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In the reconstruction process of unknown multiple scattering objects ininverse medium scattering problems, the first important step is to effectivelylocate some approximate domains that contain all inhomogeneous media. Withoutsuch an effective step, one may have to take a much larger computational domainthan actually needed in the reconstruction of all scattering objects, thusresulting in a huge additional computational efforts. In this work we propose asimple and efficient multilevel reconstruction algorithm to help locate anaccurate position and shape of each inhomogeneous medium. Then other existingeffective but computationally more demanding reconstruction algorithms may beapplied in these initially located computational domains to achieve moreaccurate 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 withscatterers of special shapes, and advantages in computational complexity.

A Multilevel Sampling Algorithm for Locating Inhomogeneous Media