基于实验数据的非线性SAR成像凸化反演方法
Convexification inversion method for nonlinear SAR imaging with experimentally collected data
摘要：
本文研究了一种直接应用于合成孔径雷达（SAR）成像的全局收敛凸化方法。数值测试的结果提出了一个假地雷的实验收集的数据。合成孔径雷达成像技术是一种常用的工具，用于绘制地球或其他行星表面的部分地图。最近，它已被应用于军事和民用服务的建筑物的非侵入性检查。目前，任何SAR成像软件都是基于玻恩近似的，玻恩近似是对原始波动型偏微分方程的线性化。这种线性化过程需要的基本假设之一是，只有那些介电常数被成像，其值接近恒定的背景。在这项工作中，我们提出了一个全新的想法：工作没有任何线性化，同时仍然使用相同的数据作为传统的SAR成像技术使用。我们构建了一个二维图像的介电常数函数使用的一些一维图像的这个功能，通过解决一个双曲型方程的一维系数反问题（CIP）。与我们以往对凸化方法的研究主要集中在梯度投影法的全局收敛性上不同，这次我们证明了梯度下降法的整体收敛，这种方法更容易数值实现。
英文摘要：
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.
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