A sparsity-constrained sampling method with applications to communications and inverse scattering
Abstract
We introduce the sparse direct sampling method (DSM) to estimate properties of a region from signals that probe the region. We demonstrate the sparse-DSM on two separate problems: estimating both the angle-of-arrival of a radio wave impinging on an array and the location and shape of an inhomogeneity from scattered acoustic waves. The sparse-DSM is qualitative in nature, so it does not require the simulation of a forward problem to solve the inverse problem. The method generalizes of two older qualitative methods, one which has low-resolution reconstructions but uses few measurements and one which is high-resolution but has higher measurement cost. The sparse-DSM inherits positive qualities from both. We demonstrate the technique on measured and simulated examples.
Cite
@article{arxiv.2010.08032,
title = {A sparsity-constrained sampling method with applications to communications and inverse scattering},
author = {Isaac Harris and Jacob D Rezac},
journal= {arXiv preprint arXiv:2010.08032},
year = {2020}
}