A non-iterative method for the electrical impedance tomography based on joint sparse recovery *This work is supported by the Korean Ministry of Education, Sciences and Technology through NRF grant No. NRF-2010-0017532 (to H K), the Korean Ministry of Science, ICT & Future Planning; through NRF grant No. NRF-2013R1A1A3012931 (to M L), the R&D Convergence Program of NST (National Research Council of Science & Technology) of Republic of Korea (Grant CAP-13-3-KERI) (to O K L and J C Y). (19th May 2015)

• Record Type: Journal Article
• Authors: Lee, Ok Kyun; Kang, Hyeonbae; Ye, Jong Chul; Lim, Mikyoung
• Is Part Of: Inverse problems. Volume 31:Number 7(2015:Jul.)
• Publication Date: 2015-05-19
• Subjects: electrical impedance tomography -- joint sparsity recovery -- small anomalies -- compressed sensing -- non-iterative recovery; AMS subject classifications (2010). 35R30 -- 65F50; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/31/7/075002
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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.