Greedy pursuit algorithms (GPAs) are widely used to reconstruct sparse signals. Even though many electromagnetic (EM) inverse scattering problems are solved on sparse investigation domains, GPAs have rarely been used for this purpose. This is because (i) they require a priori knowledge of the sparsity level in the investigation domain, which is often not available in EM imaging applications, and (ii) the EM scattering matrix does not satisfy the restricted isometric property. In this work, these challenges are respectively addressed by (i) using an artificial neural network (ANN) to estimate the sparsity level, and (ii) adding a Tikhonov regularization term to the diagonal elements of the scattering matrix. These enhancements permit the compressive sampling matching pursuit (CoSaMP) algorithm to be efficiently used to solve the two-dimensional EM inverse scattering problem, which is linearized using the Born approximation, on spatially sparse investigation domains. Numerical results, which demonstrate the efficiency and applicability of the proposed ANN-enhanced CoSaMP algorithm, are provided.