The factorization method for a penetrable cavity scattering with interior near-field measurements

Abstract

Abstract This paper is concerned with the inverse scattering problem of time-harmonic acoustic waves from a penetrable cavity bounded by a layered structure and seeks to determine the shape and location of the cavity from interior near-field measurements. Of particular interest is that the near-field operator does not satisfy the main theorem of the factorization method, so we introduce a modified near-field operator and prove that it can be used to reconstruct the cavity. Numerical examples demonstrate the feasibility and effectiveness of our algorithm.