An Empirical Bayes Em-Wavelet Unification for Simultaneous Denoising, Interpolation, and/Or Demosaicing

We present a unified framework for coupling the EM algorithm with the Bayesian hierarchical modeling of neighboring wavelet coefficients of image signals. Within this framework, problems with missing pixels or pixel components, and hence unobservable wavelet coefficients, are handled simultaneously with denoising. The hyper-parameters of the model are estimated via the marginal likelihood by the EM algorithm, and a part of the output of its E-step automatically provide optimal estimates, given the specified Bayesian model, of the noise-free image. This unified empirical-Bayes based framework, therefore, offers a statistically principled and extremely flexible approach to a wide range of pixel estimation problems including image denoising, image interpolation, demosaicing, or any combinations of them.