Kernel Belief Propagation

We propose a nonparametric generalization of belief propagation, Kernel Belief Propagation (KBP), for pairwise Markov random fields. Messages are represented as functions in a reproducing kernel Hilbert space (RKHS), and message updates are simple linear operations in the RKHS. KBP makes none of the assumptions commonly required in classical BP algorithms: the variables need not arise from a finite domain or a Gaussian distribution, nor must their relations take any particular parametric form. Rather, the relations between variables are represented implicitly, and are learned nonparametrically from training data. KBP has the advantage that it may be used on any domain where kernels are defined (Rd, strings, groups), even where explicit parametric models are not known, or closed form expressions for the BP updates do not exist. The computational cost of message updates in KBP is polynomial in the training data size. We also propose a constant time approximate message update procedure by representing messages using a small number of basis functions. In experiments, we apply KBP to image denoising, depth prediction from still images, and protein configuration prediction: KBP is faster than competing classical and nonparametric approaches (by orders of magnitude, in some cases), while providing significantly more accurate results

Universal Denoising Networks : A Novel CNN Architecture for Image Denoising

We design a novel network architecture for learning discriminative image models that are employed to efficiently tackle the problem of grayscale and color image denoising. Based on the proposed architecture, we introduce two different variants. The first network involves convolutional layers as a core component, while the second one relies instead on non-local filtering layers and thus it is able to exploit the inherent non-local self-similarity property of natural images. As opposed to most of the existing deep network approaches, which require the training of a specific model for each considered noise level, the proposed models are able to handle a wide range of noise levels using a single set of learned parameters, while they are very robust when the noise degrading the latent image does not match the statistics of the noise used during training. The latter argument is supported by results that we report on publicly available images corrupted by unknown noise and which we compare against solutions obtained by competing methods. At the same time the introduced networks achieve excellent results under additive white Gaussian noise (AWGN), which are comparable to those of the current state-of-the-art network, while they depend on a more shallow architecture with the number of trained parameters being one order of magnitude smaller. These properties make the proposed networks ideal candidates to serve as sub-solvers on restoration methods that deal with general inverse imaging problems such as deblurring, demosaicking, superresolution, etc.Comment: Camera ready paper to appear in the Proceedings of CVPR 201

Adaptive Image Denoising by Targeted Databases

We propose a data-dependent denoising procedure to restore noisy images. Different from existing denoising algorithms which search for patches from either the noisy image or a generic database, the new algorithm finds patches from a database that contains only relevant patches. We formulate the denoising problem as an optimal filter design problem and make two contributions. First, we determine the basis function of the denoising filter by solving a group sparsity minimization problem. The optimization formulation generalizes existing denoising algorithms and offers systematic analysis of the performance. Improvement methods are proposed to enhance the patch search process. Second, we determine the spectral coefficients of the denoising filter by considering a localized Bayesian prior. The localized prior leverages the similarity of the targeted database, alleviates the intensive Bayesian computation, and links the new method to the classical linear minimum mean squared error estimation. We demonstrate applications of the proposed method in a variety of scenarios, including text images, multiview images and face images. Experimental results show the superiority of the new algorithm over existing methods.Comment: 15 pages, 13 figures, 2 tables, journa