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

TL;DR

The paper presents a sparse direct sampling method (DSM) that efficiently estimates properties of regions from signals, combining low measurement cost with high resolution, demonstrated in radio wave and acoustic wave applications.

Contribution

Introduction of a sparse-DSM that generalizes older qualitative methods, reducing measurement needs while maintaining high resolution in inverse problems.

Findings

Effective in estimating angle-of-arrival of radio waves

Accurately locates and shapes inhomogeneities from acoustic data

Works on both measured and simulated data

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.