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The linear sampling method (LSM) is a simple and effective approach to image the shape of unknown targets via the solution of a linear inverse problem. In this paper, we show that the LSM can also be exploited to devise a novel effective approximation of the scattering phenomenon, that leads to a new noniterative linear inversion method for the estimation of the target's electric contrast. Since the introduced approximation relies on the broad applicability of the LSM, the proposed inversion method is suitable to tackle inverse scattering problems involving nonweak scatterers. As such, it represents an innovative, yet effective, way to tackle quantitative imaging. Examples with numerical and experimental data are given to show the performance of the approach. In particular, results obtained with Fresnel data-sets show that the proposed method is capable of successfully imaging targets which have been so far processed using nonlinear iterative schemes and taking advantage of frequency diversity.