Information Content of EIT Measurements

Abstract

Electrical Impedance Tomography (EIT) calculates internal conductivity from surface measurements;image reconstruction is most commonly formulated as an inverse problem using regularization techniques. Regularization adds "prior information" to adress the solution ill-conditioning. This paper presents a novel approach to understand and quantify this information. We ask: how many bits of information (in the Shannon sense) do we get from an EIT data frame. We define the term information in measurements (IM) as the: decrease in uncertainty about the contents of a medium, due to a set of measurements. Before the measurements, we know the prior information (inter-class model, q). The measured data tell us about the medium (which, corrupted by noise, gives the intra-class model, p). The measurement information is given by the relative entropy (or Kullback-Leibler divergence).