Détection statistique d'une anomalie à partir de projections tomographiques

- La détection d'une anomalie à partir de quelques projections tomographiques bruitées est considérée d'un point de vue statistique. La scène bidimensionnelle étudiée est composée d'un environnement inconnu, considéré comme un paramètre de nuisance, et d'une éventuelle anomalie. Un test invariant optimal est alors proposé pour détecter l'anomalie

Minimax Classifier with Box Constraint on the Priors

Learning a classifier in safety-critical applications like medicine raises several issues. Firstly, the class proportions, also called priors, are in general imbalanced or uncertain. Sometimes, experts are able to provide some bounds on the priors and taking into account this knowledge can improve the predictions. Secondly, it is also necessary to consider any arbitrary loss function given by experts to evaluate the classification decision. Finally, the dataset may contain both categorical and numeric features. In this paper, we propose a box-constrained minimax classifier which addresses all the mentioned issues. To deal with both categorical and numeric features, many works have shown that discretizing the numeric attributes can lead to interesting results. Here, we thus consider that numeric features are discretized. In order to address the class proportions issues, we compute the priors which maximize the empirical Bayes risk over a box-constrained probabilistic simplex. This constraint is defined as the intersection between the simplex and a box constraint provided by experts, which aims at bounding independently each class proportions. Our approach allows to find a compromise between the empirical Bayes classifier and the standard minimax classifier, which may appear too pessimistic. The standard minimax classifier, which has not been studied yet when considerring discrete features, is still accessible by our approach. When considering only discrete features, we show that, for any arbitrary loss function, the empirical Bayes risk, considered as a function of the priors, is a concave non-differentiable multivariate piecewise affine function. To compute the box-constrained least favorable priors, we derive a projected subgradient algorithm. The convergence of our algorithm is established. The performance of our algorithm is illustrated with experiments on the Framingham study database to predict the risk of Coronary Heart Disease (CHD)

Constrained Convex Neyman-Pearson Classification Using an Outer Approximation Splitting Method

This paper presents an algorithm for Neyman-Pearson classification. While empirical riskminimization approaches focus on minimizing a global risk, the Neyman-Pearson frameworkminimizes the type II risk under an upper bound constraint on the type I risk. Sincethe 0=1 loss function is not convex, optimization methods employ convex surrogates thatlead to tractable minimization problems. As shown in recent work, statistical bounds canbe derived to quantify the cost of using such surrogates instead of the exact 1/0 loss.However, no specific algorithm has yet been proposed to actually solve the resulting minimizationproblem numerically. The contribution of this paper is to propose an efficientsplitting algorithm to address this issue. Our method alternates a gradient step on the objectivesurrogate risk and an approximate projection step onto the constraint set, which isimplemented by means of an outer approximation subgradient projection algorithm. Experimentson both synthetic data and biological data show the efficiency of the proposed method

Dynamic Quantization using Spike Generation Mechanisms

This paper introduces a neuro-inspired co-ding/decoding mechanism of a constant real value by using a Spike Generation Mechanism (SGM) and a combination of two Spike Interpretation Mechanisms (SIM). One of the most efficient and widely used SGMs to encode a real value is the Leaky-Integrate and Fire (LIF) model which produces a spike train. The duration of the spike train is bounded by a given time constraint. Seeking for a simple solution of how to interpret the spike train and to reconstruct the input value, we combine two different kinds of SIMs, the time-SIM and the rate-SIM. The time-SIM allows a high quality interpretation of the neural code and the rate-SIM allows a simple decoding mechanism by couting the spikes. The resulting coding/decoding process, called the Dual-SIM Quantizer (Dual-SIMQ), is a non-uniform quantizer. It is shown that it coincides with a uniform scalar quantizer under certain assumptions. Finally, it is also shown that the time constraint can be used to control automatically the reconstruction accuracy of this time-dependent quantizer

