A new non-iterative inversion method for electrical resistance tomography

In this paper, the inverse problem of resistivity retrieval is addressed in the frame of electrical resistance tomography (ERT). The ERT data is a set of measurements of the dc resistances between pairs of electrodes in contact with the conductor under investigation. This paper is focused on a non-iterative inversion method based on the monotonicity of the resistance matrix (and of its numerical approximations). The main features of the proposed inversion method are its low computational cost requiring the solution of O(n) direct problems, where n is the number of parameters used to represent the unknown resistivity, and its very simple numerical implementation.