An improved algorithm for reconstruction of small inhomogeneities from acoustic measurements

Reconstruction of unknown medium characteristics such as shape, refractive index by measurements of scattered acoustic wave data has wide application in nondestructive detection for engineering and medical use, which is a typical nonlinear and severely ill-posed problem. Under the setting of a smooth background containing a small number of unknown small inhomogeneous inclusions, we propose in this paper an efficient algorithm to reconstruct these inhomogeneities from scattered wave measurement data incited by a single-frequency acoustic wave. The proposed algorithm includes a modified treatment of quadrature rule for the singular kernel in the fundamental solution of Helmholtz equation, which enables a more accurate evaluation of the simulated total field. Numerical experiments validate the effectiveness and robustness of this algorithm in reconstructing small inhomogeneous medium in two dimensions.