This paper studies the problem of classifying some Gaussian samples into one of two parametric probabilistic models, also called sources, when the parameter and the a priori probability of each source are unknown. Each source is governed by an univariate normal distribution whose mean is unknown. A training sequence is available for each source in order to compensate the lack of prior information. An almost optimal most stringent test is proposed to solve this classification problem subject to a constrained false alarm probability. This learning-based test minimizes its maximum shortcoming with respect to the most powerful test which knows exactly the parameters of the sources. It also guarantees a prescribed false alarm probability whatever the size of the training sequences. The threshold, the probability of false alarm and the probability of correct detection are calculated analytically.

This paper addresses the detection of a suddenly arriving dynamic profile of a finite duration often called a transient change. In contrast to the traditional abrupt change detection, where the post-change period is assumed to be infinitely long, the detection of a suddenly arriving transient change should be done before it disappears. The detection of transient changes after their disappearance is considered as missed. Hence, the traditional quickest change detection criterion, minimizing the average detection delays provided a prescribed false alarm rate, is compromised. The proposed optimality criterion minimizes the worst case probability of missed detection provided that the worst case probability of false alarm during a certain period is upper bounded. A suboptimal CUSUM-type transient change detection algorithm, based on a subclass of truncated Sequential Probability Ratio Tests, is proposed. The optimization of the proposed algorithm in this subclass leads to a specially designed Finite Moving Average Test. The proposed method is analyzed theoretically and by simulation. A special attention is paid to the case of Gaussian observations with a dynamic profile.

The sensor calibration is an important issue in the theory and practice of measurements. The calibration consists of comparing the output of the instrument or sensor under test against the output of an instrument of known accuracy when the same input is applied to both instruments. The goal of the sensor calibration is twofold: first, it is necessary to detect (and to remove) systematic biases in the sensor outputs; second it is necessary to adjust the model of random sensor error in order to get an optimal estimation of the measured parameters. This second task is especially important if the sensor outputs are processed by using the least-squares (LS) filter or the Kalman filter. The paper is devoted to the sensor calibration by using the sensor bias detection and the parameter estimation in the nonlinear model of the sensor heteroscedasticity. The heteroscedasticity occurs in regression when the measurement noise variance is non-constant. Both method, the bias detection test, and the sensor noise estimator, are based on a linear quasi-maximum likelihood estimator.

The paper addresses random field time series analysis and simulation. The analysis constrains a spatial isotropic fractional Brownian field to a dynamic temporal behavior from separable time varying Hurst parameters. The constrained dynamic applies by embedding the wavelet packet spectrum of the input random field into different spectra associated with the same random family (exponential spectrum decay). The paper highlights the relevance of the approach for representing and simulating isotropic light source and cloud dynamics.

The goal of this paper is to propose the optimal statistical test based on the modeling of discrete cosine transform (DCT) coefficients with a quantified Laplacian distribution. This paper focuses on the detection of hidden information embedded in bits of the DCT coefficients of a JPEG image. This problem is difficult, in terms of statistical decision, for two main reasons: first, the number of DCT coefficients used to conceal the hidden bits is random; second, the JPEG image compression induces a strong quantization of DCT coefficients. The proposed test explicitly takes into account the randomness of the number of DCT coefficients used. It maximizes the probability of hidden information detection by ensuring a prescribed level of false alarm.

This paper addresses the problem of anomaly detection and classification by using a noisy measurement vector corrupted by some linear unknown nuisance parameters. An invariant constrained asymptotically uniformly minimax test is proposed. It minimizes the maximum false classification probability as the signal-to-noise ratio becomes arbitrary large, uniformly with respect to the unknown anomaly amplitude and independently on the nuisance parameters. The probability of maximum classification error is calculated in a closed-form.

In the last two decades substantial progress has been made in the detection of hidden information or hidden communication channels in media files or streams. Typically, it is necessary to reliably detect in a huge set of files (image, audio, and video) which of these files contain the hidden information. The goal of this paper is to study the problem of hypothesis testing based on quantized observations by using a parametric statistical model with nuisance parameters and to apply the obtained tests to the hidden information detection.

Anomaly detection is addressed within a statistical framework. Often the statistical model is composed of two types of parameters : the informative parameters and the nuisance ones. The nuisance parameters are of no interest for detection but they are necessary to complete the model. In the case of unknown, non-random nuisance parameters, their elimination is unavoidable. Some approaches addressing the cases where the nuisance parameters, belonging to a subspace, interfere with the informative ones in a linear manner, use the theory of invariance to reject the nuisance. Sometimes this leads to a certain degradation of the detector performances because some faults become undetectable, masked by the nuisance. Nevertheless, in many cases the physical nature of nuisance parameters is (partially) known, and this knowledge may allow us to define inequality bounds to limit the variations of these parameters. The goal of this paper is to study the statistical performances of the constrained generalized likelihood ratio test used to detect an additive anomaly in the case of bounded nuisance parameters. An example of the integrity monitoring of GNSS train navigation illustrates the relevance of the proposed method.

