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58
Novel Bayesian Multiscale Method for Speckle Removal in Medical Ultrasound Images
 IEEE TRANS. MED. IMAG
, 2001
"... A novel speckle suppression method for medical ultrasound images is presented. First, the logarithmic transform of the original image is analyzed into the multiscale wavelet domain. We show that the subband decompositions of ultrasound images have significantly nonGaussian statistics that are best ..."
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Cited by 75 (11 self)
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A novel speckle suppression method for medical ultrasound images is presented. First, the logarithmic transform of the original image is analyzed into the multiscale wavelet domain. We show that the subband decompositions of ultrasound images have significantly nonGaussian statistics that are best described by families of heavytailed distributions such as the alphastable. Then, we design a Bayesian estimator that exploits these statistics. We use the alphastable model to develop a blind noiseremoval processor that performs a nonlinear operation on the data. Finally, we compare our technique with current stateoftheart soft and hard thresholding methods applied on actual ultrasound medical images and we quantify the achieved performance improvement.
SAR Image Denoising via Bayesian Wavelet Shrinkage Based on HeavyTailed Modeling
, 2003
"... Synthetic aperture radar (SAR) images are inherently affected by multiplicative speckle noise, which is due to the coherent nature of the scattering phenomenon. This paper proposes a novel Bayesianbased algorithm within the framework of wavelet analysis, which reduces speckle in SAR images while pr ..."
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Cited by 57 (8 self)
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Synthetic aperture radar (SAR) images are inherently affected by multiplicative speckle noise, which is due to the coherent nature of the scattering phenomenon. This paper proposes a novel Bayesianbased algorithm within the framework of wavelet analysis, which reduces speckle in SAR images while preserving the structural features and textural information of the scene. First,
Hidden messages in heavytails: DCTdomain watermark detection using alphastable models
 IEEE Transactions on Multimedia
"... Abstract—This paper addresses issues that arise in copyright protection systems of digital images, which employ blind watermark verification structures in the discrete cosine transform (DCT) domain. First, we observe that statistical distributions with heavy algebraic tails, such as the alphastable ..."
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Cited by 18 (1 self)
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Abstract—This paper addresses issues that arise in copyright protection systems of digital images, which employ blind watermark verification structures in the discrete cosine transform (DCT) domain. First, we observe that statistical distributions with heavy algebraic tails, such as the alphastable family, are in many cases more accurate modeling tools for the DCT coefficients of JPEGanalyzed images than families with exponential tails such as the generalized Gaussian. Motivated by our modeling results, we then design a new processor for blind watermark detection using the Cauchy member of the alphastable family. The Cauchy distribution is chosen because it is the only nonGaussian symmetric alphastable distribution that exists in closed form and also because it leads to the design of a nearly optimum detector with robust detection performance. We analyze the performance of the new detector in terms of the associated probabilities of detection and false alarm and we compare it to the performance of the generalized Gaussian detector by performing experiments with various test images. Index Terms—Alphastable distributions, discrete cosine transform, image watermarking, Neyman–Pearson detector, statistical modeling. I.
Empirical Characteristic Function in Time Series Estimation
, 2001
"... Since the empirical characteristic function (ECF) is the Fourier transform of the empirical distribution function, it retains all the information in the sample but can overcome di#culties arising from the likelihood. This paper discusses an estimation method via the ECF for strictly stationary proce ..."
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Cited by 17 (0 self)
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Since the empirical characteristic function (ECF) is the Fourier transform of the empirical distribution function, it retains all the information in the sample but can overcome di#culties arising from the likelihood. This paper discusses an estimation method via the ECF for strictly stationary processes. Under some regularity conditions, the resulting estimators are shown to be consistent and asymptotically normal. The method is applied to estimate the stable ARMA models. For the general stable ARMA model for which the maximum likelihood approach is not feasible, Monte Carlo evidence shows that the ECF method is a viable estimation method for all the parameters of interest. For the Gaussian ARMA model, a particular stable ARMA model, the optimal weight functions and estimating equations are given. Monte Carlo studies highlight the finite sample performances of the ECF method relative to the exact and conditional maximum likelihood methods.
Some improvements in numerical evaluation of symmetric stable density and its derivatives
 Communications in StatisticsTheory and Methods
"... CIRJE Discussion Papers can be downloaded without charge from: ..."
