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35
A primaldual proximal splitting approach for restoring data corrupted with PoissonGaussian noise
 in Proc. Int. Conf. Acoust. Speech Signal Process
, 2012
"... A PoissonGaussian model accurately describes the noise present in many imaging systems such as CCD cameras or fluorescence microscopy. However most existing restoration strategies rely on approximations of the PoissonGaussian noise statistics. We propose a convex optimization algorithm for the rec ..."
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Cited by 9 (8 self)
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A PoissonGaussian model accurately describes the noise present in many imaging systems such as CCD cameras or fluorescence microscopy. However most existing restoration strategies rely on approximations of the PoissonGaussian noise statistics. We propose a convex optimization algorithm for the reconstruction of signals degraded by a linear operator and corrupted with mixed PoissonGaussian noise. The originality of our approach consists of considering the exact continuousdiscrete model corresponding to the data statistics. After establishing the Lipschitz differentiability of the PoissonGaussian loglikelihood, we derive a primaldual iterative scheme for minimizing the associated penalized criterion. The proposed method is applicable to a large choice of penalty terms. The robustness of our scheme allows us to handle computational difficulties due to infinite sums arising from the computation of the gradient of the criterion. The proposed approach is validated on image restoration examples. Index Terms — convex optimization, image restoration, denoising, deconvolution. 1.
Nonlocal hierarchical dictionary learning using wavelets for image denoising
 IEEE Transactions on Image Processing
"... Abstract — Exploiting the sparsity within representation models for images is critical for image denoising. The best currently available denoising methods take advantage of the sparsity from image selfsimilarity, prelearned, and fixed representations. Most of these methods, however, still have dif ..."
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Cited by 9 (0 self)
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Abstract — Exploiting the sparsity within representation models for images is critical for image denoising. The best currently available denoising methods take advantage of the sparsity from image selfsimilarity, prelearned, and fixed representations. Most of these methods, however, still have difficulties in tackling high noise levels or noise models other than Gaussian. In this paper, the multiresolution structure and sparsity of wavelets are employed by nonlocal dictionary learning in each decomposition level of the wavelets. Experimental results show that our proposed method outperforms two stateoftheart image denoising algorithms on higher noise levels. Furthermore, our approach is more adaptive to the less extensively researched uniform noise. Index Terms — Image denoising, wavelets, sparse coding, multiscale, nonlocal.
Image denoising with multilayer perceptrons, part 2: training tradeoffs and analysis of their mechanisms
 JOURNAL OF MACHINE LEARNING RESEARCH (JMLR)
, 2012
"... Image denoising can be described as the problem of mapping from a noisy image to a noisefree image. In Burger et al. (2012), we show that multilayer perceptrons can achieve outstanding image denoising performance for various types of noise (additive white Gaussian noise, mixed PoissonGaussian noi ..."
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Cited by 6 (3 self)
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Image denoising can be described as the problem of mapping from a noisy image to a noisefree image. In Burger et al. (2012), we show that multilayer perceptrons can achieve outstanding image denoising performance for various types of noise (additive white Gaussian noise, mixed PoissonGaussian noise, JPEG artifacts, saltandpepper noise and noise resembling stripes). In this work we discuss in detail which tradeoffs have to be considered during the training procedure. We will show how to achieve good results and which pitfalls to avoid. By analysing the activation patterns of the hidden units we are able to make observations regarding the functioning principle of multilayer perceptrons trained for image denoising.
A Dictionary Learning Approach for Poisson Image Deblurring
, 2013
"... The restoration of images corrupted by blur and Poisson noise is a key issue in medical and biological image processing. While most existing methods are based on variational models, generally derived from a Maximum A Posteriori (MAP) formulation, recently sparse representations of images have shown ..."
