Esa Ollila

Bio: Esa Ollila is an academic researcher from Aalto University. The author has contributed to research in topics: Estimator & Covariance matrix. The author has an hindex of 28, co-authored 128 publications receiving 2625 citations. Previous affiliations of Esa Ollila include University of Helsinki & Helsinki University of Technology.

Complex Elliptically Symmetric Distributions: Survey, New Results and Applications

Abstract: Complex elliptically symmetric (CES) distributions have been widely used in various engineering applications for which non-Gaussian models are needed. In this overview, circular CES distributions are surveyed, some new results are derived and their applications e.g., in radar and array signal processing are discussed and illustrated with theoretical examples, simulations and analysis of real radar data. The maximum likelihood (ML) estimator of the scatter matrix parameter is derived and general conditions for its existence and uniqueness, and for convergence of the iterative fixed point algorithm are established. Specific ML-estimators for several CES distributions that are widely used in the signal processing literature are discussed in depth, including the complex t -distribution, K-distribution, the generalized Gaussian distribution and the closely related angular central Gaussian distribution. A generalization of ML-estimators, the M-estimators of the scatter matrix, are also discussed and asymptotic analysis is provided. Applications of CES distributions and the adaptive signal processors based on ML- and M-estimators of the scatter matrix are illustrated in radar detection problems and in array signal processing applications for Direction-of-Arrival (DOA) estimation and beamforming. Furthermore, experimental validation of the usefulness of CES distributions for modelling real radar data is given.

On the Circularity of a Complex Random Variable

Abstract: An important characteristic of a complex random variable z is the so-called circularity property or lack of it. We study the properties of the degree of circularity based on second-order moments, called circularity quotient, that is shown to possess an intuitive geometrical interpretation: the modulus and phase of its principal square-root are equal to the eccentricity and angle of orientation of the ellipse defined by the covariance matrix of the real and imaginary part of z. Hence, when the eccentricity approaches the minimum zero (ellipse is a circle), the circularity quotient vanishes; when the eccentricity approaches the maximum one, the circularity quotient lies on the unit complex circle. Connection with the correlation coefficient rho is established and bounds on rho given the circularity quotient (and vice versa) are derived. A generalized likelihood ratio test (GLRT) of circularity assuming complex normal sample is shown to be a function of the modulus of the circularity quotient with asymptotic chi2 2 distribution.

Robust Statistics for Signal Processing

Abstract: Understand the benefits of robust statistics for signal processing with this authoritative yet accessible text. The first ever book on the subject, it provides a comprehensive overview of the field, moving from fundamental theory through to important new results and recent advances. Topics covered include advanced robust methods for complex-valued data, robust covariance estimation, penalized regression models, dependent data, robust bootstrap, and tensors. Robustness issues are illustrated throughout using real-world examples and key algorithms are included in a MATLAB Robust Signal Processing Toolbox accompanying the book online, allowing the methods discussed to be easily applied and adapted to multiple practical situations. This unique resource provides a powerful tool for researchers and practitioners working in the field of signal processing.

Compound-Gaussian Clutter Modeling With an Inverse Gaussian Texture Distribution

Abstract: The compound-Gaussian (CG) distributions have been successfully used for modelling the non-Gaussian clutter measured by high-resolution radars. Within the CG class, the complex K -distribution and the complex t-distribution have been used for modelling sea clutter which is often heavy-tailed or spiky in nature. In this paper, a heavy-tailed CG model with an inverse Gaussian texture distribution is proposed and its distributional properties such as closed-form expressions for its probability density function (p.d.f.) as well as its amplitude p.d.f., amplitude cumulative distribution function and its kurtosis parameter are derived. Experimental validation of its usefulness for modelling measured real-world radar lake-clutter is provided where it is shown to yield better fits than its widely used competitors.

Regularized M-estimators of scatter matrix

Abstract: In this paper, a general class of regularized M-estimators of scatter matrix are proposed that are suitable also for low or insufficient sample support (small n and large p) problems. The considered class constitutes a natural generalization of M-estimators of scatter matrix (Maronna, 1976) and are defined as a solution to a penalized M-estimation cost function. Using the concept of geodesic convexity, we prove the existence and uniqueness of the regularized M-estimators of scatter and the existence and uniqueness of the solution to the corresponding M-estimating equations under general conditions. Unlike the non-regularized M-estimators of scatter, the regularized estimators are shown to exist for any data configuration. An iterative algorithm with proven convergence to the solution of the regularized M-estimating equation is also given. Since the conditions for uniqueness do not include the regularized versions of Tyler's M-estimator, necessary and sufficient conditions for their uniqueness are established separately. For the regularized Tyler's M-estimators, we also derive a simple, closed form, and data-dependent solution for choosing the regularization parameter based on shape matrix matching in the mean-squared sense. Finally, some simulations studies illustrate the improved accuracy of the proposed regularized M-estimators of scatter compared to their non-regularized counterparts in low sample support problems. An example of radar detection using normalized matched filter (NMF) illustrate that an adaptive NMF detector based on regularized M-estimators are able to maintain accurately the preset CFAR level.

Random graphs

Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Independent Component Analysis

Abstract: Independent component models have gained increasing interest in various fields of applications in recent years. The basic independent component model is a semiparametric model assuming that a p-variate observed random vector is a linear transformation of an unobserved vector of p independent latent variables. This linear transformation is given by an unknown mixing matrix, and one of the main objectives of independent component analysis (ICA) is to estimate an unmixing matrix by means of which the latent variables can be recovered. In this article, we discuss the basic independent component model in detail, define the concepts and analysis tools carefully, and consider two families of ICA estimates. The statistical properties (consistency, asymptotic normality, efficiency, robustness) of the estimates can be analyzed and compared via the so called gain matrices. Some extensions of the basic independent component model, such as models with additive noise or models with dependent observations, are briefly discussed. The article ends with a short example. Keywords: blind source separation; fastICA; independent component model; independent subspace analysis; mixing matrix; overcomplete ICA; undercomplete ICA; unmixing matrix