Practical Poissonian-Gaussian Noise Modeling and Fitting for Single- Image Raw-Data Reporter: 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 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

Two segments S obtained for = 0.01 (left) and = (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