Image noises removal on alpha-stable via Bayesian estimator

A maximum likelihood Bayesian estimator that recovers the signal component of the wavelet coefficients from original images by using an α-stable signal prior distribution is discussed. As we discussed in our earlier paper that the Bayesian estimator can approximate impulsive noise more accurately than other models and that the general case of the Bayesian processor does not have a closed-form expression. The attentions drawn by this paper is the behaviours of α ∈ (0.1] following we discussed α ∈ [D. L. Donoho and I. M. Juhnstone, 1995] [D. L. Donoho, May 1995] in our earlier paper [X. Huang et al., 2002]. Closer to a realistic situation, and unlike conventional methods used for Bayesian estimator, for the case discussed here it is not necessary to know the variance of the noise. The parameters relative to Bayesian estimators of the model built up are carefully investigated after an investigation of α-stable simulations for a maximum likelihood estimator. As an example, an improved Bayesian estimator that is a natural extension of the Wiener solution and other wavelet denoising (soft and hard threshold methods), is presented for illustration purposes.