Summary: The inverse scattering problem for objects characterized by compactly supported scattering potentials embedded in a known inhomogeneous background medium given single-frequency, multistatic data is addressed within the distorted wave Born approximation (DWBA). The DWBA formulation of the multistatic data matrix is found to be in the form of a linear mapping from the Hilbert space of compactly supported scattering potentials to the finite-dimensional space \(C^N\) of complex \(N\)-tuples where \(N = N_\beta \times N_\alpha\) is the product of the number of receiver elements \(N_\beta\) with the number of transmitter elements \(N_\alpha\). A pseudo-inverse of this mapping is shown to be representable as a series of products of complex conjugate background Green functions whose expansion coefficients are readily found by inverting a set of \(N\) simultaneous linear algebraic equations in \(N\) unknowns. An expression for the point spread function of the inversion algorithm is computed that is object independent and only a function of the background Green function and the measurement geometry, and thus allows the user to access 'image quality' of the algorithm as a function of these quantities. The paper includes a number of computer simulations illustrating the reconstruction algorithm developed in the paper.