(untitled) (Communications in Computational Physics, 2019)
In this work, we have proven the inhomogeneous obstacle can be uniquely determined by the measured acoustic pressure data and have proposed an extended multilevel sampling method. The extended recovery approach only applies the matrix-vector operations to estimate the inhomogeneous media from the received partial data. In practice, the method is capable of reconstructing the objects of different shapes and locations, robust against noise, computationally fairly cheap and easy to carry out. We can consider it as a simple and direct algorithm to supply satisfactory initial locations for the application of any existing more refined and precise but computationally more demanding techniques to achieve accurate reconstructions of physical features of scatterers.