Multi-noise removal from images by wavelet-based Bayesian estimator

Images are in many cases degraded even before they are encoded. The major noise sources, in terms of distributions, are Gaussian noise and Poisson noise. Noise acquired by images during transmission would be Gaussian in distribution, while images such as 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. In our previous papers we discussed a wavelet-based maximum likelihood for Bayesian estimator that recovers the signal component of wavelet coefficients in original images using an alpha-stable signal prior distribution. In this paper, it is demonstrated that the method can be extended to multi-noise sources comprising both Gaussian and Poisson distributions. Results of varying the parameters of the Bayesian estimators of the model are presented after an investigation of a-stable simulations for a maximum likelihood estimator. As an example, a colour image is processed and presented to illustrate our discussion.