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Cited by 5 (0 self)
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The restoration of images corrupted by blur and Poisson noise is a key issue in medical and biological image processing. While most existing methods are based on variational models, generally derived from a Maximum A Posteriori (MAP) formulation, recently sparse representations of images have shown to be efficient approaches for image recovery. Following this idea, we propose in this paper a model containing three terms: a patchbased sparse representation prior over a learned dictionary, the pixelbased total variation regularization term and a datafidelity term capturing the statistics of Poisson noise. The resulting optimization problem can be solved by an alternating minimization technique combined with variable splitting. Extensive experimental results suggest that in terms of visual quality, PSNR value and the method noise, the proposed algorithm outperforms stateoftheart methods.
An EM Approach for PoissonGaussian Noise Modeling ∗
, 2012
"... The problem of estimating the parameters of a PoissonGaussian model from experimental data has recently raised much interest in various applications, especially for CCD imaging systems. In this context, a field of independent random variables is observed, which is varying both in time and space. Ea ..."
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Cited by 4 (1 self)
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The problem of estimating the parameters of a PoissonGaussian model from experimental data has recently raised much interest in various applications, especially for CCD imaging systems. In this context, a field of independent random variables is observed, which is varying both in time and space. Each variable is a sum of two components, one following a Poisson and the other a Gaussian distribution. In this paper, a general formulation is considered where the associated Poisson process is nonstationary in space and also exhibits an exponential decay in time, whereas the Gaussian component corresponds to a stationary white noise with arbitrary mean. To solve the considered parametric estimation problem, an iterative ExpectationMaximization (EM) approach is proposed. Much attention is paid to the initialization of the EM algorithm for which an adequate momentbased method using recent optimization tools is proposed. In addition, a performance analysis of the proposed approach is carried out by computing the CramerRao bounds on the estimated variables. The performance of the proposed estimation procedure is illustrated on both synthetic data and real fluorescence microscopy image sequences. The algorithm is shown to provide reliable estimates of the mean/variance of the Gaussian noise and of the scale parameter of the Poisson component, as well as of its exponential decay rate.
POISSONGAUSSIAN DENOISING USING THE EXACT UNBIASED INVERSE OF THE GENERALIZED ANSCOMBE TRANSFORMATION
"... The characteristic errors of many digital imaging devices can be modelled as PoissonGaussian noise, the removal of which can be approached indirectly through variance stabilization. The generalized Anscombe transformation (GAT) is commonly used for stabilization, but rigorous studies regarding its ..."
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Cited by 4 (0 self)
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The characteristic errors of many digital imaging devices can be modelled as PoissonGaussian noise, the removal of which can be approached indirectly through variance stabilization. The generalized Anscombe transformation (GAT) is commonly used for stabilization, but rigorous studies regarding its unbiased inverse transformation have been neglected. We introduce the exact unbiased inverse of the GAT, show that it is of essential importance for ensuring accurate denoising, and demonstrate that our approach leads to stateoftheart results. This paper generalizes our earlier work, in which we presented an exact unbiased inverse of the Anscombe transformation for the case of pure Poisson noise removal. Index Terms — denoising, photonlimited imaging, variance stabilization, PoissonGaussian noise. 1.
An EM approach for timevariant PoissonGaussian model parameter estimation
 IEEE Trans. Image Process
, 2013
"... The problem of estimating the parameters of a PoissonGaussian model from experimental data has recently raised much interest in various applications, for instance in confocal fluorescence microscopy. In this context, a field of independent random variables is observed, which is varying both in time ..."
