Estimation of parameters for generalized Gaussian distribution

Roenko, Alexey; Djurović, Igor; Simeunović, Marko

doi:10.1109/isccsp.2014.6877892

Cited by 20 publications

(7 citation statements)

References 15 publications

(24 reference statements)

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“…3,2]. This observation is consistent with earlier works that have attempted to learn GGMM shape parameters from data [51]. Given n training clean patches of size P and an initialization for the K parameters w k > 0, Σ k ∈ R P ×P and ν k ∈ R P , for k = 1, .…”

Section: Learning Ggmmssupporting

confidence: 86%

Image Denoising with Generalized Gaussian Mixture Model Patch Priors

Deledalle¹,

Parameswaran²,

Nguyen³

2018

SIAM J. Imaging Sci.

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Patch priors have become an important component of image restoration. A powerful approach in this category of restoration algorithms is the popular Expected Patch Log-Likelihood (EPLL) algorithm. EPLL uses a Gaussian mixture model (GMM) prior learned on clean image patches as a way to regularize degraded patches. In this paper, we show that a generalized Gaussian mixture model (GGMM) captures the underlying distribution of patches better than a GMM. Even though GGMM is a powerful prior to combine with EPLL, the non-Gaussianity of its components presents major challenges to be applied to a computationally intensive process of image restoration. Specifically, each patch has to undergo a patch classification step and a shrinkage step. These two steps can be efficiently solved with a GMM prior but are computationally impractical when using a GGMM prior. In this paper, we provide approximations and computational recipes for fast evaluation of these two steps, so that EPLL can embed a GGMM prior on an image with more than tens of thousands of patches. Our main contribution is to analyze the accuracy of our approximations based on thorough theoretical analysis. Our evaluations indicate that the GGMM prior is consistently a better fit for modeling image patch distribution and performs better on average in image denoising task.

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Section: Learning Ggmmssupporting

confidence: 86%

Image Denoising with Generalized Gaussian Mixture Model Patch Priors

Deledalle¹,

Parameswaran²,

Nguyen³

2018

SIAM J. Imaging Sci.

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“…2b, -upper The weighting coefficients w 01 and w 02 have been determined during the calculation of the GMM and normalized so that w 01 + w 02 = 1. To avoid the necessity of using sophisticated estimators based on maximum likelihood, moments, entropy matching or global convergence [27], the values of the four GGD parameters: shape parameter p, location parameter μ, variance of the distribution λ, and standard deviation σ, as well as parameters of the GMM2, have been determined using the fast approximated method based on the standardized moment, described in the paper [8].…”

Section: Improved Two-step Binarization Algorithmmentioning

confidence: 99%

Improved Two-Step Binarization of Degraded Document Images Based on Gaussian Mixture Model

Krupiński

Lech

Okarma

2020

Lecture Notes in Computer Science

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Image binarization is one of the most relevant preprocessing operations influencing the results of further image analysis conducted for many purposes. During this step a significant loss of information occurs and the use of inappropriate thresholding methods may cause difficulties in further shape analysis or even make it impossible to recognize different shapes of objects or characters. Some of the most typical applications utilizing the analysis of binary images are Optical Character Recognition (OCR) and Optical Mark Recognition (OMR), which may also be applied for unevenly illuminated natural images, as well as for challenging degraded historical document images, considered as typical benchmarking tools for image binarization algorithms.To face the still valid challenge of relatively fast and simple, but robust binarization of degraded document images, a novel two-step algorithm utilizing initial thresholding, based on the modelling of the simplified image histogram using Gaussian Mixture Model (GMM) and the Monte Carlo method, is proposed in the paper. This approach can be considered as the extension of recently developed image preprocessing method utilizing Generalized Gaussian Distribution (GGD), based on the assumption of its similarity to the histograms of ground truth binary images distorted by Gaussian noise. The processing time of the first step, producing the intermediate images with partially removed background information, may be significantly reduced due to the use of the Monte Carlo method.The proposed improved approach leads to even better results, not only for well-known DIBCO benchmarking databases, but also for more demanding Bickley Diary dataset, allowing the use of some well-known classical binarization methods, including the global ones, in the second step of the algorithm.

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“…In order to deal with this issue and take full advantage of the potential robustness properties of the correntropy, the generalized Gaussian density function was proposed as a kernel function of the correntropy in Reference [ 21 ]. The generalized Gaussian density function with zero-mean is given by References [ 18 , 19 ] as follows:

where

is the gamma function,

denotes the shape parameter and

denotes the scale parameter. For simplicity,

is usually set as an integer value.…”

Section: Sgmcc Algorithmmentioning

confidence: 99%

“…In recent years, a generalized maximum correntropy criterion (GMCC) has been proposed, which adopts the generalized Gaussian density [ 18 , 19 , 20 ] function as the kernel function (not necessarily a Mercer kernel [ 21 ]) and the type of this correntropy is called the generalized correntropy. Similar to the original correntropy with Gaussian kernel, the generalized correntropy can also be used as an optimization cost in the estimation-related problems.…”

Section: Introductionmentioning

confidence: 99%

A Smoothed Algorithm with Convergence Analysis under Generalized Maximum Correntropy Criteria in Impulsive Interference

Shi

Zhao

2019

Entropy

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The generalized maximum correntropy criterion (GMCC) algorithm is computationally simple and robust against impulsive noise but it suffers from slow convergence speed as it is derived and based on stochastic gradient, which only use the current data sample. In order to deal with this issue, a smoothed GMCC algorithm (SGMCC) is proposed. In the SGMCC algorithm, instead of taking the exponential weighted average of gradient vector to approximate the expectation of the gradient vector, we take the exponential weighted average of the variable step-size so that the SGMCC algorithm can be viewed as a sign GMCC algorithm with smoothed variable step-size. Moreover, convergence performance analyses are derived in terms of variable step-size, mean-square stability and steady-state behavior to demonstrate the robustness of the proposed algorithm. At last, simulation comparisons show that the proposed algorithm is robust against impulsive noise and converges fast with lower computational complexity. Also, for the steady-state behavior, simulation results verify that the simulated value matches well with the theoretical one.

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Estimation of parameters for generalized Gaussian distribution

Cited by 20 publications

References 15 publications

Image Denoising with Generalized Gaussian Mixture Model Patch Priors

Image Denoising with Generalized Gaussian Mixture Model Patch Priors

Improved Two-Step Binarization of Degraded Document Images Based on Gaussian Mixture Model

A Smoothed Algorithm with Convergence Analysis under Generalized Maximum Correntropy Criteria in Impulsive Interference

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