Compressive sensing approaches for the prediction of scattered electromagnetic fields.

We present a novel method based on Huygens' principle and compressive sensing to predict the electromagnetic (EM) fields in arbitrary scattering environments by making a few measurements of the field. In doing so, we assume a homogeneous medium between the scatterers, though we do not assume prior knowledge of the permittivities or the exact geometry of the scatterers. The major contribution of this work is a compressive sensing-based subspace optimization method (CS-SOM).

Iteratively reweighted ℓ-ℓ norm minimization using wavelets in inverse scattering: publisher's note.

This publisher's note corrects the author list in J. Opt. Soc.

Iteratively reweighted ℓ-ℓ norm minimization using wavelets in inverse scattering.

Recently, many techniques have been employed to solve inverse scattering problems by exploiting the sparsity of the scatterer in the wavelet basis. In this paper, we propose an iteratively reweighted $ {\ell _1} $ norm regularization scheme within the settings of the Born iterative method (BIM) to effectively leverage the sparsity of the wavelet coefficients. This "iteratively reweighted $ {\ell _1} $ minimization" method is then used along with $ {\ell _2} $ norm minimization in order to achieve solutions that are not over-smoothened at the discontinuities.