  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.
