Using Alternating Minimization and Convexified Carleman Weighted Objective Functional for a Time-Domain Inverse Scattering Problem

This paper considers a 1D time-domain inverse scattering problem for the Helmholtz equation in which penetrable scatterers are to be determined from boundary measurements of data. It is formulated as coefficient identification wave equation. Using Laplace transform, converted into an overdetermined nonlinear system partial differential equations. To solve this system, Carleman weighted objective functional, proved strictly convex arbitrary set Hilbert space, constructed. An alternating minimization algorithm used minimize functional. Numerical results presented illustrate performance proposed algorithm.