2020/10/15 by Isaac Harris, Harris, Isaac, Jacob D. Rezac +1
Engineering · #Analysis of PDEs (math.AP) #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Sparse and Compressive Sensing Techniques #Ultrasonics and Acoustic Wave Propagation
paper · pdf · doi:10.48550/arxiv.2010.08032
openalex publication_date 2020/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.