Wavelet-based Bayesian estimator for Poisson noise removal from images

Images are, in many cases, degraded even before they are encoded. Emission and transmission tomography images, X-ray films, and photographs taken by satellites are usually contaminated by quantum noise, which is Poisson distributed. Poisson shot noise is a natural generalization of a compound Poisson process when the summands are stochastic processes starting at the points of the underlying Poisson process. Unlike additive Gaussian noise, Poisson noise is signal-dependent and separating signal from noise is a difficult task. A wavelet-based maximum likelihood for a Bayesian estimator that recovers the signal component of the wavelet coefficients in original images by using an alpha-stable signal prior distribution is extended to the Poisson noise removal from a previous investigation. As we discussed in our earlier papers that Bayesian estimator can approximate impulsive noise more accurately than other models and that in the general case the Bayesian processor does not have a closed-form expression. The parameters relative to Bayesian estimators of the model are carefully investigated after an investigation of a-stable simulations for a maximum likelihood estimator. As an example, an improved Bayesian estimator that is a natural extension of other wavelet denoising (soft and hard threshold methods) via a colour image is presented to illustrate our discussion.