Feature-Enhancing Inverse Methods for Limited-View Tomographic Imaging Problems

In this paper we overview current efforts in the development of inverse methods which directly extract target-relevant features from a limited data set. Such tomographic imaging problems arise in a wide range of fields making use of a number of different sensing modalities. Drawing these problem areas together is the similarity in the underlying physics governing the relationship between that which is sought and the data collected by the sensors. After presenting this physical model, we explore its use in two classes of feature-based inverse methods. Microlocal techniques are shown to provide a natural mathematical framework for processing synthetic aperture radar data in a manner that recovers the edges in the resulting image. For problems of diffusive imaging, we describe our recent efforts in parametric, shape-based techniques for directly estimating the geometric structure of an anomalous region located against a perhaps partially-known background.