Statistically based methods for anomaly characterization in images from observations of scattered radiation

In this paper, we present an algorithm for the detection, localization, and characterization of anomalous structures in an overall region of interest given observations of scattered electromagnetic fields obtained along the boundary of the region. Such anomaly detection problems are encountered in applications including medical imaging, radar signal processing, and geophysical exploration. The techniques developed in this work are based on a nonlinear scattering model relating the anomalous structures to the observed data. A sequence of M-ary hypothesis tests are employed first to localize anomalous behavior to large areas and then to refine these initial estimates to better characterize the true target structures. We introduce a method for the incorporation of prior information into the processing which reflects constraints relevant directly to the anomaly detection problem such as the number, shapes, and sizes of anomalies present in the region. The algorithm is demonstrated using a low-frequency, inverse conductivity problem found in geophysical applications.