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An inversion algorithm is presented that is based on hybridization of the adjoint scheme for calculating gradient directions with the method of moments. The goal is to reconstruct the shapes of 3D objects immersed in a lossy medium. The irregular shape of the reference object is modeled by a representation with spherical harmonics functions, whereas during the reconstruction, individual surface nodes are updated. In the adjoint scheme, gradient directions for the least squares data misfit cost functional are calculated by solving the forward problem twice in each iteration, regardless of the number of spherical harmonics parameters used in the reference model or the number of surface nodes used for the discretization of the shapes. The numerical results show that implementing the well known frequency hopping technique helps the algorithm avoid dropping in local minima.