The need for fast on-line algorithms to analyze high data-rate measurements is a vital element in production settings. Given the ever-increasing number of data sources coupled with increasing complexity of applications, and workload patterns, anomaly detection methods should be light-weight and must operate in real-time. In many modern applications, data arrive in a streaming fashion. Therefore, the underlying assumption of classical methods that the data is a sample from a stable distribution is not valid, and Gaussian and non-parametric based methods such as the control chart and boxplot are inadequate. Streaming data is an ever-changing superposition of distributions. Detection of such changes in real-time is one of the fundamental challenges. We propose low-complexity robust modifications to the conventional Tukey boxplot based on fast highly efficient robust estimates of scale. Results using synthetic as well as real-world data show that our methods outperform the Tukey boxplot and methods based on Gaussian limits.

The distributed detection problem in wireless sensor networks is studied under the impulsive α-stable noise assumption. Since symmetric α-stable density does not have a closed form, its approximation, the bi-parameter Cauchy Gaussian mixture model, is used to describe the impulsive behavior of α-stable noises. With this model, we propose a low-complexity robust fusion rule by taking the maximin setting with respect to the detection probability. An explicit formula for the detection probability is derived. Robustness of the proposed maximin fusion rule is justified by numerical and simulation results for α-stable noises.

In practical problems of signal detection, it is quite common that the underlying noise distribution is not Gaussian and may vary in a wide range from light- to heavy-tailed forms. To design a robust fusion rule for distributed detection in wireless sensor networks, an asymptotic maximin approach is used by introducing weak signals in the canonical parallel fusion model. Explicit formulas for the detection and false alarm probabilities are derived. The analytic results are written out for the classes of nondegenerate, with a bounded variance and contaminated Gaussian noise distributions. Numerical and simulation results are obtained to justify robustness and asymptotic characteristics of the proposed fusion rule.

Distributed detection has newly received research interest due to the success of the emerging wireless sensor network (WSN) technology. To deal with the problem of distributed detection for the WSN having the energy constraint, the fusion of decisions modeled as weak signals is studied. By using the weak signal model and additive non-Gaussian noise channels in the canonical parallel fusion scheme, we propose an asymptotic fusion rule applicable for wide classes of noise probability density functions (pdfs). In the particular case of a known pdf, an optimal detection rule is given. Both asymptotic analysis and Monte Carlo simulation are used to examine the performance of the proposed detection fusion rule.

This paper presents two novel transforms based on the discrete Radon transform. The proposed transforms smartly solve two inherent problems of the Radon transform in rotation estimation in digital images, i.e., direction-dependency and nonhomogeneity, that come from the different numbers of pixels projected on a line for different directions and/or coordinates of a direction. While the first transform considers the sample mean operator on the same sets of pixels for a direction instead of summation in the discrete Radon transform, the second transform uses the mean operator on sets of pixels with the equal number of elements. In order to show the efficiency of the proposed transforms, we apply them on image collections from the Brodatz album for estimating the directional information. Experimental results show a significant increase in correct estimation as well as in the processing time compared to the conventional Radon transform

In practical communication environments, it is frequently observed that the underlying noise distribution is not Gaussian and may vary in a wide range from short-tailed to heavy-tailed forms. To describe partially known noise distribution densities, a distribution class characterized by the upper-bounds upon a noise variance and a density dispersion in the central part is used. The results on the minimax variance estimation in the Huber sense are applied to the problem of asymptotically minimax detection of a weak signal. The least favorable density minimizing Fisher information over this class is called the Weber-Hermite density and it has the Gaussian and Laplace densities as limiting cases. The subsequent minimax detector has the following form: i) with relatively small variances, it is the minimum L2-norm distance rule; ii) with relatively large variances, it is the L1-norm distance rule; iii) it is a compromise between these extremes with relatively moderate variances. It is shown that the proposed minimax detector is robust and close to Huber's for heavy-tailed distributions and more efficient than Huber's for short-tailed ones both in asymptotics and on finite samples

In practical communication environments, it is frequently observed that the underlying noise PDF is not Gaussian and may vary in a wide range from short-tailed to heavy-tailed forms. To provide stable and high quality detection of a known signal, we design an asymptotically minimax (in the Huber sense) minimum distance detection rule under rather general conditions of regularity imposed upon noise PDFs and derive the closed expression for its probability of detection error. In several PDF classes, the least favorable PDFs and corresponding minimax detectors are written down. The minimax robust detectors exhibit robustness of detection in heavy-tailed noise and efficiency in short-tailed noise, both in asymptotics and on finite samples.

No abstract available.