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Cited by 14 (4 self)
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CIRJE Discussion Papers can be downloaded without charge from:
MAXIMUM LIKELIHOOD ESTIMATION FOR αSTABLE AUTOREGRESSIVE PROCESSES
, 908
"... We consider maximum likelihood estimation for both causal and noncausal autoregressive time series processes with nonGaussian αstable noise. A nondegenerate limiting distribution is given for maximum likelihood estimators of the parameters of the autoregressive model equation and the parameters of ..."
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Cited by 11 (0 self)
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We consider maximum likelihood estimation for both causal and noncausal autoregressive time series processes with nonGaussian αstable noise. A nondegenerate limiting distribution is given for maximum likelihood estimators of the parameters of the autoregressive model equation and the parameters of the stable noise distribution. The estimators for the autoregressive parameters are n 1/αconsistent and converge in distribution to the maximizer of a random function. The form of this limiting distribution is intractable, but the shape of the distribution for these estimators can be examined using the bootstrap procedure. The bootstrap is asymptotically valid under general conditions. The estimators for the parameters of the stable noise distribution have the traditional n 1/2 rate of convergence and are asymptotically normal. The behavior of the estimators for finite samples is studied via simulation, and we use maximum likelihood estimation to fit a noncausal autoregressive model to the natural logarithms of volumes of WalMart stock traded daily on the New York Stock Exchange. 1. Introduction. Many
Modeling financial data with stable distributions
, 2005
"... Stable distributions are a class of probability distributions that allow heavy tails and skewness. In addition to theoretical reasons for using stable laws, they are a rich family that can accurately model different kinds of financial data. We review the basic facts, describe programs that make it p ..."
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Cited by 8 (0 self)
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Stable distributions are a class of probability distributions that allow heavy tails and skewness. In addition to theoretical reasons for using stable laws, they are a rich family that can accurately model different kinds of financial data. We review the basic facts, describe programs that make it practical to use stable distributions, and give examples of these distributions in finance. A nontechnical introduction to multivariate stable laws is also given. 1 Basic facts about stable distributions Stable distributions are a class of probability laws that have intriguing theoretical and practical properties. Their applications to financial modeling comes from the fact that they generalize the normal (Gaussian) distribution and allow heavy tails and skewness, which are frequently seen in financial data. In this chapter, we focus on the basic definition and properties of stable laws, and show how they can be used in practice. We give no proofs; interested readers can find
Diverging Moments and Parameter Estimation
, 2002
"... Heavy tailed distributions which allow for values far from the mean to occur with considerable probability are of increasing importance in various applications as the arsenal of analytical and numerical tools grows. Examples of interest are the Stable and more generally the Pareto distributions f ..."
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Cited by 8 (4 self)
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Heavy tailed distributions which allow for values far from the mean to occur with considerable probability are of increasing importance in various applications as the arsenal of analytical and numerical tools grows. Examples of interest are the Stable and more generally the Pareto distributions for which moments of sufficiently large order diverge. In fact, the asymptotic powerlaws of the distribution function at infinity and zero are directly related to the existence of positive and negative order moments, respectively. In practice, however, when dealing with finite size data sets of an unknown distribution, standard empirical estimators of moments will typically fail to reflect the theoretical divergence of moments and provide finite estimates for all order moments. The main contribution of this paper is an empirical waveletbased estimator for the characteristic exponents and of a random variable, which bound the interval of all orders r with finite moment IEjxj . This objective is achieved by deriving a theoretical equivalence between finiteness of moments and the local Hölder regularity of the characteristic function at the origin and by deriving a wavelet based estimation scheme which is particularly suited to characteristic functions.
An Asymmetric Generalization of Gaussian and Laplace Laws
 Journal of Probability and Statistical Science
, 2003
"... Abstract: We study a class of skew continuous distributions on the real line that arises from symmetric exponential power laws by incorporating inverse scale factors into the positive and negative orthants. Skew and symmetric Laplace and normal laws are included in this class as special cases. We pr ..."
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Cited by 3 (0 self)
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Abstract: We study a class of skew continuous distributions on the real line that arises from symmetric exponential power laws by incorporating inverse scale factors into the positive and negative orthants. Skew and symmetric Laplace and normal laws are included in this class as special cases. We present main properties of skew exponential power laws, derive maximum likelihood estimators of their parameters, and discuss their applications in finance.