The non-Bayesian detection of an anomaly from a single or a few noisy tomographic projections is considered as a statistical hypotheses testing problem. It is supposed that a radiography is composed of an imaged nonanomalous background medium, considered as a deterministic nuisance parameter, with a possibly hidden anomaly. Because the full voxel-by-voxel reconstruction is impossible, an original tomographic method based on the parametric models of the nonanomalous background medium and radiographic process is proposed to fill up the gap in the missing data. Exploiting this "parametric tomography," a new detection scheme with a limited loss of optimality is proposed as an alternative to the nonlinear generalized likelihood ratio test, which is untractable in the context of nondestructive testing for the objects with uncertainties in their physical/geometrical properties. The theoretical results are illustrated by the processing of real radiographies for the nuclear fuel rod inspection.

The paper concerns the radiographic non-destructive testing of well-manufactured objects. The detection of anomalies is addressed from the statistical point of view as a binary hypothesis testing problem with nonlinear nuisance parameters. A new detection scheme is proposed as an alternative to the classical GLR test. It is shown that this original decision rule detects anomalies with a loss of a negligible (epsiv) part of optimality with respect to an optimal invariant test designed for the "closest" hypothesis testing problem with linear nuisance parameters

The problem of detecting an anomaly/target from a limited number of noisy tomographic projections is addressed from the statistical point of view. An unknown 2D (or 3D) scene is composed of an environment, considered as a nuisance parameter, with a possibly hidden anomaly/target. A parametric approach is proposed to reduce the lack of a priori information and two statistical tests are discussed : the first one, invariant, is devoted to simply detect the presence of an unspecified anomaly and the second one is able to simultaneously detect and localize the projection of a size limited anomaly.

We address the problem of minimax detecting and isolating abrupt changes in random signals. The criterion of optimality consists in minimizing the maximum mean detection/isolation delay for a given maximum probability of false isolation and mean time before a false alarm. It seems that such a criterion has many practical applications, especially for safety-critical applications, in monitoring dangerous industrial processes and also when the decision should be made in a hostile environment. The redundant strapdown inertial reference unit integrity monitoring problem is discussed. An asymptotic lower bound for the mean detection/isolation delay is given.

We address the problem of detecting changes in multivariate Gaussian random signals with an unknown mean after the change. The window-limited generalized-likelihood ratio (GLR) scheme is a well-known approach to solve this problem. However, this algorithm involves at least (log /spl gamma/)//spl rho/ likelihood-ratio computations at each stage, where /spl gamma/(/spl gamma//spl rarr//spl infin/) is the mean time before a false alarm and /spl rho/ is the Kullback-Leibler information. We establish a new suboptimal recursive approach which is based on a collection of L parallel recursive /spl chi//sup 2/ tests instead of the window-limited GLR scheme. This new approach involves only a fixed number L of likelihood-ratio computations at each stage for any combinations of /spl gamma/ and /spl rho/. By choosing an acceptable value of nonoptimality, the designer can easily find a tradeoff between the complexity of the quadratic change detection algorithm and its efficiency.

We address the problem of detecting and isolating abrupt changes in random signals. An asymptotic optimal solution to this problem, which has been proposed in previous works, involve the number of computations at time t which grows to infinity with t. We propose another more realistic criterion, establish a new simple recursive change detection/isolation algorithm, and investigate its statistical properties.

The comparison between optimal sequential and nonsequential (fixed-size sample) strategies in the problem of abrupt change detection and isolation is discussed. In particular, we show that sometimes a simple fixed-size sample algorithm is almost as efficient as an optimal sequential algorithm which leads to a burdensome number of arithmetical operations.

The purpose of this paper is to give a new statistical approach to the change diagnosis (detection/isolation) problem. The change detection problem has received extensive research attention; however, the change isolation problem has, for the most part, been ignored. We consider a stochastic dynamical system with abrupt changes and investigate the multiple hypotheses extension of Lorden's (1971) results. We introduce a joint criterion of optimality for the detection/isolation problem and then design a change detection/isolation algorithm. We also investigate the statistical properties of this algorithm. We prove a lower bound for the criterion in a class of sequential change detection/isolation algorithms. It is shown that the proposed algorithm is asymptotically optimal in this class. The theoretical results are applied to the case of additive changes in linear stochastic models.>