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

Published

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

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 August 18, 2022)
Created February 15, 2022, Updated February 23, 2022