This paper is devoted to the resolution of an inverse scattering problem. Such problems are known to be highly nonlinear and ill-posed. In our case, the reconstruction is rendered all the more difficult by the high contrast: the physical characteristics of the scattering object greatly differ from those of the surrounding medium. To properly counterbalance the ill-posedness of the problem, an original shape model taking into account precise prior information about the geometry of the scattering object is proposed. Moreover, the scatterer shape is described with a reduced number of variables and the parametrization enables one to solve the inverse problem with a gradient-based algorithm. This contributes to reduce the computation cost. Tests conducted on synthetic datasets reveal good performance of the proposed algorithm, contrary to more classical approaches based on a Tikhonov regularization scheme or the use of an edge-preserving penalization function.