text: We propose a novel deep network architecture for image denoising based on a Gaussian Conditional Random Field (GCRF) model. In contrast to the existing discriminative denoising methods that train a separate model for each noise level, the proposed deep network explicitly models the input noise variance and hence is capable of handling a range of noise levels. Our deep network, which we refer to as deep GCRF network, consists of two sub-networks: (i) a parameter generation network that generates the pairwise potential parameters based on the noisy input image, and (ii) an inference network whose layers perform the computations involved in an iterative GCRF inference procedure. We train the entire deep GCRF network (both parameter generation and inference networks) discriminatively in an end-to-end fashion by maximizing the peak signal-to-noise ratio measure. Experiments on Berkeley segmentation and PASCALVOC datasets show that the proposed deep GCRF network outperforms state-of-the-art image denoising approaches for several noise levels.
  @cite_27: 
  @cite_4: 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.
  @cite_12: Markov random field (MRF) models are a popular tool for vision and image processing. Gaussian MRF models are particularly convenient to work with because they can be implemented using matrix and linear algebra routines. However, recent research has focused on on discrete-valued and non-convex MRF models because Gaussian models tend to over-smooth images and blur edges. In this paper, we show how to train a Gaussian conditional random field (GCRF) model that overcomes this weakness and can outperform the non-convex field of experts model on the task of denoising images. A key advantage of the GCRF model is that the parameters of the model can be optimized efficiently on relatively large images. The competitive performance of the GCRF model and the ease of optimizing its parameters make the GCRF model an attractive option for vision and image processing applications.
summary: GCRFs were first introduced in @cite_12 by modeling the parameters of the conditional distribution of output given input as a function of the input image. The precision matrix associated with each image patch was modeled as a linear combination of twelve derivative filter-based matrices. The combination weights were chosen as a parametric function of the responses of the input image to a set of oriented edge and bar filters, and the parameters were learned using discriminative training. This GCRF model was extended to Regression Tree Fields (RTFs) in @cite_27 , where regression trees were used for selecting the parameters of Gaussians defined over image patches. These regression trees used responses of the input image to various hand-chosen filters for selecting an appropriate leaf node for each image patch. This RTF-based model was trained by iteratively growing the regression trees and optimizing the Gaussian parameters at leaf nodes. Recently, a cascade of RTFs @cite_4 has also been used for image restoration tasks. In contrast to the RTF-based approaches, all the components of our network are differentiable, and hence it can be trained end-­to-­end using standard gradient-based techniques.