Practical Poissonian-Gaussian Noise Modeling and Fitting for Single-

Image Raw-DataReporter:沈廷翰 陳奇業

Poissonian-Gaussian Modeling

• : 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

• : Poissonian signal-dependent component– the Poissonian has varying variance that

depends on the value of– ,

• : 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 , restricted on the set of smoothness

Poissonian-Gaussian Modeling

• detail coefficients , restricted on the set of smoothness

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