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Proceedings Paper

Subspace-based analysis of the ERT inverse problem
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Paper Abstract

In a previous work, we proposed a source-type formulation to the electrical resistance tomography (ERT) problem. Specifically, we showed that inhomogeneities in the medium can be viewed as secondary sources embedded in the homogeneous background medium and located at positions associated with variation in electrical conductivity. Assuming a piecewise constant conductivity distribution, the support of equivalent sources is equal to the boundary of the inhomogeneity. The estimation of the anomaly shape takes the form of an inverse source-type problem. In this paper, we explore the use of subspace methods to localize the secondary equivalent sources associated with discontinuities in the conductivity distribution. Our first alternative is the multiple signal classification (MUSIC) algorithm which is commonly used in the localization of multiple sources. The idea is to project a finite collection of plausible pole (or dipole) sources onto an estimated signal subspace and select those with largest correlations. In ERT, secondary sources are excited simultaneously but in different ways, i.e. with distinct amplitude patterns, depending on the locations and amplitudes of primary sources. If the number of receivers is "large enough", different source configurations can lead to a set of observation vectors that span the data subspace. However, since sources that are spatially close to each other have highly correlated signatures, seperation of such signals becomes very difficult in the presence of noise. To overcome this problem we consider iterative MUSIC algorithms like R-MUSIC and RAP-MUSIC. These recursive algorithms pose a computational burden as they require multiple large combinatorial searches. Results obtained with these algorithms using simulated data of different conductivity patterns are presented.

Paper Details

Date Published: 21 May 2004
PDF: 12 pages
Proc. SPIE 5299, Computational Imaging II, (21 May 2004); doi: 10.1117/12.523385
Show Author Affiliations
Mohamed Khames Ben Hadj Miled, Northeastern Univ. (United States)
Eric L. Miller, Northeastern Univ. (United States)


Published in SPIE Proceedings Vol. 5299:
Computational Imaging II
Charles A. Bouman; Eric L. Miller, Editor(s)

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