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20
Bivariate Shrinkage Functions for WaveletBased Denoising Exploiting Interscale Dependency
, 2002
"... Most simple nonlinear thresholding rules for waveletbased denoising assume that the wavelet coefficients are independent. However, wavelet coefficients of natural images have significant dependencies. In this paper, we will only consider the dependencies between the coefficients and their parents i ..."
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Cited by 135 (4 self)
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Most simple nonlinear thresholding rules for waveletbased denoising assume that the wavelet coefficients are independent. However, wavelet coefficients of natural images have significant dependencies. In this paper, we will only consider the dependencies between the coefficients and their parents in detail. For this purpose, new nonGaussian bivariate distributions are proposed, and corresponding nonlinear threshold functions (shrinkage functions) are derived from the models using Bayesian estimation theory. The new shrinkage functions do not assume the independence of wavelet coefficients. We will show three image denoising examples in order to show the performance of these new bivariate shrinkage rules. In the second example, a simple subbanddependent datadriven image denoising system is described and compared with effective datadriven techniques in the literature, namely VisuShrink, SureShrink, BayesShrink, and hidden Markov models. In the third example, the same idea is applied to the dualtree complex wavelet coefficients.
Hyperspectral Image Processing for Automatic Target Detection Applications
, 2003
"... This article presents an overview of the theoretical and practical issues associated with the development, analysis, and application of detection algorithms to exploit hyperspectral imaging data. We focus on techniques that exploit spectral information exclusively to make decisions regarding the ty ..."
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Cited by 23 (0 self)
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This article presents an overview of the theoretical and practical issues associated with the development, analysis, and application of detection algorithms to exploit hyperspectral imaging data. We focus on techniques that exploit spectral information exclusively to make decisions regarding the type of each pixel—target or nontarget—on a pixelbypixel basis in an image. First we describe the fundamental structure of the hyperspectral data and explain how these data influence the signal models used for the development and theoretical analysis of detection algorithms. Next we discuss the approach used to derive detection algorithms, the performance metrics necessary for the evaluation of these algorithms, and a taxonomy that presents the various algorithms in a systematic manner. We derive the basic algorithms in each family, explain how they work, and provide results for their theoretical performance. We conclude with empirical results that use hyperspectral imaging data from the HYDICE and Hyperion sensors to illustrate the operation and performance of various detectors.
Nonlinear Extraction of Independent Components of Natural Images Using Radial Gaussianization
, 2009
"... We consider the problem of efficiently encoding a signal by transforming it to a new representation whose components are statistically independent. A widely studied linear solution, known as independent component analysis (ICA), exists for the case when the signal is generated as a linear transforma ..."
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Cited by 14 (4 self)
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We consider the problem of efficiently encoding a signal by transforming it to a new representation whose components are statistically independent. A widely studied linear solution, known as independent component analysis (ICA), exists for the case when the signal is generated as a linear transformation of independent nongaussian sources. Here, we examine a complementary case, in which the source is nongaussian and elliptically symmetric. In this case, no invertible linear transform suffices to decompose the signal into independent components, but we show that a simple nonlinear transformation, which we call radial gaussianization (RG), is able to remove all dependencies. We then examine this methodology in the context of natural image statistics. We first show that distributions of spatially proximal bandpass filter responses are better described as elliptical than as linearly transformed independent sources. Consistent with this, we demonstrate that the reduction in dependency achieved by applying RG to either nearby pairs or blocks of bandpass filter responses is significantly greater than that achieved by ICA. Finally, we show that the RG transformation may be closely approximated by divisive normalization, which has been used to model the nonlinear response properties of visual neurons.
Optimality of KLT for HighRate Transform Coding of Gaussian VectorScale Mixtures: Application to Reconstruction, Estimation and Classification ∗
"... The KarhunenLoève transform (KLT) is known to be optimal for highrate transform coding of Gaussian vectors for both fixedrate and variablerate encoding. The KLT is also known to be suboptimal for some nonGaussian models. This paper proves highrate optimality of the KLT for variablerate encod ..."
