Image Noise Level Estimation by Principal Component Analysis
01 Feb 2013-IEEE Transactions on Image Processing (IEEE Trans Image Process)-Vol. 22, Iss: 2, pp 687-699
TL;DR: This paper shows that the noise variance can be estimated as the smallest eigenvalue of the image block covariance matrix, which is at least 15 times faster than methods with similar accuracy, and at least two times more accurate than other methods.
Abstract: The problem of blind noise level estimation arises in many image processing applications, such as denoising, compression, and segmentation. In this paper, we propose a new noise level estimation method on the basis of principal component analysis of image blocks. We show that the noise variance can be estimated as the smallest eigenvalue of the image block covariance matrix. Compared with 13 existing methods, the proposed approach shows a good compromise between speed and accuracy. It is at least 15 times faster than methods with similar accuracy, and it is at least two times more accurate than other methods. Our method does not assume the existence of homogeneous areas in the input image and, hence, can successfully process images containing only textures.
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TL;DR: This paper describes a recently created image database, TID2013, intended for evaluation of full-reference visual quality assessment metrics, and methodology for determining drawbacks of existing visual quality metrics is described.
Abstract: This paper describes a recently created image database, TID2013, intended for evaluation of full-reference visual quality assessment metrics. With respect to TID2008, the new database contains a larger number (3000) of test images obtained from 25 reference images, 24 types of distortions for each reference image, and 5 levels for each type of distortion. Motivations for introducing 7 new types of distortions and one additional level of distortions are given; examples of distorted images are presented. Mean opinion scores (MOS) for the new database have been collected by performing 985 subjective experiments with volunteers (observers) from five countries (Finland, France, Italy, Ukraine, and USA). The availability of MOS allows the use of the designed database as a fundamental tool for assessing the effectiveness of visual quality. Furthermore, existing visual quality metrics have been tested with the proposed database and the collected results have been analyzed using rank order correlation coefficients between MOS and considered metrics. These correlation indices have been obtained both considering the full set of distorted images and specific image subsets, for highlighting advantages and drawbacks of existing, state of the art, quality metrics. Approaches to thorough performance analysis for a given metric are presented to detect practical situations or distortion types for which this metric is not adequate enough to human perception. The created image database and the collected MOS values are freely available for downloading and utilization for scientific purposes. We have created a new large database.This database contains larger number of distorted images and distortion types.MOS values for all images are obtained and provided.Analysis of correlation between MOS and a wide set of existing metrics is carried out.Methodology for determining drawbacks of existing visual quality metrics is described.
943 citations
15 Jun 2019
TL;DR: CBDNet as discussed by the authors proposes to train a convolutional blind denoising network with more realistic noise model and real-world clean image pairs to improve the generalization ability of deep CNN denoisers.
Abstract: 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 pho- tographs clearly demonstrate the superior performance of CBDNet over state-of-the-arts in terms of quantitative met- rics and visual quality. The code has been made available at https://github.com/GuoShi28/CBDNet.
745 citations
01 Jun 2006
TL;DR: An apposite and eminently readable reference for all behavioral science research and development.
Abstract: An apposite and eminently readable reference for all behavioral science research and development
649 citations
TL;DR: A patch-based noise level estimation algorithm that selects low-rank patches without high frequency components from a single noisy image and estimates the noise level based on the gradients of the patches and their statistics is proposed.
Abstract: Noise level is an important parameter to many image processing applications. For example, the performance of an image denoising algorithm can be much degraded due to the poor noise level estimation. Most existing denoising algorithms simply assume the noise level is known that largely prevents them from practical use. Moreover, even with the given true noise level, these denoising algorithms still cannot achieve the best performance, especially for scenes with rich texture. In this paper, we propose a patch-based noise level estimation algorithm and suggest that the noise level parameter should be tuned according to the scene complexity. Our approach includes the process of selecting low-rank patches without high frequency components from a single noisy image. The selection is based on the gradients of the patches and their statistics. Then, the noise level is estimated from the selected patches using principal component analysis. Because the true noise level does not always provide the best performance for nonblind denoising algorithms, we further tune the noise level parameter for nonblind denoising. Experiments demonstrate that both the accuracy and stability are superior to the state of the art noise level estimation algorithm for various scenes and noise levels.
381 citations
Cites background from "Image Noise Level Estimation by Pri..."
...[7], in which a number of patches with largest variances are discarded....
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...In patch-based approaches [2], [5], [7], images are decomposed into a number of patches....
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07 Dec 2015
TL;DR: This paper derives a new nonparametric algorithm for efficient noise level estimation based on the observation that patches decomposed from a clean image often lie around a low-dimensional subspace and outperforms existing state-of-the-art algorithms on estimating noise level with the least executing time.