Box-constrained optimization for minimax supervised learning***

In this paper, we present the optimization procedure for computing the discrete boxconstrained minimax classifier introduced in [1, 2]. Our approach processes discrete or beforehand discretized features. A box-constrained region defines some bounds for each class proportion independently. The box-constrained minimax classifier is obtained from the computation of the least favorable prior which maximizes the minimum empirical risk of error over the box-constrained region. After studying the discrete empirical Bayes risk over the probabilistic simplex, we consider a projected subgradient algorithm which computes the prior maximizing this concave multivariate piecewise affine function over a polyhedral domain. The convergence of our algorithm is established

Détection statistique d'information cachée dans des images naturelles

La nécessité de communiquer de façon sécurisée n est pas chose nouvelle : depuis l antiquité des méthodes existent afin de dissimuler une communication. La cryptographie a permis de rendre un message inintelligible en le chiffrant, la stéganographie quant à elle permet de dissimuler le fait même qu un message est échangé. Cette thèse s inscrit dans le cadre du projet "Recherche d Informations Cachées" financé par l Agence Nationale de la Recherche, l Université de Technologie de Troyes a travaillé sur la modélisation mathématique d une image naturelle et à la mise en place de détecteurs d informations cachées dans les images. Ce mémoire propose d étudier la stéganalyse dans les images naturelles du point de vue de la décision statistique paramétrique. Dans les images JPEG, un détecteur basé sur la modélisation des coefficients DCT quantifiés est proposé et les calculs des probabilités du détecteur sont établis théoriquement. De plus, une étude du nombre moyen d effondrements apparaissant lors de l insertion avec les algorithmes F3 et F4 est proposée. Enfin, dans le cadre des images non compressées, les tests proposés sont optimaux sous certaines contraintes, une des difficultés surmontées étant le caractère quantifié des donnéesThe need of secure communication is not something new: from ancient, methods exist to conceal communication. Cryptography helped make unintelligible message using encryption, steganography can hide the fact that a message is exchanged.This thesis is part of the project "Hidden Information Research" funded by the National Research Agency, Troyes University of Technology worked on the mathematical modeling of a natural image and creating detectors of hidden information in digital pictures.This thesis proposes to study the steganalysis in natural images in terms of parametric statistical decision. In JPEG images, a detector based on the modeling of quantized DCT coefficients is proposed and calculations of probabilities of the detector are established theoretically. In addition, a study of the number of shrinkage occurring during embedding by F3 and F4 algorithms is proposed. Finally, for the uncompressed images, the proposed tests are optimal under certain constraints, a difficulty overcome is the data quantizationTROYES-SCD-UTT (103872102) / SudocSudocFranceF

Statistical Detection of LSB Matching Using Hypothesis Testing Theory

This paper investigates the detection of information hidden by the Least Significant Bit (LSB) matching scheme. In a theoretical context of known image media parameters, two important results are presented. First, the use of hypothesis testing theory allows us to design the Most Powerful (MP) test. Second, a study of the MP test gives us the opportunity to analytically calculate its statistical performance in order to warrant a given probability of false-alarm. In practice when detecting LSB matching, the unknown image parameters have to be estimated. Based on the local estimator used in the Weighted Stego-image (WS) detector, a practical test is presented. A numerical comparison with state-of-the-art detectors shows the good performance of the proposed tests and highlights the relevance of the proposed methodology

On the Epsilon Most Stringent Test Between Two Vector Lines in Gaussian Noise

International audienc

Adaptive Steganalysis of Least Significant Bit Replacement in Grayscale Natural Images

International audienceThis paper deals with the detection of hidden bits in the Least Significant Bit (LSB) plane of a natural image. The mean level and the covariance matrix of the image, considered as a quantized Gaussian random matrix, are unknown. An adaptive statistical test is designed such that its probability distribution is always independent of the unknown image parameters, while ensuring a high probability of hidden bits detection. This test is based on the likelihood ratio test except that the unknown parameters are replaced by estimates based on a local linear regression model. It is shown that this test maximizes the probability of detection as the image size becomes arbitrarily large and the quantization step vanishes. This provides an asymptotic upper-bound for the detection of hidden bits based on the LSB replacement mechanism. Numerical results on real natural images show the relevance of the method and the sharpness of the asymptotic expression for the probability of detection