text: Blind image denoising is an important yet very challenging problem in computer vision due to the complicated acquisition process of real images. In this work we propose a new variational inference method, which integrates both noise estimation and image denoising into a unique Bayesian framework, for blind image denoising. Specifically, an approximate posterior, parameterized by deep neural networks, is presented by taking the intrinsic clean image and noise variances as latent variables conditioned on the input noisy image. This posterior provides explicit parametric forms for all its involved hyper-parameters, and thus can be easily implemented for blind image denoising with automatic noise estimation for the test noisy image. On one hand, as other data-driven deep learning methods, our method, namely variational denoising network (VDN), can perform denoising efficiently due to its explicit form of posterior expression. On the other hand, VDN inherits the advantages of traditional model-driven approaches, especially the good generalization capability of generative models. VDN has good interpretability and can be flexibly utilized to estimate and remove complicated non-i.i.d. noise collected in real scenarios. Comprehensive experiments are performed to substantiate the superiority of our method in blind image denoising.
  @cite_30: A constrained optimization type of numerical algorithm for removing noise from images is presented. The total variation of the image is minimized subject to constraints involving the statistics of the noise. The constraints are imposed using Lagrange multipliers. The solution is obtained using the gradient-projection method. This amounts to solving a time dependent partial differential equation on a manifold determined by the constraints. As t--- 0o the solution converges to a steady state which is the denoised image. The numerical algorithm is simple and relatively fast. The results appear to be state-of-the-art for very noisy images. The method is noninvasive, yielding sharp edges in the image. The technique could be interpreted as a first step of moving each level set of the image normal to itself with velocity equal to the curvature of the level set divided by the magnitude of the gradient of the image, and a second step which projects the image back onto the constraint set.
  @cite_13: 
  @cite_18: Arguably several thousands papers are dedicated to image denoising. Most papers assume a fixed noise model, mainly white Gaussian or Poissonian. This assumption is only valid for raw images. Yet, in most images handled by the public and even by scientists, the noise model is imperfectly known or unknown. End users only dispose the result of a complex image processing chain effectuated by uncontrolled hardware and software (and sometimes by chemical means). For such images, recent progress in noise estimation permits to estimate from a single image a noise model, which is simultaneously signal and frequency dependent. We propose here a multiscale denoising algorithm adapted to this broad noise model. This leads to a blind denoising algorithm which we demonstrate on real JPEG images and on scans of old photographs for which the formation model is unknown. The consistency of this algorithm is also verified on simulated distorted images. This algorithm is finally compared with the unique state of the art previous blind denoising method.
  @cite_8: Most existing image denoising approaches assumed the noise to be homogeneous white Gaussian distributed with known intensity. However, in real noisy images, the noise models are usually unknown beforehand and can be much more complex. This paper addresses this problem and proposes a novel blind image denoising algorithm to recover the clean image from noisy one with the unknown noise model. To model the empirical noise of an image, our method introduces the mixture of Gaussian distribution, which is flexible enough to approximate different continuous distributions. The problem of blind image denoising is reformulated as a learning problem. The procedure is to first build a two-layer structural model for noisy patches and consider the clean ones as latent variable. To control the complexity of the noisy patch model, this work proposes a novel Bayesian nonparametric prior called “Dependent Dirichlet Process Tree” to build the model. Then, this study derives a variational inference algorithm to estimate model parameters and recover clean patches. We apply our method on synthesis and real noisy images with different noise models. Comparing with previous approaches, ours achieves better performance. The experimental results indicate the efficiency of the proposed algorithm to cope with practical image denoising tasks.
  @cite_9: Most of existing image denoising methods assume the corrupted noise to be additive white Gaussian noise (AWGN). However, the realistic noise in real-world noisy images is much more complex than AWGN, and is hard to be modeled by simple analytical distributions. As a result, many state-of-the-art denoising methods in literature become much less effective when applied to real-world noisy images captured by CCD or CMOS cameras. In this paper, we develop a trilateral weighted sparse coding (TWSC) scheme for robust real-world image denoising. Specifically, we introduce three weight matrices into the data and regularization terms of the sparse coding framework to characterize the statistics of realistic noise and image priors. TWSC can be reformulated as a linear equality-constrained problem and can be solved by the alternating direction method of multipliers. The existence and uniqueness of the solution and convergence of the proposed algorithm are analyzed. Extensive experiments demonstrate that the proposed TWSC scheme outperforms state-of-the-art denoising methods on removing realistic noise.
  @cite_21: 
  @cite_32: As a convex relaxation of the low rank matrix factorization problem, the nuclear norm minimization has been attracting significant research interest in recent years. The standard nuclear norm minimization regularizes each singular value equally to pursue the convexity of the objective function. However, this greatly restricts its capability and flexibility in dealing with many practical problems (e.g., denoising), where the singular values have clear physical meanings and should be treated differently. In this paper we study the weighted nuclear norm minimization (WNNM) problem, where the singular values are assigned different weights. The solutions of the WNNM problem are analyzed under different weighting conditions. We then apply the proposed WNNM algorithm to image denoising by exploiting the image nonlocal self-similarity. Experimental results clearly show that the proposed WNNM algorithm outperforms many state-of-the-art denoising algorithms such as BM3D in terms of both quantitative measure and visual perception quality.