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Cited by 2 (2 self)
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The problem of estimating the parameters of a PoissonGaussian model from experimental data has recently raised much interest in various applications, for instance in confocal fluorescence microscopy. In this context, a field of independent random variables is observed, which is varying both in time and space. Each variable is a sum of two components, one following a Poisson and the other a Gaussian distribution. In this paper, a general formulation is considered where the associated Poisson process is nonstationary in space and also exhibits an exponential decay in time, whereas the Gaussian component corresponds to a stationary white noise with arbitrary mean. To solve the considered parametric estimation problem, we follow an iterative ExpectationMaximization (EM) approach. The parameter update equations involve deriving finite approximation of infinite sums. Expressions for the maximum error incurred in the process are also given. Since the problem is nonconvex, we pay attention to the EM initialization, using a momentbased method where recent optimization tools come into play. We carry out a performance analysis by computing the CramerRao bounds on the estimated variables. The practical performance of the proposed estimation procedure is illustrated on both synthetic data and real fluorescence macroscopy image sequences. The algorithm is shown to provide reliable estimates of the mean/variance of the
Nonparametric noise estimation method for raw images
, 2013
"... Optimal denoising works at best on raw images (the image formed at the output of the focal plane, at the CCD or CMOS detector), which display a white signaldependent noise. The noise model of the raw image is characterized by a function that given the intensity of a pixel in the noisy image returns ..."
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Optimal denoising works at best on raw images (the image formed at the output of the focal plane, at the CCD or CMOS detector), which display a white signaldependent noise. The noise model of the raw image is characterized by a function that given the intensity of a pixel in the noisy image returns the corresponding standard deviation; the plot of this function is the noise curve. This paper develops a nonparametric approach estimating the noise curve directly from a single raw image. An extensive crossvalidation procedure is described to compare this new method with stateoftheart parametric methods and with laboratory calibration methods giving a reliable ground truth, even for nonlinear detectors. © 2014 Optical Society of America OCIS codes: (040.1520) CCD, chargecoupled device; (100.2960) Image analysis; (110.4280) Noise in imaging systems; (040.0040) Detectors; (040.3780) Low light level; (100.2980) Image enhancement.
A CURE for Noisy Magnetic Resonance Images: ChiSquare Unbiased Risk Estimation
"... Abstract — In this paper, we derive an unbiased expression for the expected meansquared error associated with continuously differentiable estimators of the noncentrality parameter of a chisquare random variable. We then consider the task of denoising squaredmagnitude magnetic resonance (MR) image ..."
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Abstract — In this paper, we derive an unbiased expression for the expected meansquared error associated with continuously differentiable estimators of the noncentrality parameter of a chisquare random variable. We then consider the task of denoising squaredmagnitude magnetic resonance (MR) image data, which are well modeled as independent noncentral chisquare random variables on two degrees of freedom. We consider two broad classes of linearly parameterized shrinkage estimators that can be optimized using our risk estimate, one in the general context of undecimated filterbank transforms, and the other in the specific case of the unnormalized Haar wavelet transform. The resultant algorithms are computationally tractable and improve upon most stateoftheart methods for both simulated and actual MR image data. Index Terms — Chisquare distribution, filterbank transform, image denoising, magnetic resonance (MR) imaging, Rician noise,
LLSURE: Local linear surebased edgepreserving image filtering
 IEEE Trans. Image Process
, 2013
"... AbstractIn this paper, we propose a novel approach for performing highquality edgepreserving image filtering. Based on a local linear model and using the principle of Stein's unbiased risk estimate as an estimator for the mean squared error from the noisy image only, we derive a simple expl ..."
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AbstractIn this paper, we propose a novel approach for performing highquality edgepreserving image filtering. Based on a local linear model and using the principle of Stein's unbiased risk estimate as an estimator for the mean squared error from the noisy image only, we derive a simple explicit image filter which can filter out noise while preserving edges and finescale details. Moreover, this filter has a fast and exact lineartime algorithm whose computational complexity is independent of the filtering kernel size; thus, it can be applied to real time image processing tasks. The experimental results demonstrate the effectiveness of the new filter for various computer vision applications, including noise reduction, detail smoothing and enhancement, high dynamic range compression, and flash/noflash denoising. Index TermsEdgepreserving image filtering, high dynamic range (HDR) compression, local linear model, Stein's unbiased risk estimate (SURE).