  We propose an adaptive learning procedure to learn patch-based image priors
for image denoising. The new algorithm, called the Expectation-Maximization
(EM) adaptation, takes a generic prior learned from a generic external database
and adapts it to the noisy image to generate a specific prior. Different from
existing methods that combine internal and external statistics in ad-hoc ways,
the proposed algorithm is rigorously derived from a Bayesian hyper-prior
perspective. There are two contributions of this paper: First, we provide full
derivation of the EM adaptation algorithm and demonstrate methods to improve
the computational complexity. Second, in the absence of the latent clean image,
we show how EM adaptation can be modified based on pre-filtering. Experimental
results show that the proposed adaptation algorithm yields consistently better
denoising results than the one without adaptation and is superior to several
state-of-the-art algorithms.
