Noises removal for images by wavelet-based Bayesian estimator via levy process analysis

There are many noise sources for images. Images are, in many cases, degraded even before they are encoded. In our previous paper [1], we focused on Poisson noise. Unlike additive Gaussian noise, Poisson noise is signal-dependent and separating signal from noise is a difficult task. A wavelet-based maximum likelihood method for Bayesian estimator that recovers the signal component of the wavelet coefficients in original images by using an alpha-stable signal prior distribution is demonstrated to the Poisson noise removal. Current paper is to extend out previous results to more complex cases that noises comprised of compound Poisson and Gaussian via Levy process analysis. 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, even though computers did not know the noise, this method works well.