Classical multivariate statistical methods concern models, distributions and inference based on the Gaussian distribution. These are the topics in the first textbook for mathematical statisticians by T.W. Anderson that was published in 1958 and that appeared as a slightly expanded 3rd edition in 2003. Matrix theory and notation is used there extensively to efficiently derive properties of the multivariate Gaussian or the Wishart distribution, of principal components, of canonical correlation and discriminant analysis and of the general multivariate linear model in which a Gaussian response vector variable Ya has linear least-squares regression on all components of an explanatory vector variable Yb. In contrast, many methods for analysing sets of observed variables have been developed first within special substantive fields and some or all of the models in a given class were justified in terms of probabilistic and statistical theory much later. Among them are factor analysis, path analysis, structural equation models, and models for which partial-least squares estimation have been proposed. Other multivariate techniques such as cluster analysis and multidimensional scaling have been often used, but the result of such an analysis cannot be formulated as a hypothesis to be tested in a new study and satisfactory theoretical justifications are still lacking. Factor analysis was proposed by psychologist C. Spearman (1904), (1926) and, at the time, thought of as a tool for measuring human intelligence. Such a model has one or several latent variables. These are hidden or unobserved and are to explain the observed correlations among a set of observed variables, called items in that context. The difficult task is to decide how many and which of a possibly large set of items to include into a model. But, given a set of latent variables, a classical factor analysis model specifies for a joint Gaussian distribution mutual independence of the observed variables given the latent variables. This can be recognized to be one special type of a graphical Markov model; see Cox and Wermuth (1996), Edwards (2000), Lauritzen (1996), Whittaker (1990).

Multivariate Statistical Analysis.

https://www.jstage.jst.go.jp/article/jsprs1975/37/6/37_6_39/_pdf

1998 IEEE International Conference on SMCに参加して

Sensor systems typically operate under resource constraints that prevent the simultaneous use of all resources all of the time. Sensor management becomes relevant when the sensing system has the capability of actively managing these resources; i.e., changing its operating configuration during deployment in reaction to previous measurements. Examples of systems in which sensor management is currently used or is likely to be used in the near future include autonomous robots, surveillance and reconnaissance networks, and waveform-agile radars. This paper provides an overview of the theory, algorithms, and applications of sensor management as it has developed over the past decades and as it stands today.

Sensor Management: Past, Present, and Future

In this two-part paper, we consider the problem of adaptive multidimensional/multichannel signal detection in Gaussian noise with unknown covariance matrix. The test data (primary data) is assumed as a collection of sample vectors, arranged as the columns of a rectangular data array. The rows and columns of the signal matrix are both assumed to lie in known subspaces, but with unknown coordinates. Due to this feature of the signal structure, we name this kind of signal as the double subspace signal. Part I of this paper focuses on the adaptive detection in homogeneous environments, while Part II deals with the adaptive detection in partially homogeneous environments. Precisely, in this part, we derive the generalized likelihood ratio test (GLRT), Rao test, Wald test, as well as their two-step variations, in homogeneous environments. Three types of spectral norm tests (SNTs) are also introduced. All these detectors are shown to possess the constant false alarm rate (CFAR) property. Moreover, we discuss the differences between them and show how they work. Another contribution is that we investigate various special cases of these detectors. Remarkably, some of them are well-known existing detectors, while some others are still new. At the stage of performance evaluation, conducted by Monte Carlo simulations, both matched and mismatched signals are dealt with. For each case, more than one scenario is considered.

Adaptive Double Subspace Signal Detection in Gaussian Background—Part I: Homogeneous Environments

Underwater image processing is an intelligence research field that has great potential to help developers better explore the underwater environment. Underwater image processing has been used in a wide variety of fields, such as underwater microscopic detection, terrain scanning, mine detection, telecommunication cables, and autonomous underwater vehicles. However, underwater imagery suffers from strong absorption, scattering, color distortion, and noise from the artificial light sources, causing image blur, haziness, and a bluish or greenish tone. Therefore, the enhancement of underwater imagery can be divided into two methods: 1) underwater image dehazing and 2) underwater image color restoration. This paper presents the reason for underwater image degradation, surveys the state-of-the-art intelligence algorithms like deep learning methods in underwater image dehazing and restoration, demonstrates the performance of underwater image dehazing and color restoration with different methods, introduces an underwater image color evaluation metric, and provides an overview of the major underwater image applications. Finally, we summarize the application of underwater image processing.

A Review on Intelligence Dehazing and Color Restoration for Underwater Images

We address adaptive radar detection of targets embedded in ground clutter dominated environments characterized by a symmetrically structured power spectral density. At the design stage, we leverage on the spectrum symmetry for the interference to come up with decision schemes capable of capitalizing the a-priori information on the covariance structure. To this end, we prove that the detection problem at hand can be formulated in terms of real variables and, then, we apply design procedures relying on the GLRT, the Rao test, and the Wald test. Specifically, the estimates of the unknown parameters under the target presence hypothesis are obtained through an iterative optimization algorithm whose convergence and quality guarantee is thoroughly proved. The performance analysis, both on simulated and on real radar data, confirms the superiority of the considered architectures over their conventional counterparts which do not take advantage of the clutter spectral symmetry.

Adaptive Detection of Point-Like Targets in Spectrally Symmetric Interference

This letter deals with the problem of adaptive detection in partially-homogeneous Gaussian disturbance with unknown but persymmetric structured covariance matrix. Since no uniformly most powerful test exists for the problem at hand, we devise and assess two detection strategies based on the Rao test and the Wald test design criteria. Remarkably, both detectors ensure the constant false alarm rate property with respect to both the structure of the covariance matrix as well as the power level. The preliminary performance assessment, conducted by resorting to simulated data, has confirmed the effectiveness of the newly proposed detectors.

Persymmetric Rao and Wald Tests for Partially Homogeneous Environment

Persymmetric adaptive detection of distributed targets in partially-homogeneous environment

The problem of detecting a subspace signal is studied in colored Gaussian noise with an unknown covariance matrix. In the subspace model, the target signal belongs to a known subspace, but with unknown coordinates. We first present a new derivation of the Rao test based on the subspace model, and then propose a modified Rao test (MRT) by introducing a tunable parameter. The MRT is more general, which includes the Rao test and the generalized likelihood ratio test as special cases. Moreover, closed-form expressions for the probabilities of false alarm and detection of the MRT are derived, which show that the MRT bears a constant false alarm rate property against the noise covariance matrix. Numerical results demonstrate that the MRT can offer the flexibility of being adjustable in the mismatched case where the target signal deviates from the presumed signal subspace. In particular, the MRT provides better mismatch rejection capacities as the tunable parameter increases.

Modified Rao Test for Multichannel Adaptive Signal Detection

We address adaptive radar detection of targets embedded in clutter characterized by a symmetrically structublack power spectral density (PSD) and persymmetric covariance matrix. At the design stage, such properties are jointly exploited to come up with decision schemes capable of guaranteeing superior detection performances with respect to architectures which incorporate either persymmetry or clutter PSD symmetry. The performance analysis, both on simulated and on real radar data, confirms the superiority of the newly proposed architectures over their natural counterparts which do not take advantage of both the sources of a priori information.

Chengpeng Hao

Papers

Adaptive Detection of Point-Like Targets in Spectrally Symmetric Interference

Persymmetric Rao and Wald Tests for Partially Homogeneous Environment

Persymmetric adaptive detection of distributed targets in partially-homogeneous environment

Modified Rao Test for Multichannel Adaptive Signal Detection

Knowledge-Based Adaptive Detection: Joint Exploitation of Clutter and System Symmetry Properties