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.
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.
@cite_30 @cite_13 @cite_18 @cite_8 @cite_9 @cite_21 @cite_32 @cite_6 @cite_19 @cite_40 @cite_23 @cite_10 @cite_25
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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. Natural image modeling plays a key role in many vision problems such as image denoising. Image priors are widely used to regularize the denoising process, which is an illposed inverse problem. One category of denoising methods exploit the priors (e.g., TV, sparsity) learned from external clean images to reconstruct the given noisy image, while another category of methods exploit the internal prior (e.g., self-similarity) to reconstruct the latent image. Though the internal prior based methods have achieved impressive denoising results, the improvement of visual quality will become very difficult with the increase of noise level. In this paper, we propose to exploit image external patch prior and internal self-similarity prior jointly, and develop an external patch prior guided internal clustering algorithm for image denoising. It is known that natural image patches form multiple subspaces. By utilizing Gaussian mixture models (GMMs) learning, image similar patches can be clustered and the subspaces can be learned. The learned GMMs from clean images are then used to guide the clustering of noisypatches of the input noisy images, followed by a low-rank approximation process to estimate the latent subspace for image recovery. Numerical experiments show that the proposed method outperforms many state-of-the-art denoising algorithms such as BM3D and WNNM. Image denoising is a central problem in image processing and it is often a necessary step prior to higher level analysis such as segmentation, reconstruction, or super-resolution. The nonlocal means (NL-means) perform denoising by exploiting the natural redundancy of patterns inside an image; they perform a weighted average of pixels whose neighborhoods (patches) are close to each other. This reduces significantly the noise while preserving most of the image content. While it performs well on flat areas and textures, it suffers from two opposite drawbacks: it might over-smooth low-contrasted areas or leave a residual noise around edges and singular structures. Denoising can also be performed by total variation minimization-the Rudin, Osher and Fatemi model-which leads to restore regular images, but it is prone to over-smooth textures, staircasing effects, and contrast losses. We introduce in this paper a variational approach that corrects the over-smoothing and reduces the residual noise of the NL-means by adaptively regularizing nonlocal methods with the total variation. The proposed regularized NL-means algorithm combines these methods and reduces both of their respective defaults by minimizing an adaptive total variation with a nonlocal data fidelity term. Besides, this model adapts to different noise statistics and a fast solution can be obtained in the general case of the exponential family. We develop this model for image denoising and we adapt it to video denoising with 3D patches. 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. Patch based image modeling has achieved a great success in low level vision such as image denoising. In particular, the use of image nonlocal self-similarity (NSS) prior, which refers to the fact that a local patch often has many nonlocal similar patches to it across the image, has significantly enhanced the denoising performance. However, in most existing methods only the NSS of input degraded image is exploited, while how to utilize the NSS of clean natural images is still an open problem. In this paper, we propose a patch group (PG) based NSS prior learning scheme to learn explicit NSS models from natural images for high performance denoising. PGs are extracted from training images by putting nonlocal similar patches into groups, and a PG based Gaussian Mixture Model (PG-GMM) learning algorithm is developed to learn the NSS prior. We demonstrate that, owe to the learned PG-GMM, a simple weighted sparse coding model, which has a closed-form solution, can be used to perform image denoising effectively, resulting in high PSNR measure, fast speed, and particularly the best visual quality among all competing methods. 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 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. Purpose: To investigate a novel locally adaptive projection space denoising algorithm for low-dose CT data. Methods: The denoising algorithm is based on bilateral filtering, which smooths values using a weighted average in a local neighborhood, with weights determined according to both spatial proximity and intensity similarity between the center pixel and the neighboring pixels. This filtering is locally adaptive and can preserve important edge information in the sinogram, thus maintaining high spatial resolution. A CTnoise model that takes into account the bowtie filter and patient-specific automatic exposure control effects is also incorporated into the denoising process. The authors evaluated the noise-resolution properties of bilateral filtering incorporating such a CTnoise model in phantom studies and preliminary patient studies with contrast-enhanced abdominal CT exams. Results: On a thin wire phantom, the noise-resolution properties were significantly improved with the denoising algorithm compared to commercial reconstruction kernels. The noise-resolution properties on low-dose (40 mA s) data after denoising approximated those of conventional reconstructions at twice the dose level. A separate contrast plate phantom showed improved depiction of low-contrast plates with the denoising algorithm over conventional reconstructions when noise levels were matched. Similar improvement in noise-resolution properties was found on CT colonography data and on five abdominal low-energy (80 kV) CT exams. In each abdominal case, a board-certified subspecialized radiologist rated the denoised 80 kV images markedly superior in image quality compared to the commercially available reconstructions, and denoising improved the image quality to the point where the 80 kV images alone were considered to be of diagnostic quality. Conclusions: