John C. Schotland

Liliana Borcea, Wei Li, Alexander V. Mamonov et al.

We consider the problem of optical imaging of small nonlinear scatterers in random media. We propose an extension of coherent interferometric imaging (CINT) that applies to scatterers that emit second-harmonic light. We compare this method to a nonlinear version of migration imaging and find that the images obtained by CINT are more robust to statistical fluctuations. This finding is supported by a resolution analysis that is carried out in the setting of geometrical optics in random media. It is also consistent with numerical simulations for which the assumptions of the geometrical optics model do not hold.

John C. Schotland, Shenwen Yu

We investigate inverse scattering problems for Dirac equations that arise as continuum models of waveguide arrays. We first establish the well-posedness of the forward models. For the associated inverse problems, we develop the inverse Born series and the reduced inverse Born series, providing analysis of convergence and rigorous error estimates. Numerical experiments are presented to validate the proposed algorithms and demonstrate their effectiveness.

Anna C. Gilbert, Howard W. Levinson, John C. Schotland

We consider the inverse scattering problem for sparse scatterers. An image reconstruction algorithm is proposed that is based on a nonlinear generalization of iterative hard thresholding. The convergence and error of the method was analyzed by means of coherence estimates and compared to numerical simulations.