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It has been demonstrated that the MUltiple SIgnal Classification (MUSIC)algorithm is fast, stable, and effective for localizing small anomalies inmicrowave imaging. For the successful application of MUSIC, exact values ofpermittivity, conductivity, and permeability of the background must be known.If one of these values is unknown, it will fail to identify the location of ananomaly. However, to the best of our knowledge, no explanation of this failurehas been provided yet. In this paper, we consider the application of MUSIC tothe localization of a small anomaly from scattering parameter data whencomplete information of the background is not available. Thanks to theframework of the integral equation formulation for the scattering parameterdata, an analytical expression of the MUSIC-type imaging function in terms ofthe infinite series of Bessel functions of integer order is derived. Based onthe theoretical result, we confirm that the identification of a small anomalyis significantly affected by the applied values of permittivity andconductivity. However, fortunately, it is possible to recognize the anomaly ifthe applied value of conductivity is small. Simulation results with syntheticdata are reported to demonstrate the theoretical result.

Application of MUSIC-type imaging for anomaly detection without background information