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.
Recently, @cite_0 proposed a cascade of shrinkage fields for image restoration tasks. They learned a separate filter bank and shrinkage function for each stage of their cascade using discriminative training. Though this model can also be seen as a cascade of GCRFs, the filter banks and shrinkage functions used in the cascade do not depend on the noisy input image during test time. In contrast to this, the pairwise potential functions used in our GCRF model are generated by our PgNets based on the noisy input image.
@cite_0
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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. Many state-of-the-art image restoration approaches do not scale well to larger images, such as megapixel images common in the consumer segment. Computationally expensive optimization is often the culprit. While efficient alternatives exist, they have not reached the same level of image quality. The goal of this paper is to develop an effective approach to image restoration that offers both computational efficiency and high restoration quality. To that end we propose shrinkage fields, a random field-based architecture that combines the image model and the optimization algorithm in a single unit. The underlying shrinkage operation bears connections to wavelet approaches, but is used here in a random field context. Computational efficiency is achieved by construction through the use of convolution and DFT as the core components, high restoration quality is attained through loss-based training of all model parameters and the use of a cascade architecture. Unlike heavily engineered solutions, our learning approach can be adapted easily to different trade-offs between efficiency and image quality. We demonstrate state-of-the-art restoration results with high levels of computational efficiency, and significant speedup potential through inherent parallelism. In this work, we propose the construction of two-channel wavelet filter banks for analyzing functions defined on the vertices of any arbitrary finite weighted undirected graph. These graph based functions are referred to as graph-signals as we build a framework in which many concepts from the classical signal processing domain, such as Fourier decomposition, signal filtering and downsampling can be extended to graph domain. Especially, we observe a spectral folding phenomenon in bipartite graphs which occurs during downsampling of these graphs and produces aliasing in graph signals. This property of bipartite graphs, allows us to design critically sampled two-channel filter banks, and we propose quadrature mirror filters (referred to as graph-QMF) for bipartite graph which cancel aliasing and lead to perfect reconstruction. For arbitrary graphs we present a bipartite subgraph decomposition which produces an edge-disjoint collection of bipartite subgraphs. Graph-QMFs are then constructed on each bipartite subgraph leading to “multi-dimensional” separable wavelet filter banks on graphs. Our proposed filter banks are critically sampled and we state necessary and sufficient conditions for orthogonality, aliasing cancellation and perfect reconstruction. The filter banks are realized by Chebychev polynomial approximations. After a decade of rapid progress in image denoising, recent methods seem to have reached a performance limit. Nonetheless, we find that state-of-the-art denoising methods are visually clearly distinguishable and possess complementary strengths and failure modes. Motivated by this observation, we introduce a powerful non-parametric image restoration framework based on Regression Tree Fields (RTF). Our restoration model is a densely-connected tractable conditional random field that leverages existing methods to produce an image-dependent, globally consistent prediction. We estimate the conditional structure and parameters of our model from training data so as to directly optimize for popular performance measures. In terms of peak signal-to-noise-ratio (PSNR), our model improves on the best published denoising method by at least 0.26dB across a range of noise levels. Our most practical variant still yields statistically significant improvements, yet is over 20× faster than the strongest competitor. Our approach is well-suited for many more image restoration and low-level vision problems, as evidenced by substantial gains in tasks such as removal of JPEG blocking artefacts.