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This paper presents a linear synthetic focusing method (SFM) in order to mitigate the drawbacks of the classical multiple signal classification (MUSIC) algorithm for microwave imaging (MI). The determination of noise subspace dimension for MUSIC algorithm is a challenge when imaging an extended target. That is because an extended target comprises many point scatterers and a practical MI system provides an incomplete multistatic response (IMSR) matrix. The SFM obtains a focused multistatic response matrix for each location in the imaging region, which contains, mostly, the scattered field of a point scatterer at that location. In this way, the signal subspace is reduced to the one for a point scatterer, whose singular values are well-separated from those of the noise subspace. The proposed SFM is applied to the breast cancer detection using synthetic data. It is also applied to the experimental data given by Institute Fresnel to test the SFM for scenarios other than biomedical uses. It is shown that the SFM provides superior results over the classical MUSIC algorithm, especially for extended targets and IMSR matrices. [ABSTRACT FROM AUTHOR]