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A non-iterative method for the electrical impedance tomography based on joint sparse recovery. (English) Zbl 1319.35301

Summary: The purpose of this paper is to propose a non-iterative method for the inverse conductivity problem of recovering multiple small anomalies from the boundary measurements. When small anomalies are buried in a conducting object, the electric potential values inside the object can be expressed by integrals of densities with a common sparse support on the location of anomalies. Based on this integral expression, we formulate the reconstruction problem of small anomalies as a joint sparse recovery and present an efficient non-iterative recovery algorithm of small anomalies. Furthermore, we also provide a slightly modified algorithm to reconstruct an extended anomaly. We validate the effectiveness of the proposed algorithm over the linearized method and the multiple signal classification algorithm by numerical simulations.

MSC:

35R30 Inverse problems for PDEs
45Q05 Inverse problems for integral equations
65F50 Computational methods for sparse matrices
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
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