The results demonstrate that bilateral filtering incorporating a CTnoise model can achieve a significantly better noise-resolution trade-off than a series of commercial reconstruction kernels. This improvement in noise-resolution properties can be used for improving image quality in CT and can be translated into substantial dose reduction. A deep learning approach to blind denoising of images without complete knowledge of the noise statistics is considered. We propose DN-ResNet, which is a deep convolutional neural network (CNN) consisting of several residual blocks (ResBlocks). With cascade training, DN-ResNet is more accurate and more computationally efficient than the state of art denoising networks. An edge-aware loss function is further utilized in training DN-ResNet, so that the denoising results have better perceptive quality compared to conventional loss function. Next, we introduce the depthwise separable DN-ResNet (DS-DN-ResNet) utilizing the proposed Depthwise Seperable ResBlock (DS-ResBlock) instead of standard ResBlock, which has much less computational cost. DS-DN-ResNet is incrementally evolved by replacing the ResBlocks in DN-ResNet by DS-ResBlocks stage by stage. As a result, high accuracy and good computational efficiency are achieved concurrently. Whereas previous state of art deep learning methods focused on denoising either Gaussian or Poisson corrupted images, we consider denoising images having the more practical Poisson with additive Gaussian noise as well. The results show that DN-ResNets are more efficient, robust, and perform better denoising than current state of art deep learning methods, as well as the popular variants of the BM3D algorithm, in cases of blind and non-blind denoising of images corrupted with Poisson, Gaussian or Poisson-Gaussian noise. Our network also works well for other image enhancement task such as compressed image restoration. Image denoising can be described as the problem of mapping from a noisy image to a noise-free image. The best currently available denoising methods approximate this mapping with cleverly engineered algorithms. In this work we attempt to learn this mapping directly with plain multi layer perceptrons (MLP) applied to image patches. We will show that by training on large image databases we are able to outperform the current state-of-the-art image denoising methods. In addition, our method achieves results that are superior to one type of theoretical bound and goes a large way toward closing the gap with a second type of theoretical bound. Our approach is easily adapted to less extensively studied types of noise, such as mixed Poisson-Gaussian noise, JPEG artifacts, salt-and-pepper noise and noise resembling stripes, for which we achieve excellent results as well. We will show that combining a block-matching procedure with MLPs can further improve the results on certain images. In a second paper, we detail the training trade-offs and the inner mechanisms of our MLPs. 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. In this paper, we propose a very simple and elegant patch-based, machine learning technique for image denoising using the higher order singular value decomposition (HOSVD). The technique simply groups together similar patches from a noisy image (with similarity defined by a statistically motivated criterion) into a 3D stack, computes the HOSVD coefficients of this stack, manipulates these coefficients by hard thresholding, and inverts the HOSVD transform to produce the final filtered image. Our technique chooses all required parameters in a principled way, relating them to the noise model. We also discuss our motivation for adopting the HOSVD as an appropriate transform for image denoising. We experimentally demonstrate the excellent performance of the technique on grayscale as well as color images. On color images, our method produces state-of-the-art results, outperforming other color image denoising algorithms at moderately high noise levels. A criterion for optimal patch-size selection and noise variance estimation from the residual images (after denoising) is also presented. Abstract Image denoising algorithms are evaluated using images corrupted by artificial noise, which may lead to incorrect conclusions about their performances on real noise. In this paper we introduce a dataset of color images corrupted by natural noise due to low-light conditions, together with spatially and intensity-aligned low noise images of the same scenes. We also introduce a method for estimating the true noise level in our images, since even the low noise images contain small amounts of noise. We evaluate the accuracy of our noise estimation method on real and artificial noise, and investigate the Poisson-Gaussian noise model. Finally, we use our dataset to evaluate six denoising algorithms: Active Random Field, BM3D, Bilevel-MRF, Multi-Layer Perceptron, and two versions of NL-means. We show that while the Multi-Layer Perceptron, Bilevel-MRF, and NL-means with soft threshold outperform BM3D on gray images with synthetic noise, they lag behind on our dataset. We develop a Bayesian nonparametric model for reconstructing magnetic resonance images (MRIs) from highly undersampled (k ) -space data. We perform dictionary learning as part of the image reconstruction process. To this end, we use the beta process as a nonparametric dictionary learning prior for representing an image patch as a sparse combination of dictionary elements. The size of the dictionary and patch-specific sparsity pattern are inferred from the data, in addition to other dictionary learning variables. Dictionary learning is performed directly on the compressed image, and so is tailored to the MRI being considered. In addition, we investigate a total variation penalty term in combination with the dictionary learning model, and show how the denoising property of dictionary learning removes dependence on regularization parameters in the noisy setting. We derive a stochastic optimization algorithm based on Markov chain Monte Carlo for the Bayesian model, and use the alternating direction method of multipliers for efficiently performing total variation minimization. We present empirical results on several MRI, which show that the proposed regularization framework can improve reconstruction accuracy over other methods.