A measure of the information content of EIT data

Adler, Andy and Youmaran, Richard and Lionheart, William R.B. (2008) A measure of the information content of EIT data. [MIMS Preprint]

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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

Item Type:	MIMS Preprint
Uncontrolled Keywords:	Measurement Information, Kullback Leibler Divergence, Electrical Impedance Tomography
Subjects:	PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 41 Electromagnetism; electron and ion optics PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 80 INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY > 87 Biological and medical physics
Depositing User:	Prof WRB Lionheart
Date Deposited:	24 Apr 2008
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1091

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