Model Parameters Estimation Using Jeffrey Divergence

Abstract

The most efficient image noise removal methods are based on the statistical models of the wavelet coefficients. These statistical models can be one or two dimensional. This paper deals with the method based on the generalized Laplacian probability density function (PDF). The generalized Laplacian PDF allows to model the histogram of the details bands of the discrete wavelet transform (DWT). This model serves as prior information about the image. So it is quite evident that when the suitable model was chosen then its parameters must be estimated using the feasible estimation method. A number of the methods for parameters estimation in many statistical books were described. Many of these are quite suboptimal, because it is impossible to estimate the model parameters directly from noisy wavelet coefficients. So because of this the method using Jeffrey divergence (JD) was proposed. This method for parameters estimation is based on minimizing of JD between the noisy wavelet coefficients histogram and the modeled noisy PDF. The above mentioned model will be utilized by the Bayesian estimators, where will be served as a prior information about the signal. There will be discussed the Bayesian least square error (BLSE) estimator and maximum a posteriori (MAP) estimator.