Convexification inversion method for nonlinear SAR imaging with experimentally collected data.

This paper is concerned with the study of a version of the globally convergent convexification 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 the Earth or other planets. Recently, it has been applied in the context of non-invasive inspections of buildings in military and civilian services. Nowadays, any SAR imaging software is based on the Born 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 dielectric constants are imaged whose values are close to the constant background. In this work, we propose a radically new idea: to work without any linearization while still using the same data as the conventional SAR imaging technique uses. We construct a 2D image of the dielectric constant function using a number of 1D images of this function obtained via solving a 1D coefficient inverse problem (CIP) for a hyperbolic equation. Different from our previous studies on the convexification method with concentration on the global convergence of the gradient projection method, this time we prove the global convergence of the gradient descent method, which is easier to implement numerically.