2017/05/02 by Emilia Blåsten, Hongyu Liu, Blåsten, Emilia +1 · 1 citation
Engineering · Mathematics · #35P25 #35R30 #58J50 #81V80 #Analysis of PDEs (math.AP) #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1705.00815
openalex publication_date 2017/05/02 · openalex created_date 2017/05/12 · openalex updated_date 2026/07/28
We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a perturbation to the refractive index on the corners of its support. These assumptions are satisfied for example in the low acoustic frequency regime. As a consequence if the perturbation is piecewise constant with either a polyhedral nest geometry or a known polyhedral cell geometry, such as a pixel or voxel array, we establish the injectivity of the perturbation to far-field map given a fixed incident wave. This is the first unique determinancy result of its type in the literature, and all of the existing results essentially make use of infinitely many measurements.