A kepstrum approach to filtering, smoothing and prediction

The kepstrum (or complex cepstrum) method is revisited and applied to the problem of spectral factorization where the spectrum is directly estimated from observations. The solution to this problem in turn leads to a new approach to optimal filtering, smoothing and prediction using the Wiener theory. Unlike previous approaches to adaptive and self-tuning filtering, the technique, when implemented, does not require a priori information on the type or order of the signal generating model. And unlike other approaches - with the exception of spectral subtraction - no state-space or polynomial model is necessary. In this first paper results are restricted to stationary signal and additive white noise

Detection of network anomalies and novel attacks in the internet via statistical network traffic separation and normality prediction

With the advent and the explosive growth of the global Internet and the electronic commerce environment, adaptive/automatic network and service anomaly detection is fast gaining critical research and practical importance. If the next generation of network technology is to operate beyond the levels of current networks, it will require a set of well-designed tools for its management that will provide the capability of dynamically and reliably identifying network anomalies. Early detection of network anomalies and performance degradations is a key to rapid fault recovery and robust networking, and has been receiving increasing attention lately. In this dissertation we present a network anomaly detection methodology, which relies on the analysis of network traffic and the characterization of the dynamic statistical properties of traffic normality, in order to accurately and timely detect network anomalies. Anomaly detection is based on the concept that perturbations of normal behavior suggest the presence of anomalies, faults, attacks etc. This methodology can be uniformly applied in order to detect network attacks, especially in cases where novel attacks are present and the nature of the intrusion is unknown. Specifically, in order to provide an accurate identification of the normal network traffic behavior, we first develop an anomaly-tolerant non-stationary traffic prediction technique, which is capable of removing both pulse and continuous anomalies. Furthermore we introduce and design dynamic thresholds, and based on them we define adaptive anomaly violation conditions, as a combined function of both the magnitude and duration of the traffic deviations. Numerical results are presented that demonstrate the operational effectiveness and efficiency of the proposed approach, under different anomaly traffic scenarios and attacks, such as mail-bombing and UDP flooding attacks. In order to improve the prediction accuracy of the statistical network traffic normality, especially in cases where high burstiness is present, we propose, study and analyze a new network traffic prediction methodology, based on the frequency domain traffic analysis and filtering, with the objective_of enhancing the network anomaly detection capabilities. Our approach is based on the observation that the various network traffic components, are better identified, represented and isolated in the frequency domain. As a result, the traffic can be effectively separated into a baseline component, that includes most of the low frequency traffic and presents low burstiness, and the short-term traffic that includes the most dynamic part. The baseline traffic is a mean non-stationary periodic time series, and the Extended Resource-Allocating Network (BRAN) methodology is used for its accurate prediction. The short-term traffic is shown to be a time-dependent series, and the Autoregressive Moving Average (ARMA) model is proposed to be used for the accurate prediction of this component. Furthermore, it is demonstrated that the proposed enhanced traffic prediction strategy can be combined with the use of dynamic thresholds and adaptive anomaly violation conditions, in order to improve the network anomaly detection effectiveness. The performance evaluation of the proposed overall strategy, in terms of the achievable network traffic prediction accuracy and anomaly detection capability, and the corresponding numerical results demonstrate and quantify the significant improvements that can be achieved

Rational Covariance Extension, Multivariate Spectral Estimation, and Related Moment Problems: Further Results and Applications

This dissertation concerns the problem of spectral estimation subject to moment constraints. Its scalar counterpart is well-known under the name of rational covariance extension which has been extensively studied in past decades. The classical covariance extension problem can be reformulated as a truncated trigonometric moment problem, which in general admits infinitely many solutions. In order to achieve positivity and rationality, optimization with entropy-like functionals has been exploited in the literature to select one solution with a fixed zero structure. Thus spectral zeros serve as an additional degree of freedom and in this way a complete parametrization of rational solutions with bounded degree can be obtained. New theoretical and numerical results are provided in this problem area of systems and control and are summarized in the following. First, a new algorithm for the scalar covariance extension problem formulated in terms of periodic ARMA models is given and its local convergence is demonstrated. The algorithm is formally extended for vector processes and applied to finite-interval model approximation and smoothing problems. Secondly, a general existence result is established for a multivariate spectral estimation problem formulated in a parametric fashion. Efforts are also made to attack the difficult uniqueness question and some preliminary results are obtained. Moreover, well-posedness in a special case is studied throughly, based on which a numerical continuation solver is developed with a provable convergence property. In addition, it is shown that solution to the spectral estimation problem is generally not unique in another parametric family of rational spectra that is advocated in the literature. Thirdly, the problem of image deblurring is formulated and solved in the framework of the multidimensional moment theory with a quadratic penalty as regularization

Detection and restoration of click degraded audio based on high-order sparse linear prediction

Clicks are short-duration defects that affect most archived audio media. Linear prediction (LP) modeling for the representation and restoration of audio signals that have been corrupted by click degradation has been extensively studied. The use of high-order sparse linear prediction for the restoration of clickdegraded audio given the time location of samples affected by click degradation has been shown to lead to significant restoration improvement over conventional LP-based approaches. For the practical usage of such methods, the identification of the time location of samples affected by click degradation is critical. High-order sparse linear prediction has been shown to lead to better modeling of audio resulting in better restoration of click degraded archived audio. In this paper, the use of high-order sparse linear prediction for the detection and restoration of click degraded audio is proposed. Results in terms of click duration estimation, SNR improvement and perceptual audio quality show that the proposed approach based on high-order sparse linear prediction leads to better performance compared to state of the art LP-based approaches.&nbsp