  In the reconstruction process of unknown multiple scattering objects in
inverse medium scattering problems, the first important step is to effectively
locate some approximate domains that contain all inhomogeneous media. Without
such an effective step, one may have to take a much larger computational domain
than actually needed in the reconstruction of all scattering objects, thus
resulting in a huge additional computational efforts. In this work we propose a
simple and efficient multilevel reconstruction algorithm to help locate an
accurate position and shape of each inhomogeneous medium. Then other existing
effective but computationally more demanding reconstruction algorithms may be
applied in these initially located computational domains to achieve more
accurate shapes of the scatter and the contrast values over each medium domain.
The new algorithm exhibits several strengths: robustness against noise,
requiring less incidences, fast convergence, flexibility to deal with
scatterers of special shapes, and advantages in computational complexity.
