This paper discusses a nonlinear diffractive inversion of the Helmholtz equation for multiscattering configurations, where the scatterers are embedded in an inhomogeneous background medium. Using the finite element model to iteratively compute the scattered field in conjunction with a novel discrete cosine transform (DCT) representation of the object function permits the development of an efficient nonlinear inversion algorithm. The object function expansion is obtained by applying the DCT to sampling points which are chosen at the zeros of the Chebyshev polynomials, and achieves an accuracy comparable to the more popular sinc basis with far fewer expansion terms. After the inverse scattering formulation is converted into a nonlinear parameter estimation problem, the final matrix equation is linearized and solved by a standard least‐squares algorithm. Several examples of two‐dimensional single‐ and multiple‐scattering configurations for both homogeneous and inhomogeneous acoustic backgrounds will illustrate the efficacy of the diffractive inverse algorithm.
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