  Patch priors have become an important component of image restoration. A
powerful approach in this category of restoration algorithms is the popular
Expected Patch Log-Likelihood (EPLL) algorithm. EPLL uses a Gaussian mixture
model (GMM) prior learned on clean image patches as a way to regularize
degraded patches. In this paper, we show that a generalized Gaussian mixture
model (GGMM) captures the underlying distribution of patches better than a GMM.
Even though GGMM is a powerful prior to combine with EPLL, the non-Gaussianity
of its components presents major challenges to be applied to a computationally
intensive process of image restoration. Specifically, each patch has to undergo
a patch classification step and a shrinkage step. These two steps can be
efficiently solved with a GMM prior but are computationally impractical when
using a GGMM prior. In this paper, we provide approximations and computational
recipes for fast evaluation of these two steps, so that EPLL can embed a GGMM
prior on an image with more than tens of thousands of patches. Our main
contribution is to analyze the accuracy of our approximations based on thorough
theoretical analysis. Our evaluations indicate that the GGMM prior is
consistently a better fit formodeling image patch distribution and performs
better on average in image denoising task.
