A measure of the information content of EIT data
We ask: how many bits of information (in the Shannon sense) do we get from a set of EIT measurements? Here, the term information in measurements (IM) is defined as: the decrease in uncertainty about the contents of a medium, due to a set of measurements. This decrease in uncertainty is quantified by the change from the inter-class model, q, defined by the prior information, to the intra-class model, p, given by the measured data (corrupted by noise). IM is measured by the expected relative entropy (Kullback-Leibler divergence) between distributions q and p, and corresponds to the channel capacity in an analogous communications system. Based on a Gaussian model of the measurement noise, Σn, and a prior model of the image element covariances Σx, we calculate IM = 1/2 Σ log2([SNR] i + 1), where [SNR]i is the signal-to-noise ratio for each independent measurement calculated from the prior and noise models. For an example, we consider saline tank measurements from a 16 electrode EIT system, with a 2 cm radius non-conductive target, and calculate IM = 179 bits. Temporal sequences of frames are considered, and formulae for IM as a function of temporal image element correlations are derived. We suggest that this measure may allow novel insights into questions such as distinguishability limits, optimal measurement schemes and data fusion.
|Keywords||Electrical impedance tomography, Kullback-Leibler divergence, Measurement information|
Adler, A, Youmaran, R. (Richard), & Lionheart, W.R.B. (William R. B.). (2008). A measure of the information content of EIT data. Physiological Measurement, 29(6). doi:10.1088/0967-3334/29/6/S09