Bayesian Image Super-Resolution with Deep Modeling of Image Statistics

Modeling statistics of image priors is useful for image super-resolution, but little attention has been paid from the massive works of deep learning-based methods. In this work, we propose a Bayesian image restoration framework, where natural image statistics are modeled with the combination of smoothness and sparsity priors. Concretely, firstly we consider an ideal image as the sum of a smoothness component and a sparsity residual, and model real image degradation including blurring, downscaling, and noise corruption. Then, we develop a variational Bayesian approach to infer their posteriors. Finally, we implement the variational approach for single image super-resolution (SISR) using deep neural networks, and propose an unsupervised training strategy. The experiments on three image restoration tasks, \textit{i.e.,} ideal SISR, realistic SISR, and real-world SISR, demonstrate that our method has superior model generalizability against varying noise levels and degradation kernels and is effective in unsupervised SISR. The code and resulting models are released via \url{https://zmiclab.github.io/projects.html}.Comment: 45 page

Bayesian Convolutional Neural Networks for Compressed Sensing Restoration

Deep Neural Networks (DNNs) have aroused great attention in Compressed Sensing (CS) restoration. However, the working mechanism of DNNs is not explainable, thereby it is unclear that how to design an optimal DNNs for CS restoration. In this paper, we propose a novel statistical framework to explain DNNs, which proves that the hidden layers of DNNs are equivalent to Gibbs distributions and interprets DNNs as a Bayesian hierarchical model. The framework provides a Bayesian perspective to explain the working mechanism of DNNs, namely some hidden layers learn a prior distribution and other layers learn a likelihood distribution. Moreover, the framework provides insights into DNNs and reveals two inherent limitations of DNNs for CS restoration. In contrast to most previous works designing an end-to-end DNNs for CS restoration, we propose a novel DNNs to model a prior distribution only, which can circumvent the limitations of DNNs. Given the prior distribution generated from the DNNs, we design a Bayesian inference algorithm to realize CS restoration in the framework of Bayesian Compressed Sensing. Finally, extensive simulations validate the proposed theory of DNNs and demonstrate that the proposed algorithm outperforms the state-of-the-art CS restoration methods

Deep Regression Bayesian Network and Its Applications

Deep directed generative models have attracted much attention recently due to their generative modeling nature and powerful data representation ability. In this paper, we review different structures of deep directed generative models and the learning and inference algorithms associated with the structures. We focus on a specific structure that consists of layers of Bayesian Networks due to the property of capturing inherent and rich dependencies among latent variables. The major difficulty of learning and inference with deep directed models with many latent variables is the intractable inference due to the dependencies among the latent variables and the exponential number of latent variable configurations. Current solutions use variational methods often through an auxiliary network to approximate the posterior probability inference. In contrast, inference can also be performed directly without using any auxiliary network to maximally preserve the dependencies among the latent variables. Specifically, by exploiting the sparse representation with the latent space, max-max instead of max-sum operation can be used to overcome the exponential number of latent configurations. Furthermore, the max-max operation and augmented coordinate ascent are applied to both supervised and unsupervised learning as well as to various inference. Quantitative evaluations on benchmark datasets of different models are given for both data representation and feature learning tasks.Comment: Accepted to IEEE Signal Processing Magazin

Image Restoration from Parametric Transformations using Generative Models

When images are statistically described by a generative model we can use this information to develop optimum techniques for various image restoration problems as inpainting, super-resolution, image coloring, generative model inversion, etc. With the help of the generative model it is possible to formulate, in a natural way, these restoration problems as Statistical estimation problems. Our approach, by combining maximum a-posteriori probability with maximum likelihood estimation, is capable of restoring images that are distorted by transformations even when the latter contain unknown parameters. The resulting optimization is completely defined with no parameters requiring tuning. This must be compared with the current state of the art which requires exact knowledge of the transformations and contains regularizer terms with weights that must be properly defined. Finally, we must mention that we extend our method to accommodate mixtures of multiple images where each image is described by its own generative model and we are able of successfully separating each participating image from a single mixture

Unrolled Optimization with Deep Priors

A broad class of problems at the core of computational imaging, sensing, and low-level computer vision reduces to the inverse problem of extracting latent images that follow a prior distribution, from measurements taken under a known physical image formation model. Traditionally, hand-crafted priors along with iterative optimization methods have been used to solve such problems. In this paper we present unrolled optimization with deep priors, a principled framework for infusing knowledge of the image formation into deep networks that solve inverse problems in imaging, inspired by classical iterative methods. We show that instances of the framework outperform the state-of-the-art by a substantial margin for a wide variety of imaging problems, such as denoising, deblurring, and compressed sensing magnetic resonance imaging (MRI). Moreover, we conduct experiments that explain how the framework is best used and why it outperforms previous methods.Comment: First two authors contributed equall

