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

Isaac Harris; Jacob D Rezac

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arXiv · 2010.08032

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

Isaac Harris·Jacob D Rezac

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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.

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Isaac Harris, Jacob D Rezac. 2020-10-15. A sparsity-constrained sampling method with applications to communications and inverse scattering. https://arxiv.org/abs/2010.08032

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