: the ideal signal
: zero-mean independent random noise with
standard deviation equal to 1
• : function of that gives the standard deviation of
the overall noise component
Poissonian-Gaussian Modeling
Poissonian-Gaussian Modeling
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: Poissonian signal-dependent component
– the Poissonian
has varying variance that
depends on the value of
–
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: Gaussian signal-independent component
– constant variance equal to
The Algorithm
• Our goal is to estimate the function of the
observation model from a noisy image
• local estimation of multiple expectation/
standard-deviation pairs
• global parametric model fitting to these local
estimates
– Maximum-Likelihood Fitting of a Global
Parametric Model
The Algorithm
Poissonian-Gaussian Modeling
• Wavelet approximation
the set of smoothness
, restricted on
Poissonian-Gaussian Modeling
• detail coefficients
of smoothness
, restricted on the set
Poissonian-Gaussian Modeling
• two level-sets ,
• : allowed deviation
Poissonian-Gaussian Modeling
Poissonian-Gaussian Modeling
• Two segments S obtained for = 0.01 (left)
and = 0.0001(right).
• The value of is the same for both segments
The Algorithm
• The solid line shows the maximum-likelihood
estimate
of the true standard-deviation
function
• Estimates the parameters of the noise
The Algorithm
• posterior likelihood
Conclusion
• Utilizes a special ML fitting of the parametric
model on a collection of local wavelet-domain
estimates of mean and standard-deviation