Lee, Ok Kyun; Kang, Hyeonbae; Ye, Jong Chul; Lim, Mikyoung A non-iterative method for the electrical impedance tomography based on joint sparse recovery. (English) Zbl 1319.35301 Inverse Probl. 31, No. 7, Article ID 075002, 23 p. (2015). 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. Cited in 1 Document 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 Keywords:electrical impedance tomography; joint sparsity recovery; small anomalies; compressed sensing; non-iterative recovery PDFBibTeX XMLCite \textit{O. K. Lee} et al., Inverse Probl. 31, No. 7, Article ID 075002, 23 p. (2015; Zbl 1319.35301) Full Text: DOI arXiv