  Conditional random fields (CRFs) are popular discriminative models for
computer vision and have been successfully applied in the domain of image
restoration, especially to image denoising. For image deblurring, however,
discriminative approaches have been mostly lacking. We posit two reasons for
this: First, the blur kernel is often only known at test time, requiring any
discriminative approach to cope with considerable variability. Second, given
this variability it is quite difficult to construct suitable features for
discriminative prediction. To address these challenges we first show a
connection between common half-quadratic inference for generative image priors
and Gaussian CRFs. Based on this analysis, we then propose a cascade model for
image restoration that consists of a Gaussian CRF at each stage. Each stage of
our cascade is semi-parametric, i.e. it depends on the instance-specific
parameters of the restoration problem, such as the blur kernel. We train our
model by loss minimization with synthetically generated training data. Our
experiments show that when applied to non-blind image deblurring, the proposed
approach is efficient and yields state-of-the-art restoration quality on images
corrupted with synthetic and real blur. Moreover, we demonstrate its
suitability for image denoising, where we achieve competitive results for
grayscale and color images.
