Anomaly detection in three dimensional data based on Gauss Markov random field modeling

We present an anomaly detection approach for three dimensional data. We pre-process the 3D data using the Karhunen-Loeve transform (KLT), to remove correlation between data layers. Each layer is modeled as a Gauss Markov random field (GMRF). We present an efficient least squares method for model estimation. Anomaly detection is carried out in each data layer independently. We assume the anomalies lie in a known signal subspace. A different subspace is assumed for each data layer, such that a-priori knowledge about the sensors used to capture the data, or about the anomalies can be incorporated into the subspace. A parametric form of the model inverse covariance matrix is utilized to yield a computationally efficient detection. We demonstrate the performance of our approach by applying it to the detection of defects in wafer images and to detection of faults in 3D seismic data.