The Nishimori line and Bayesian Statistics

``Nishimori line'' is a line or hypersurface in the parameter space of systems with quenched disorder, where simple expressions of the averages of physical quantities over the quenched random variables are obtained. It has been playing an important role in the theoretical studies of the random frustrated systems since its discovery around 1980. In this paper, a novel interpretation of the Nishimori line from the viewpoint of statistical information processing is presented. Our main aim is the reconstruction of the whole theory of the Nishimori line from the viewpoint of Bayesian statistics, or, almost equivalently, from the viewpoint of the theory of error-correcting codes. As a byproduct of our interpretation, counterparts of the Nishimori line in models without gauge invariance are given. We also discussed the issues on the ``finite temperature decoding'' of error-correcting codes in connection with our theme and clarify the role of gauge invariance in this topic.Comment: 16 pages, 1 table, no figures, using Iopart.cls and Iopart10.clo, submitted to Journal of Physics A (Mathematical and General), this cond-mat version contains full titles of the reference

Deep Gaussian Conditional Random Field Network: A Model-based Deep Network for Discriminative Denoising

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.Comment: 10 pages, 5 figure

Non-Local Video Denoising by CNN

Non-local patch based methods were until recently state-of-the-art for image denoising but are now outperformed by CNNs. Yet they are still the state-of-the-art for video denoising, as video redundancy is a key factor to attain high denoising performance. The problem is that CNN architectures are hardly compatible with the search for self-similarities. In this work we propose a new and efficient way to feed video self-similarities to a CNN. The non-locality is incorporated into the network via a first non-trainable layer which finds for each patch in the input image its most similar patches in a search region. The central values of these patches are then gathered in a feature vector which is assigned to each image pixel. This information is presented to a CNN which is trained to predict the clean image. We apply the proposed architecture to image and video denoising. For the latter patches are searched for in a 3D spatio-temporal volume. The proposed architecture achieves state-of-the-art results. To the best of our knowledge, this is the first successful application of a CNN to video denoising.Comment: A shorter version of this work has been accepted at ICIP 2019 (A NON-LOCAL CNN FOR VIDEO DENOISING). The results of v2 were improved compared to v1 and the code was updated accordingly. Code is available at: https://github.com/axeldavy/vnlne

Toward Convolutional Blind Denoising of Real Photographs

While deep convolutional neural networks (CNNs) have achieved impressive success in image denoising with additive white Gaussian noise (AWGN), their performance remains limited on real-world noisy photographs. The main reason is that their learned models are easy to overfit on the simplified AWGN model which deviates severely from the complicated real-world noise model. In order to improve the generalization ability of deep CNN denoisers, we suggest training a convolutional blind denoising network (CBDNet) with more realistic noise model and real-world noisy-clean image pairs. On the one hand, both signal-dependent noise and in-camera signal processing pipeline is considered to synthesize realistic noisy images. On the other hand, real-world noisy photographs and their nearly noise-free counterparts are also included to train our CBDNet. To further provide an interactive strategy to rectify denoising result conveniently, a noise estimation subnetwork with asymmetric learning to suppress under-estimation of noise level is embedded into CBDNet. Extensive experimental results on three datasets of real-world noisy photographs clearly demonstrate the superior performance of CBDNet over state-of-the-arts in terms of quantitative metrics and visual quality. The code has been made available at https://github.com/GuoShi28/CBDNet

Model-blind Video Denoising Via Frame-to-frame Training

Modeling the processing chain that has produced a video is a difficult reverse engineering task, even when the camera is available. This makes model based video processing a still more complex task. In this paper we propose a fully blind video denoising method, with two versions off-line and on-line. This is achieved by fine-tuning a pre-trained AWGN denoising network to the video with a novel frame-to-frame training strategy. Our denoiser can be used without knowledge of the origin of the video or burst and the post processing steps applied from the camera sensor. The on-line process only requires a couple of frames before achieving visually-pleasing results for a wide range of perturbations. It nonetheless reaches state of the art performance for standard Gaussian noise, and can be used off-line with still better performance.Comment: CVPR 201