In the past few years, supervised networks have achieved promising performance on image denoising. These methods learn image priors and synthetic noise statistics from plenty pairs of noisy and clean images. Recently, several unsupervised denoising networks are proposed only using external noisy images for training. However, the networks learned from external data inherently suffer from the domain gap dilemma, i.e., the image priors and noise statistics are very different between the training data and the corrupted test images. This dilemma becomes more clear when dealing with the signal dependent realistic noise in real photographs. In this work, we provide a statistically useful conclusion: it is possible to learn an unsupervised network only with the corrupted image, approximating the optimal parameters of a supervised network learned with pairs of noisy and clean images. This is achieved by proposing a "Noisy-As-Clean" strategy: taking the corrupted image as "clean" target and the simulated noisy images (based on the corrupted image) as inputs. Extensive experiments show that the unsupervised denoising networks learned with our "Noisy-As-Clean" strategy surprisingly outperforms previous supervised networks on removing several typical synthetic noise and realistic noise. The code will be publicly released.
are widely used for different image restoration tasks @cite_46 @cite_53 @cite_15 @cite_43 @cite_54 @cite_0 . They can be divided into internal priors and external priors. The internal image priors are directly learned on the input test image itself, while the external image priors need to be learned with external images (as long as not the test input). The internal priors are adaptive to its contents, but somewhat affected by the corruptions @cite_46 @cite_53 @cite_15 . By contrast, the external priors are effective for restoring general images, but not optimal for specific test image @cite_43 @cite_54 @cite_0 .
@cite_15 @cite_54 @cite_53 @cite_0 @cite_43 @cite_46
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Statistics of ‘natural images’ provides useful priors for solving under-constrained problems in Computer Vision. Such statistics is usually obtained from large collections of natural images. We claim that the substantial internal data redundancy within a single natural image (e.g., recurrence of small image patches), gives rise to powerful internal statistics, obtained directly from the image itself. While internal patch recurrence has been used in various applications, we provide a parametric quantification of this property. We show that the likelihood of an image patch to recur at another image location can be expressed parametricly as a function of the spatial distance from the patch, and its gradient content. This “internal parametric prior” is used to improve existing algorithms that rely on patch recurrence. Moreover, we show that internal image-specific statistics is often more powerful than general external statistics, giving rise to more powerful image-specific priors. In particular: (i) Patches tend to recur much more frequently (densely) inside the same image, than in any random external collection of natural images. (ii) To find an equally good external representative patch for all the patches of an image, requires an external database of hundreds of natural images. (iii) Internal statistics often has stronger predictive power than external statistics, indicating that it may potentially give rise to more powerful image-specific priors. Learning good image priors is of utmost importance for the study of vision, computer vision and image processing applications. Learning priors and optimizing over whole images can lead to tremendous computational challenges. In contrast, when we work with small image patches, it is possible to learn priors and perform patch restoration very efficiently. This raises three questions - do priors that give high likelihood to the data also lead to good performance in restoration? Can we use such patch based priors to restore a full image? Can we learn better patch priors? In this work we answer these questions. We compare the likelihood of several patch models and show that priors that give high likelihood to data perform better in patch restoration. Motivated by this result, we propose a generic framework which allows for whole image restoration using any patch based prior for which a MAP (or approximate MAP) estimate can be calculated. We show how to derive an appropriate cost function, how to optimize it and how to use it to restore whole images. Finally, we present a generic, surprisingly simple Gaussian Mixture prior, learned from a set of natural images. When used with the proposed framework, this Gaussian Mixture Model outperforms all other generic prior methods for image denoising, deblurring and inpainting. We address the image denoising problem, where zero-mean white and homogeneous Gaussian additive noise is to be removed from a given image. The approach taken is based on sparse and redundant representations over trained dictionaries. Using the K-SVD algorithm, we obtain a dictionary that describes the image content effectively. Two training options are considered: using the corrupted image itself, or training on a corpus of high-quality image database. Since the K-SVD is limited in handling small image patches, we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image. We show how such Bayesian treatment leads to a simple and effective denoising algorithm. This leads to a state-of-the-art denoising performance, equivalent and sometimes surpassing recently published leading alternative denoising methods 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 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. Non-parametric Bayesian techniques are considered for learning dictionaries for sparse image representations, with applications in denoising, inpainting and compressive sensing (CS). The beta process is employed as a prior for learning the dictionary, and this non-parametric method naturally infers an appropriate dictionary size. The Dirichlet process and a probit stick-breaking process are also considered to exploit structure within an image. The proposed method can learn a sparse dictionary in situ; training images may be exploited if available, but they are not required. Further, the noise variance need not be known, and can be non-stationary. Another virtue of the proposed method is that sequential inference can be readily employed, thereby allowing scaling to large images. Several example results are presented, using both Gibbs and variational Bayesian inference, with comparisons to other state-of-the-art approaches.