Tzipora Halevi

Statistical Methods for Object Detection in a Three Dimensional Volume

MS Thesis
Date: August 13, 1997

Abstract:

Anomaly detection in a physical medium is a common objective in many applications, including medical imaging, geological exploration and others. The anomaly detection problem is to identify regions of the medium which have significantly different characteristics than the rest of the medium from a given set of measurements.

In this thesis we develop and implement an algorithm for detection and localization of anomalous objects in a three dimensional volume from noisy data. The algorithm is based on a multi-scale hypothesis testing approach. It starts by considering the whole volume and uses detection and estimation techniques to identify sub-regions where the anomalies are likely to be found. It then continues the search recursively proceeding to finer scale localization. The algorithm includes a mechanism to incorporate into the search prior information about the anomalies (such as the number of anomalies, their sizes and shapes) via a set of penalty functions that are used in the detection procedures. We also examine a few feedback methods to improve the outcome of the algorithm.

We present experimental results of computer simulations, using synthetically generated data consisting of a few different anomaly configurations. The tests show that the algorithm achieves very good probabilities of detection and false alarm for very low SNRs. In addition, we present a partial analysis for the complexity of the algorithm. The analysis suggests that the complexity of the algorithm is logarithmic in the size of the medium. This result is also supported by our experimental results.

Committee:

Prof. E. Miller (advisor)
Prof. A. Devaney
Prof. C. Rappaport