2008.52: A measure of the information content of EIT data

2008.52: Andy Adler, Richard Youmaran and William R.B. Lionheart (2008) A measure of the information content of EIT data.

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Abstract

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 denotned as: the decrease in uncertainty about the contents of a medium, due to a set of measurements. This decrease in uncertainly is quantified by the change from the the inter-class model, q, denotned 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, Σ_n, and a prior model of the image element covariances Σ_x, we calculate IM= (1/2) Σ log_2([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

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