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Cited by 6 (0 self)
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The KarhunenLoève transform (KLT) is known to be optimal for highrate transform coding of Gaussian vectors for both fixedrate and variablerate encoding. The KLT is also known to be suboptimal for some nonGaussian models. This paper proves highrate optimality of the KLT for variablerate encoding of a broad class of nonGaussian vectors: Gaussian vectorscale mixtures (GVSM), which extend the Gaussian scale mixture (GSM) model of natural signals. A key concavity property of the scalar GSM (same as the scalar GVSM) is derived to complete the proof. Optimality holds under a broad class of quadratic criteria, which include mean squared error (MSE) as well as generalized fdivergence loss in estimation and binary classification systems. Finally, the theory is illustrated using two applications: signal estimation in multiplicative noise and joint optimization of classification/reconstruction systems.
Using Boundary Methods for Estimating Class Separability
, 1998
"... Designing and operating a classification system becomes drastically more difficult as the data dimensionality increases. A feature extraction (FE) step is often used to reduce the data dimensionality to mitigate this complexity. Thus FE may be viewed as a form of data compression whos objective is t ..."
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Cited by 3 (0 self)
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Designing and operating a classification system becomes drastically more difficult as the data dimensionality increases. A feature extraction (FE) step is often used to reduce the data dimensionality to mitigate this complexity. Thus FE may be viewed as a form of data compression whos objective is to minimize the consequences reducing the dimensionality has on class separability. This differs from the normal objective of data compression which is to minimize distortion, typically measured in the mean squared sense. It is often unclear whether the resulting features from a FE method provide an optimum set for classification. Further, extracting discrimination features from finite data sets increases in difficulty as the dimensionality of the data increases. The need for features to reduce complexity, combined with the difficulties of extracting features, justifies the need for studying ways of ranking feature sets for classification, i.e. feature set evaluation (FSE) techniques. This ...
Expected number of maxima in the envelope of a spherically invariant random process,” revised version submitted to
 IEEE Trans. Inform. Theory
"... Abstract—In many engineering applications, specially in communication engineering, one usually encounters a bandpass nonGaussian random process, with a slowly varying envelope. Among the available models for nonGaussian random processes, spherically invariant random processes (SIRP's) play an impo ..."
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Cited by 3 (3 self)
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Abstract—In many engineering applications, specially in communication engineering, one usually encounters a bandpass nonGaussian random process, with a slowly varying envelope. Among the available models for nonGaussian random processes, spherically invariant random processes (SIRP's) play an important role. These processes are of interest mainly due to the fact that they allow one to relax the assumption of Gaussianity, while keeping many of its useful characteristics. In this paper, we have derived a simple and closedform formula for the expected number of maxima of a SIRP envelope. Since Gaussian random processes are special cases of SIRP's, this formula holds for Gaussian random processes as well. In contrast with the available complicated expression for the expected number of maxima in the envelope of a Gaussian random process, our simple result holds for an arbitrary power spectrum. The key idea in deriving this result is the application of the characteristic function, rather than the probability density function, for calculating the expected level crossing rate of a random process.
Statistical Classification for Heterogeneous Polarimetric SAR Images
 Journal of Selected Topics in Signal Processing
, 2011
"... Abstract—This paper presents a general approach for highresolution polarimetric SAR data classification in heterogeneous clutter, based on a statistical test of equality of covariance matrices. The Spherically Invariant Random Vector (SIRV) model is used to describe the clutter. Several distance mea ..."
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Cited by 3 (3 self)
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Abstract—This paper presents a general approach for highresolution polarimetric SAR data classification in heterogeneous clutter, based on a statistical test of equality of covariance matrices. The Spherically Invariant Random Vector (SIRV) model is used to describe the clutter. Several distance measures, including classical ones used in standard classification methods, can be derived from the general test. The new approach provide a threshold over which pixels are rejected from the image, meaning they are not sufficiently “close ” from any existing class. A distance measure using this general approach is derived and tested on a highresolution polarimetric data set acquired by the ONERA RAMSES system. It is compared to the results of the classical decomposition and Wishart classifier under Gaussian and SIRV assumption. Results show that the new approach rejects all pixels from heterogeneous parts of the scene and classifies its Gaussian parts. Index Terms—Image classification, nonGaussian modeling, polarimetric synthetic aperture radar, statistical analysis.
