A sparsity-constrained sampling method with applications to communications and inverse scattering

Published

February 15, 2022

Author(s)

Jake Rezac, Isaac Harris

Abstract

We introduce a technique, the sparse direct sampling method (sparse-DSM), to estimate properties of a region from signals which probe the region. We demonstrate the sparse-DSM on two separate problems: estimating both the direction-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, meaning that it does not require the simulation of a forward problem to solve the inverse problem. We recover two older qualitative methods, one which has low-resolution reconstructions but uses few measurements and one which is high-resolution but has stricter measurement requirements. The sparse-DSM inherits positive qualities from both. We demonstrate the technique on both measured and simulated data.

Citation

Siam Journal on Applied Mathematics

Volume

451

Pub Type

Journals

Download Paper

https://doi.org/10.1016/j.jcp.2021.110890

Local Download

Citation

Rezac, J. and Harris, I. (2022), A sparsity-constrained sampling method with applications to communications and inverse scattering, Siam Journal on Applied Mathematics, [online], https://doi.org/10.1016/j.jcp.2021.110890, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=930879 (Accessed October 15, 2024)