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In this paper we discuss the approximate reconstruction of inhomogeneities of small volume. The data used for the reconstruction consist of boundary integrals of the (observed) electromagnetic fields. The numerical algorithms discussed are based on highly accurate asymptotic formulae for the electromagnetic fields in the presence of small volume inhomogeneities. Mathematics Subject Classification. 35J25, 35R30, 65R99.doi:10.1051/cocv:2002071 fatcat:jhjyoigfdjdj7afljlko34f6mq