TimeVarying Fading Channels
, 2000
"... L. Moses, Introduction to Spectral Analysis, Prentice Hall, 1997. [89] Suzuki, "A statistical model for urban radio propagation", IEEE Transactions on Communications, Vol. 25, pp.6[. 1977. [90] C. Tepedelenlioglu, "Deterministic blind estimation of time and frequency selective fading channels usi ..."
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Cited by 1 (0 self)
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L. Moses, Introduction to Spectral Analysis, Prentice Hall, 1997. [89] Suzuki, "A statistical model for urban radio propagation", IEEE Transactions on Communications, Vol. 25, pp.6[. 1977. [90] C. Tepedelenlioglu, "Deterministic blind estimation of time and frequency selective fading channels using filterbank precoders", Proc. of the 2nd IEEE Workshop on Signal Proc. Advances in Wireless Communications, pp. 74  77, Annapolis (MD), May 912, 1999. [91] M.K. Tsatsanis, G.B. Giannakis, "Equalization of rapidly fading channels: selfrecovering methods", IEEE Transactions on Communications,Vol. 44, No. 5, pp.6[ May 1996[ [92] M.K. Tsatsanis, G.B. Giannakis, G. Zhou, "Estimation and equalization of fading channels with random coefficients", Signal Processing,vol. 53, No. 23, pp.211229, Sept. 1996[ [93] M.K. Tsatsanis, G.B. Giannakis, "Subspace methods for blind estimation of timevarying FIR channels", IEEE Transactions on Signal Processing,Vol. 45, No. 12 , pp. 30843093, Dec. 1
Feature Set Evaluation and Robust Neural Networks using Boundary Methods
"... In this paper we discuss the use of Boundary Methods (BM) for distribution analysis. We view these methods as tools which can be used to extract useful information from sample distributions. We believe that the information thus extracted has utility for a number of applications, but in particular we ..."
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In this paper we discuss the use of Boundary Methods (BM) for distribution analysis. We view these methods as tools which can be used to extract useful information from sample distributions. We believe that the information thus extracted has utility for a number of applications, but in particular we discuss the use of BM as a new mechanism to Feature Set Evaluation (FSE) and as an aid to constructing robust and efficient Neural Networks (NN) to solve classification problems. In the first case, BM can stablish which feature set is most appropriate for classification. We demonstrate experimentally that the derived ranking is consistent with alternative ranking techniques based on Bayes error (ffl), showing the theoretical relationship between Overlap Sum (OS), the BM measure of class separability, and ffl. Next, we investigate complexity issues associated with using BMs for FSE and compare with other techniques used for FSE. Finally, BM are used as Sample Selecction (SS) mechanism to tra...
ON THE MAP ESTIMATION IN THE CONTEXT OF ELLIPTICAL DISTRIBUTIONS
"... The purpose of this paper is to study the estimation problem of a multivariate elliptically symmetric random variable corrupted by a multivariate elliptically symmetric noise. In this study, the maximum a posteriori (MAP) approach is presented, extending recent works by Alecu et al. [1] and Selesnic ..."
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The purpose of this paper is to study the estimation problem of a multivariate elliptically symmetric random variable corrupted by a multivariate elliptically symmetric noise. In this study, the maximum a posteriori (MAP) approach is presented, extending recent works by Alecu et al. [1] and Selesnick [2, 3]: (i) the estimation is performed in a multivariate context, (ii) the corrupting noise is not limited to be Gaussian. This paper also extends our previous work that dealt with the minimum mean square error (MMSE) approach [4]. The MMSE is briefly recalled and the MAP is derived. Then the practical use of the MAP in a general setting is discussed and compared to that of the MMSE and of the Wiener estimator. Several examples illustrate the behaviors of these estimators and exhibit their performances. 1.