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The multiple signal classification (MUSIC) type method has been widely used to detect point-like scatterers embedded in a homogeneous background medium. This paper extends the MUSIC-type method to the detection of point-like scatterers that are embedded in an inhomogeneous background. Although the background Green’s function at each test point is not directly available in inhomogeneous background scenario, this paper proposes an approach, based on the finite element method, to simultaneously obtain the Green’s function at all test points. Numerical simulations illustrate the efficacy of the proposed theory and algorithm presented in this paper, and some interesting observations, which are absent in homogeneous background scenario, are highlighted and discussed. [ABSTRACT FROM AUTHOR]