PolInSAR Coherence Set Theory and Application

In this paper we investigate coherence sets in polarimetric SAR interferometry. The coherence set is closely related to the numerical range (field of values). This paper aims to bring the numerical range to the attention of the radar research community. The mathematical understanding of the numerical range helps to understand theoretical and physical properties of coherence and coherency matrix. This paper presents a structured hierarchy of coherence sets and corresponding numerical ranges. Different applications which are related to numerical ranges are reviewed. An example of the inverse analysis of the coherence set is performed to obtain information about the coherency matrix. Finally, a generalization of the coherence set applications is presented.