An efficient qualitative imaging method for acoustic non-invasive testing

In this work, we propose an efficient qualitative imaging method for acoustic non-invasive testing in two dimensions through boundary measurements. In acoustic non-invasive testing, one intends to recover the location, size and geometrical shape of unknown obstacles by the knowledge of the waves away from the objects of interest, which has many promising applications, e.g., breast cancer imaging and mine detection. The main ingredient of the method is based on the blow-up property of a specific indicator function, which is formulated as the solution of an integral equation involving boundary measurement data and the Green function. A fast qualitative imaging algorithm with two key indicator functions is proposed based on the regularized solution of the integral equation. Numerical experiments are presented to illustrate the feasibility and effectiveness of the proposed imaging scheme.