Multivariate statistical modeling for image denoising using wavelet transforms

Cho, Dongwook; Bui, Tien D.

doi:10.1016/j.image.2004.10.003

Cited by 124 publications

(63 citation statements)

References 18 publications

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“…The class of ecpe distributions is used in a crossover trial on insulin applied to rabbits in [23], in image denoising in [24] and in colour texture retrieval in [25]. Applications of multivariate g-and-h distributions to jointly modeling body mass index and lean body mass are demonstrated in [26] and accompanied by star-shaped contoured density illustrations.…”

Section: Applicationsmentioning

confidence: 99%

Estimation of Star-Shaped Distributions

Liebscher

Richter

2016

Risks

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Scatter plots of multivariate data sets motivate modeling of star-shaped distributions beyond elliptically contoured ones. We study properties of estimators for the density generator function, the star-generalized radius distribution and the density in a star-shaped distribution model. For the generator function and the star-generalized radius density, we consider a non-parametric kernel-type estimator. This estimator is combined with a parametric estimator for the contours which are assumed to follow a parametric model. Therefore, the semiparametric procedure features the flexibility of nonparametric estimators and the simple estimation and interpretation of parametric estimators. Alternatively, we consider pure parametric estimators for the density. For the semiparametric density estimator, we prove rates of uniform, almost sure convergence which coincide with the corresponding rates of one-dimensional kernel density estimators when excluding the center of the distribution. We show that the standardized density estimator is asymptotically normally distributed. Moreover, the almost sure convergence rate of the estimated distribution function of the star-generalized radius is derived. A particular new two-dimensional distribution class is adapted here to agricultural and financial data sets.

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Section: Applicationsmentioning

confidence: 99%

Estimation of Star-Shaped Distributions

Liebscher

Richter

2016

Risks

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“…Wavelet transform is known to be favorable because of its properties such as non-Gaussianity, Clustering and Persistence [5], [7], [8]. Fig.1, shows 2D discrete wavelet transform www.ijacsa.thesai.org (DWT).…”

Section: Statistical Image Modelling Using Hidden Markov Tree Modelmentioning

confidence: 99%

“…A non-parametric tree based model for joint statistics of wavelet coefficients has been discussed in [4]. To realize neighbouring dependency between wavelet coefficients across scales, a generalized Multivariate Gaussian distribution has been proposed in [5]. In [6], another tree model using hidden markov tree structure has been developed that refers to local parameterization for image denoising.…”

Section: Introductionmentioning

confidence: 99%

Denoising in Wavelet Domain Using Probabilistic Graphical Models

Haider¹,

Riaz²,

Touqir³

et al. 2016

ijacsa

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“…Cho and Bui exploited a multivariate generalized Gaussian distribution to model the dependency between wavelet coefficients 10 . The performance of the aforementioned shrinkage methods greatly depends on the effectiveness of the prior model of the wavelet coefficients.…”

Section: Introductionmentioning

confidence: 99%

A noise reduction approach based on Stein′s unbiased risk estimate

Guo¹,

Zhang²

2012

ScienceAsia

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This paper proposes a new wavelet-based shrinkage function for 1D signal noise reduction. This shrinkage function adopts the intrascale correlations between wavelet coefficients and exploits Stein's unbiased risk estimator to achieve the optimal parameter. Unlike the methods based upon Bayes estimators, the proposed method does not use any prior hypotheses on wavelet coefficients. Experiments performed on simulated signals clearly indicate that our method outperforms conventional noise reduction methods in the sense of the signal-to-noise ratio.

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Multivariate statistical modeling for image denoising using wavelet transforms

Cited by 124 publications

References 18 publications

Estimation of Star-Shaped Distributions

Estimation of Star-Shaped Distributions

Denoising in Wavelet Domain Using Probabilistic Graphical Models

A noise reduction approach based on Stein′s unbiased risk estimate

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