https://hal.archives-ouvertes.fr/hal-00417283/document

Independent component analysis, a new concept?

Statistical Analysis with Missing Data

Fundamentals Of Statistical Signal Processing

We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higher-order tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, first-order perturbation effects, etc., are analyzed. We investigate how tensor symmetries affect the decomposition and propose a multilinear generalization of the symmetric eigenvalue decomposition for pair-wise symmetric tensors.

/pdf/a-multilinear-singular-value-decomposition-5egsfnmazm.pdf

A Multilinear Singular Value Decomposition

Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).

It is the purpose of this tutorial paper to place bispectrum estimation in a digital signal processing framework in order to aid engineers in grasping the utility of the available bispectrum estimation techniques, to discuss application problems that can directly benefit from the use of the bispectrum, and to motivate research in this area Three general reasons are behind the use of bispectrum in signal processing and are addressed in the paper: to extract information due to deviations from normality, to estimate the phase of parametric signals, and to detect and characterize the properties of nonlinear mechanisms that generate time series

Bispectrum estimation: A digital signal processing framework

The Stable Distribution Symmetric Stable Random Processes Covariation and Conditional Expectation Parameter Estimates for Symmetric Stable Distributions Estimation of Covariations Parametric Models of Stable Processes Linear Theory of Stable Processes Symmetric Stable Models for Impulsive Noise Signal Detection in Stable Noise Current and Future Trends in Signal Processing with Alpha-Stable Distributions.

Signal processing with alpha-stable distributions and applications

1. Definitions and Properties of Cumulants and Cumulant Spectra. 2. Polyspectra of Deterministic Signals. 3. Conventional Methods for the Estimation of Polyspectra. 4. Nonminimum Phase Signal Reconstruction. 5. Polycepstra. 6. Parameter Estimation. 7. Adaptive Signal Processing. 8. Detection and Characterization of Nonlinearities.

Higher-Order Spectra Analysis: A Nonlinear Signal Processing Framework

Non-Gaussian statistical signal processing is important when signals and/or noise deviate from the ideal Gaussian model. Stable distributions are among the most important non-Gaussian models. They share defining characteristics with the Gaussian distribution, such as the stability property and central limit theorems, and in fact include the Gaussian distribution as a limiting case. To help engineers better understand the stable models and develop methodologies for their applications in signal processing. A tutorial review of the basic characteristics of stable distributions and stable signal processing is presented. The emphasis is on the differences and similarities between stable signal processing methods based on fractional lower-order moments and Gaussian signal processing methods based on second-order moments. >

Signal processing with fractional lower order moments: stable processes and their applications

The strengths and limitations of correlation-based signal processing methods are discussed. The definitions, properties, and computation of higher-order statistics and spectra, with emphasis on the bispectrum and trispectrum are presented. Parametric and nonparametric expressions for polyspectra of linear and nonlinear processes are described. The applications of higher-order spectra in signal processing are discussed. >

Chrysostomos L. Nikias

Papers

Bispectrum estimation: A digital signal processing framework

Signal processing with alpha-stable distributions and applications

Higher-Order Spectra Analysis: A Nonlinear Signal Processing Framework

Signal processing with fractional lower order moments: stable processes and their applications

Signal processing with higher-order spectra