  Inverse problems are more challenging when only partial data are available in
general. In this paper, we propose a two-step approach combining the extended
sampling method and the ensemble Kalman filter to reconstruct an elastic rigid
obstacle using partial data. In the first step, the approximate location of the
unknown obstacle is obtained by the extended sampling method. In the second
step, the ensemble Kalman filter is employed to reconstruct the shape. The
location obtained in the first step guides the construction of the initial
particles of the ensemble Kalman filter, which is critical to the performance
of the second step. Both steps are based on the same physical model and use the
same scattering data. Numerical examples are shown to illustrate the
effectiveness of the proposed method.
