Target Characterization Using Time-Reversal Symmetry of Wave Propagation

Over the last 15 years, there has been rapid growth in applications of time-reversal symmetry of wave propagation to enhance communications and imaging through highly scattering media. These techniques exploit both temporal and spatial reciprocity to mitigate signal distortion created from the large number of independent propagation paths between a transmitter and receiver. The time-reversal process is often described by the time-reversal operator (TRO), or equivalently by the multistatic response matrix (MRM), defined by the transmit and receive system. A singular value decomposition of this operator (or MRM) is the starting point for many of the time-reversal imaging techniques. In addition to imaging, this decomposition can also be used to extract information about objects embedded within the propagation medium, i.e., target characterization. In this paper, we review the development of target characterization in time-reversal, with an emphasis on extracting information from small targets. We will analyze the MRM for both acoustic and electromagnetic scattering and show how the symmetry of the target is reflected in the properties of the singular value spectrum. Finally, we discuss several open problems and potential applications.