  @cite_6: Simultaneous sparse coding (SSC) or nonlocal image representation has shown great potential in various low-level vision tasks, leading to several state-of-the-art image restoration techniques, including BM3D and LSSC. However, it still lacks a physically plausible explanation about why SSC is a better model than conventional sparse coding for the class of natural images. Meanwhile, the problem of sparsity optimization, especially when tangled with dictionary learning, is computationally difficult to solve. In this paper, we take a low-rank approach toward SSC and provide a conceptually simple interpretation from a bilateral variance estimation perspective, namely that singular-value decomposition of similar packed patches can be viewed as pooling both local and nonlocal information for estimating signal variances. Such perspective inspires us to develop a new class of image restoration algorithms called spatially adaptive iterative singular-value thresholding (SAIST). For noise data, SAIST generalizes the celebrated BayesShrink from local to nonlocal models; for incomplete data, SAIST extends previous deterministic annealing-based solution to sparsity optimization through incorporating the idea of dictionary learning. In addition to conceptual simplicity and computational efficiency, SAIST has achieved highly competent (often better) objective performance compared to several state-of-the-art methods in image denoising and completion experiments. Our subjective quality results compare favorably with those obtained by existing techniques, especially at high noise levels and with a large amount of missing data.
  @cite_19: Traditional image denoising algorithms always assume the noise to be homogeneous white Gaussian distributed. However, the noise on real images can be much more complex empirically. This paper addresses this problem and proposes a novel blind image denoising algorithm which can cope with real-world noisy images even when the noise model is not provided. It is realized by modeling image noise with mixture of Gaussian distribution (MoG) which can approximate large varieties of continuous distributions. As the number of components for MoG is unknown practically, this work adopts Bayesian nonparametric technique and proposes a novel Low-rank MoG filter (LR-MoG) to recover clean signals (patches) from noisy ones contaminated by MoG noise. Based on LR-MoG, a novel blind image denoising approach is developed. To test the proposed method, this study conducts extensive experiments on synthesis and real images. Our method achieves the state-of the-art performance consistently.
  @cite_40: A new definition of scale-space is suggested, and a class of algorithms used to realize a diffusion process is introduced. The diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing. It is shown that the 'no new maxima should be generated at coarse scales' property of conventional scale space is preserved. As the region boundaries in the approach remain sharp, a high-quality edge detector which successfully exploits global information is obtained. Experimental results are shown on a number of images. Parallel hardware implementations are made feasible because the algorithm involves elementary, local operations replicated over the image. >
  @cite_23: We develop a framework for learning generic, expressive image priors that capture the statistics of natural scenes and can be used for a variety of machine vision tasks. The approach provides a practical method for learning high-order Markov random field (MRF) models with potential functions that extend over large pixel neighborhoods. These clique potentials are modeled using the Product-of-Experts framework that uses non-linear functions of many linear filter responses. In contrast to previous MRF approaches all parameters, including the linear filters themselves, are learned from training data. We demonstrate the capabilities of this Field-of-Experts model with two example applications, image denoising and image inpainting, which are implemented using a simple, approximate inference scheme. While the model is trained on a generic image database and is not tuned toward a specific application, we obtain results that compete with specialized techniques.
  @cite_10: We propose a new measure, the method noise, to evaluate and compare the performance of digital image denoising methods. We first compute and analyze this method noise for a wide class of denoising algorithms, namely the local smoothing filters. Second, we propose a new algorithm, the nonlocal means (NL-means), based on a nonlocal averaging of all pixels in the image. Finally, we present some experiments comparing the NL-means algorithm and the local smoothing filters.
  @cite_25: The classical solution to the noise removal problem is the Wiener filter, which utilizes the second-order statistics of the Fourier decomposition. Subband decompositions of natural images have significantly non-Gaussian higher-order point statistics; these statistics capture image properties that elude Fourier-based techniques. We develop a Bayesian estimator that is a natural extension of the Wiener solution, and that exploits these higher-order statistics. The resulting nonlinear estimator performs a "coring" operation. We provide a simple model for the subband statistics, and use it to develop a semi-blind noise removal algorithm based on a steerable wavelet pyramid.
summary: Most classical image denoising methods belong to this category, through designing a MAP model with a fidelity loss term and a regularization one delivering the pre-known image prior. Along this line, total variation denoising @cite_30 , anisotropic diffusion @cite_40 and wavelet coring @cite_25 use the statistical regularities of images to remove the image noise. Later, the nonlocal similarity prior, meaning many small patches in a non-local image area possess similar configurations, was widely used in image denoising. Typical ones include CBM3D @cite_13 and non-local means @cite_10 . Some dictionary learning methods @cite_32 @cite_6 @cite_9 and Field-of-Experts (FoE) @cite_23 , also revealing certain prior knowledge of image patches, had also been attempted for the task. Several other approaches focusing on the fidelity term, which are mainly determined by the noise assumption on data. E.g., Mulitscale @cite_18 assumed the noise of each patch and its similar patches in the same image to be correlated Gaussian distribution, and LR-MoG @cite_19 , DP-GMM @cite_21 and DDPT @cite_8 fitted the image noise by using Mixture of Gaussian (MoG) as an approximator for noises.