Anomaly detection is an important problem that has been researched within diverse research areas and application domains. Many anomaly detection techniques have been specifically developed for certain application domains, while others are more generic. This survey tries to provide a structured and comprehensive overview of the research on anomaly detection. We have grouped existing techniques into different categories based on the underlying approach adopted by each technique. For each category we have identified key assumptions, which are used by the techniques to differentiate between normal and anomalous behavior. When applying a given technique to a particular domain, these assumptions can be used as guidelines to assess the effectiveness of the technique in that domain. For each category, we provide a basic anomaly detection technique, and then show how the different existing techniques in that category are variants of the basic technique. This template provides an easier and more succinct understanding of the techniques belonging to each category. Further, for each category, we identify the advantages and disadvantages of the techniques in that category. We also provide a discussion on the computational complexity of the techniques since it is an important issue in real application domains. We hope that this survey will provide a better understanding of the different directions in which research has been done on this topic, and how techniques developed in one area can be applied in domains for which they were not intended to begin with.

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Anomaly detection: A survey

An overview of the self-organizing map algorithm, on which the papers in this issue are based, is presented in this article.

The Self-Organizing Map

Digital watermarking is a key ingredient to copyright protection. It provides a solution to illegal copying of digital material and has many other useful applications such as broadcast monitoring and the recording of electronic transactions. Now, for the first time, there is a book that focuses exclusively on this exciting technology. Digital Watermarking covers the crucial research findings in the field: it explains the principles underlying digital watermarking technologies, describes the requirements that have given rise to them, and discusses the diverse ends to which these technologies are being applied. As a result, additional groundwork is laid for future developments in this field, helping the reader understand and anticipate new approaches and applications.

Digital Watermarking

First published in 1995, Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding. The book developed the theory in both continuous and discrete time, and presented important applications. During the past decade, it filled a useful need in explaining a new view of signal processing based on flexible time-frequency analysis and its applications. Since 2007, the authors now retain the copyright and allow open access to the book.

Wavelets and Subband Coding

1 Introduction to Wavelets 2 A Multiresolution Formulation of Wavelet Systems 3 Filter Banks and the Discrete Wavelet Transform 4 Bases, Orthogonal Bases, Biorthogonal Bases, Frames, Tight Frames, and Unconditional Bases 5 The Scaling Function and Scaling Coefficients, Wavelet and Wavelet Coefficients 6 Regularity, Moments, and Wavelet System Design 7 Generalizations of the Basic Multiresolution Wavelet System 8 Filter Banks and Transmultiplexers 9 Calculation of the Discrete Wavelet Transform 10 Wavelet-Based Signal Processing and Applications 11 Summary Overview 12 References Bibliography Appendix A Derivations for Chapter 5 on Scaling Functions Appendix B Derivations for Section on Properties Appendix C Matlab Programs Index

Introduction to Wavelets and Wavelet Transforms: A Primer

The goal of the sensor network localization problem is to determine positions of all sensor nodes in a network given certain pairwise noisy distance measurements and some anchor node positions. This paper describes a distributed localization algorithm based on second-order cone programming relaxation. We show that the sensor nodes can estimate their positions based on local information. Unlike previous approaches, we also consider the effect of inaccurate anchor positions. In the presence of anchor position errors, the localization is performed in three steps. First, the sensor nodes estimate their positions using information from their neighbors. In the second step, the anchors refine their positions using relative distance information exchanged with their neighbors and finally, the sensors refine their position estimates. We demonstrate the convergence of the algorithm numerically. Simulation study, for both uniform and irregular network topologies, illustrates the robustness of the algorithm to anchor position and distance estimation errors, and the performance gains achievable in terms of localization accuracy, problem size reduction and computational efficiency.

Distributed sensor network localization using SOCP relaxation

The parametrization of two-channel reconstruction quadrature mirror filter banks is extended to obtain a single characterization of discrete orthonormal wavelets. In particular, it is shown that discrete orthonormal wavelets of support less than 2N-1, where N is an even integer, are parametrized by N-1 real parameters, each taking values in (0, 2 pi ). A parametrization of discrete orthonormal wavelets with a number of vanishing moments greater than one is also given. >

Parametrization of compactly supported orthonormal wavelets

We present a novel technique for watermarking digital images based on its moments. The watermark is composed of the mean of several functions of the second and third order moments designed to be invariant to scaling and orthogonal transformations this has the advantage of making the watermark image dependent. The watermarked image is a linear combination of the original image and a weighted nonlinear transformation of the original. The weight is computed such that the mean of the watermarked image invariants is a predefined number. Watermark detection is as simple as computing the moment invariants of the received image. Our approach has a guaranteed visual transparency up to a contrast modification. The proposed algorithm has proved to be highly robust to all geometric manipulations, filtering, compression and small cropping which are performed as part of StirMark attacks as well as noise addition, both Gaussian and salt and pepper.

Image watermarking by moment invariants

This paper presents and studies two new wavelet transform domain least mean square (LMS) algorithms. The algorithms exploit the special sparse structure of the wavelet transform of wide classes of correlation matrices and their Cholesky factors in order to compute a whitening transformation of the input data in the wavelet domain and minimize computational complexity. The procedures differ in the exact estimates they use and in the way they identify the data dependent whitening transformation. The first approach explicitly computes a sparse estimate of the wavelet domain correlation matrix of the input process. It then computes the Cholesky factor of that matrix and uses its inverse to whiten the input. The complexity of this first approach is O[N log/sup 2/ (N)]. In contrast, the second approach computes a sparse estimate of the Cholesky factor of the wavelet domain correlation matrix of the input process directly. This second approach has a computational complexity of O[N log (N)] floating-point operations. However, it requires a more complex bookkeeping procedure. Both algorithms have a convergence rate that is faster than that of time-domain LMS and discrete Fourier transform (DFT) or discrete cosine transform (DCT)-based LMS procedures. The paper compares the two procedures and analyzes their mean and mean square performance.

Wavelet transform domain adaptive FIR filtering

We present a novel nonlinear filtering approach for detecting weak signals in heavy noise from short data records. Such detection problems arise in many applications including communications, radar, sonar, medical imaging, seismology, industrial measurements, etc. The performance of a matched filter detector of a weak signal in heavy noise is directly proportional to the observation time. We discuss an alternative detection approach that relies on a nonlinear filtering of the input signal using a bistable system. We show that by adaptively selecting the parameters of the system, it is possible to increase the ratio of the square of the amplitude of a sinusoid to that of the noise intensity around the frequency of the sinusoid (stochastic resonance). The sinusoid can then be reliably detected at the output of the nonlinear system using a suitable matched filter even when the data record is short.

A.H. Tewfik

Papers

Distributed sensor network localization using SOCP relaxation

Parametrization of compactly supported orthonormal wavelets

Image watermarking by moment invariants

Wavelet transform domain adaptive FIR filtering

Detection of weak signals using adaptive stochastic resonance