Convexification Inversion Method for Nonlinear SAR Imaging with Experimentally Collected Data

Abstract: This paper is concerned with the study of a version of the globally convergentconvexification method with direct application to synthetic aperture radar (SAR) imaging.Results of numerical testing are presented for experimentally collected data for a fake landmine.The SAR imaging technique is a common tool used to create maps of parts of the surface of theEarth or other planets. Recently, it has been applied in the context of noninvasive inspections ofbuildings in military and civilian services. Nowadays, any SAR imaging software is based on theBorn approximation which is a linearization of the original wave-like partial differential equation.One of the essential assumptions this linearization procedure needs is that only those dielectricconstants are imaged whose values are close to the constant background. In this work, we proposea radically new idea: to work without any linearization while still using the same data as theconventional SAR imaging technique uses. We construct a 2D image of the dielectric constantfunction using a number of 1D images of this function obtained via solving a 1D coefficient inverseproblem (CIP) for a hyperbolic equation. Different from our previous studies on theconvexification method with concentration on the global convergence of the gradient projectionmethod, this time we prove the global convergence of the gradient descent method, which is easierto implement numerically. © 2021, Pleiades Publishing, Ltd.