M.Sc Thesis

M.Sc StudentNoiboar Amir
SubjectAnomaly Detection Based on Wavelet Domain GARCH Random
Field Modeling
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROF. Israel Cohen
Full Thesis textFull thesis text - English Version


Image anomaly detection is the process of distilling a small number of clustered pixels, which differ from the image's general characteristics. Anomaly detection algorithms generally consist of three stages: selection of an appropriate feature space in which the distinction between the anomaly and the general clutter is possible; selection of a statistical model for the feature space representing the image clutter and selection of a detection algorithm. This last stage implies a selection of an anomaly model, which defines the type of anomaly or anomalies relevant for the application. This research focuses on the latter two stages.

The Gaussian distribution is a common basis for feature space statistical models due to its mathematical tractability. A major drawback of using the Gaussian distribution lays in its inability to appropriately model two common phenomena of often used feature spaces: heavy tails of the probability density function of the features (known as excess kurtosis) and volatility clustering (a property of many heteroscedastic stochastic processes, which means that large changes tend to follow large changes and small changes tend to follow small changes). Detection algorithms based on Gaussian models may result in high false alarm rates when applied to such feature spaces, due to the inadequacy between the model and the data.

We thus introduce an $N $ dimensional generalized autoregressive conditional heteroscedasticity (GARCH) model. The $1 $D GARCH model is widely used for modeling financial time series. Extending the GARCH model into $N $ dimensions yields a novel clutter model which is capable of taking into account important characteristics of commonly used feature spaces, namely heavy-tailed distributions and innovations clustering as well as spatial and depth correlations.

Once statistical modeling is accomplished, we are faced with the challenge of developing an appropriate detection approach. In this research we develop a detector, which is comprised of a set of multiscale Matched Subspace Detectors (MSDs). The MSD was originally developed for the detection of signal in subspace interference and additive white Gaussian noise. Our MSDs operate in additive GARCH noise.

We demonstrate the performance of the proposed approach on synthetic data and on real sea-mine side-scan sonar images. Our results show the potential of the set of MSDs, the importance of an appropriate statistical model for the background and the advantages of the GARCH statistical model.