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In this paper an approach to microwave imaging based on an inexact-Newton method within the contrast source formulation of the inverse scattering problem is considered. In this framework, the iteratively linearized equations of the inverse problem are solved by means of the regularizing truncated Landweber algorithm. This approach allows an effective and robust tool to inspect dielectric objects, as it is shown by the reported numerical results. Moreover, thanks to the structure of the involved integral equations within the contrast source formulation, computer memory saving can be obtained with respect to the electric field integral equation framework. Finally, the proposed method is validated against experimental data, kindly provided by the Institute Fresnel, Marseille, France.