2020/03/25 by Vo Anh Khoa, Grant W. Bidney, Khoa, Vo Anh +11 · 3 citations
Mathematics · Engineering · #Numerical methods in inverse problems #Microwave Imaging and Scattering Analysis #Photoacoustic and Ultrasonic Imaging
paper · pdf · doi:10.48550/arxiv.2003.11513
Inverse scattering problems of the reconstructions of physical properties of\na medium from boundary measurements are substantially challenging ones. This\nwork aims to verify the performance on experimental data of a newly developed\nconvexification method for a 3D coefficient inverse problem for the case of\nobjects buried in a sandbox a fixed frequency and the point source moving along\nan interval of a straight line. Using a special Fourier basis, the method of\nthis work strongly relies on a new derivation of a boundary value problem for a\nsystem of coupled quasilinear elliptic equations. This problem, in turn, is\nsolved via the minimization of a Tikhonov-like functional weighted by a\nCarleman Weight Function. The global convergence of the numerical procedure is\nestablished analytically. The numerical verification is performed using\nexperimental data, which are raw backscatter data of the electric field. These\ndata were collected using a microwave scattering facility at The University of\nNorth Carolina at Charlotte.\n