Optimal imaging with adaptive mesh refinement in electrical tomography

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Description/Abstract

In non-linear electrical tomography the goodness of fit of the trial images is assessed by the well-established statistical χ^2 criterion applied to the measured and predicted data sets. Further selection from the range of images that fit the data is effected by imposing an explicit constraint on the form of the image, such as minimisation of the image gradients. In particular, the logarithm of the image gradients is chosen so that conductive and resistive deviations are treated in the same way. In this paper we introduce the idea of adaptive mesh refinement to the 2-d problem so that the local scale of the mesh is always matched to the scale of the image structures. This improves the reconstruction resolution so that the image constraint adopted dominates and is not perturbed by the mesh discretization. The avoidance of unnecessary mesh elements optimises the speed of reconstruction without degrading the resulting images. Starting with a mesh scale length of the order of the electrode separation it is shown that, for data obtained at presently achievable signal-to-noise ratios of 60dB to 80dB, one or two refinement stages are sufficient to generate high quality images.