Identifying Active Anomalies in a Multilayered Medium by Passive Measurement in EIT

SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1362-1384, August 2024.
Abstract. We propose to study an inverse problem of determining multiple anomalies embedded in a multilayered background medium by the associated electric measurement which arises in Electrical Impedance Tomography (EIT). There are several salient features of our study. First, the anomaly considered in our study is extremely general which is characterized by its location, support, varying size, conductivity parameter, as well as a carry-on source intensity. Second, we make use of the measurement of the electric field generated by the active anomalies. This corresponds to a single passive measurement. Third, the background medium is of a multilayered and piecewise-constant structure and can be used to model a more general scenario from practical applications; say, e.g., the human body. Under the condition that the anomalies are small, but still in multiple scales considering their varying sizes, we derive a sharp formula of the electric field in terms of the polarization tensors, which enables us to establish comprehensive unique identifiability results in determining the characteristic parameters of the active anomalies in different situations.