Smoothness-constrained inversion for two-dimensional electrical resistance tomography

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Abstract
Two-dimensional image reconstruction in electrical resistance tomography (ERT) involves determination of the electrical conductivities throughout the cross section of the region being imaged. Quantitative image reconstruction in ERT is an ill-conditioned problem and therefore some sort of regularization is required in order to provide meaningful images. Typically, this is achieved using the Marquardt - Levenberg regularization. In this work, a new data acquisition system developed at UMIST, the Mark 2a, is briefly described and a smoothness-constrained regularization is presented, which is shown to be superior to the widely used Marquardt - Levenberg regularization in the presence of Gaussian noise in the collected data.