Abstract: In this paper, we address the problem of estimating noise level from a single image contaminated by additive zero-mean Gaussian noise. We first provide rigorous analysis on the statistical relationship between the noise variance and the eigenvalues of the covariance matrix of patches within an image, which shows that many state-of-the-art noise estimation methods underestimate the noise level of an image. To this end, we derive a new nonparametric algorithm for efficient noise level estimation based on the observation that patches decomposed from a clean image often lie around a low-dimensional subspace. The performance of our method has been guaranteed both theoretically and empirically. Specifically, our method outperforms existing state-of-the-art algorithms on estimating noise level with the least executing time in our experiments. We further demonstrate that the denoising algorithm BM3D algorithm achieves optimal performance using noise variance estimated by our algorithm.
225 citations
Cites background or methods from "Image Noise Level Estimation by Pri..."
...The authors of [19, 23] claim that these methods can accurately estimate the noise level of images without homogeneous areas....
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...Recently, new algorithms have been proposed in [19, 23] with state-of-the-art performance....
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...In both [19] and [23], researchers chose the minimum eigenvalues as their noise estimation....
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...For [19] and [23], we use the default parameters reported in their papers....
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...We compare its performance with two state-of-the-art methods [19, 23], whose source codes can be downloaded from their homepage 1 (2)....
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References
More filters
15 Oct 2005
TL;DR: Principal component analysis (PCA) as discussed by the authors replaces the p original variables by a smaller number, q, of derived variables, the principal components, which are linear combinations of the original variables.
Abstract: When large multivariate datasets are analyzed, it is often desirable to reduce their dimensionality. Principal component analysis is one technique for doing this. It replaces the p original variables by a smaller number, q, of derived variables, the principal components, which are linear combinations of the original variables. Often, it is possible to retain most of the variability in the original variables with q very much smaller than p. Despite its apparent simplicity, principal component analysis has a number of subtleties, and it has many uses and extensions. A number of choices associated with the technique are briefly discussed, namely, covariance or correlation, how many components, and different normalization constraints, as well as confusion with factor analysis. Various uses and extensions are outlined.
Keywords:
dimension reduction;
factor analysis;
multivariate analysis;
variance maximization
14,773 citations
TL;DR: The authors prove two results about this type of estimator that are unprecedented in several ways: with high probability f/spl circ/*/sub n/ is at least as smooth as f, in any of a wide variety of smoothness measures.
Abstract: Donoho and Johnstone (1994) proposed a method for reconstructing an unknown function f on [0,1] from noisy data d/sub i/=f(t/sub i/)+/spl sigma/z/sub i/, i=0, ..., n-1,t/sub i/=i/n, where the z/sub i/ are independent and identically distributed standard Gaussian random variables. The reconstruction f/spl circ/*/sub n/ is defined in the wavelet domain by translating all the empirical wavelet coefficients of d toward 0 by an amount /spl sigma//spl middot//spl radic/(2log (n)/n). The authors prove two results about this type of estimator. [Smooth]: with high probability f/spl circ/*/sub n/ is at least as smooth as f, in any of a wide variety of smoothness measures. [Adapt]: the estimator comes nearly as close in mean square to f as any measurable estimator can come, uniformly over balls in each of two broad scales of smoothness classes. These two properties are unprecedented in several ways. The present proof of these results develops new facts about abstract statistical inference and its connection with an optimal recovery model. >
9,359 citations
TL;DR: An algorithm based on an enhanced sparse representation in transform domain based on a specially developed collaborative Wiener filtering achieves state-of-the-art denoising performance in terms of both peak signal-to-noise ratio and subjective visual quality.
Abstract: We propose a novel image denoising strategy based on an enhanced sparse representation in transform domain. The enhancement of the sparsity is achieved by grouping similar 2D image fragments (e.g., blocks) into 3D data arrays which we call "groups." Collaborative Altering is a special procedure developed to deal with these 3D groups. We realize it using the three successive steps: 3D transformation of a group, shrinkage of the transform spectrum, and inverse 3D transformation. The result is a 3D estimate that consists of the jointly filtered grouped image blocks. By attenuating the noise, the collaborative filtering reveals even the finest details shared by grouped blocks and, at the same time, it preserves the essential unique features of each individual block. The filtered blocks are then returned to their original positions. Because these blocks are overlapping, for each pixel, we obtain many different estimates which need to be combined. Aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy. A significant improvement is obtained by a specially developed collaborative Wiener filtering. An algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail; an extension to color-image denoising is also developed. The experimental results demonstrate that this computationally scalable algorithm achieves state-of-the-art denoising performance in terms of both peak signal-to-noise ratio and subjective visual quality.
7,912 citations
"Image Noise Level Estimation by Pri..." refers background in this paper
...Consider noise-free signal (xk) = (2 + (−1)k) = (1, 3, 1, 3, . . .) and noisy signal (yk) = (xk + nk), where nk are realizations of a random variable with normal distribution N (0; 0.52)....
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Book•
01 Jan 1965
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.
Abstract: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography Index.
7,422 citations
TL;DR: This work addresses the image denoising problem, where zero-mean white and homogeneous Gaussian additive noise is to be removed from a given image, and uses the K-SVD algorithm to obtain a dictionary that describes the image content effectively.
Abstract: 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
5,493 citations