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This paper presents a survey of the subspace methods and their applications to electromagnetic inverse scattering problems. Subspace methods can be applied to reconstruct both small scatterers and extended scatterers, with the advantages of fast speed, good stability, and higher resolution. For inverse scattering problems involving small scatterers, the multiple signal classification method is used to determine the locations of scatterers and then the least-squares method is used to calculatedoi:10.4310/maa.2010.v17.n4.a6 fatcat:2vzu5sy4kjgtrhiv5rra6lbtea