A Neural Network Assisted Greedy Algorithm For Sparse Electromagnetic Imaging

Abstract

Greedy pursuit algorithms (GPAs), are well appreciated candidates for accurate and efficient reconstruction of sparse signal and image processing applications. Even though many electromagnetic (EM) imaging applications are naturally sparse, GPAs have rarely been explored for this purpose. This is because, for accurate reconstruction, GPAs require (i) the exact number of non-zeros, 'k', in the unknown to be reconstructed. This information is not available a-priori for EM imaging applications, and (ii) the measurement matrix to satisfy the restricted isometric property (RIP), whereas the EM scattering matrix which is obtained by sampling the Green's function between measurement locations and the unknowns does not satisfy the RIP. To address the aforementioned limitations, two solutions are proposed. First, an artificial neural network (ANN) is trained on synthetic measurements, such that given a set of measurements, the ANN produces an estimate of 'k'. Second, Tikhonov second norm regularization term is added to the diagonal elements of the scattering matrix, which scales the eigenvalues of the scattering matrix such that it satisfies the RIP. The CoSaMP algorithm, which is at the heart of GPAs, is then applied, to accurately and efficiently reconstruct the unknown. The proposed scheme implicitly imposes the sparsity constraint, as the regularization parameter is specified by the ANN, hence no additional tuning is required from the user. Numerical results demonstrate the efficiency and superiority of the proposed scheme.