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.
翻译:本文涉及研究直接应用于合成孔径雷达(SAR)成像的全球趋同凝结法的版本。数字测试的结果是用于实验收集的假地雷数据。合成孔径雷达(SAR)成像技术是用来绘制地球表面某些部分或其他行星的地图的通用工具。最近,在对军用和民用服务建筑物进行无侵入性视察的背景下应用了该技术。现在,任何合成孔径雷达成像软件都以原波状偏差方程的直线化法为基础。这种线性化程序所需要的一个基本假设是,只有那些其值接近常数背景的电离子常数常数才能被模拟。在这项工作中,我们提出了一个全新的想法:在没有线化的情况下工作,同时使用与常规的合成孔径雷达成像技术使用的同样数据。我们用一个1D图像来构建电离子常数的电常数。这个函数的直线化法是用于超偏斜方方程的1D系数(CIP)的直线化。这种直线化程序的一项基本假设是,即只有那些电动常数常数的常数,其值接近于常数的电常数的常数。我们以前关于电常数的常态常数的常数的常数的常数的常数,而我们提出的研究发现常数是用常数,我们用方法将全球渐相趋和渐变的渐趋和渐变法将的渐变法方法,我们用渐变的渐变法将的渐变法,我们测法将的渐变法在了全球渐变法将的渐变法,我们用的方法。我们的渐变法将的渐变法将了了了。我们的渐变法方法,我们的渐渐变法方法,我们用的渐变法将的渐渐渐渐渐渐渐渐渐渐渐地地地地地地地地地地地地的变法,我们的推。