Co-registered Vibrometry and Imaging: A Combined Synthetic-Aperture Radar and Fractional-Fourier Transform Approach [29U08UNMhaya]

该项目的目标是为合成孔径雷达（SAR）成像引入一种革命性的方法，该方法独特地将共配准振动传感与高分辨率成像相结合。SAR平台非常适合解决这个问题，因为(1)它已经被证明是一种高效的成像技术，(2)它本身就能够感知物体电磁回波中振动引起的多普勒频移。一个强大的信号处理工具，称为分数傅里叶变换（FRFT），在这个项目中被用作框架来设计一种新的多脉冲、多啁啾SAR成像策略，该策略产生叠加在高分辨率SAR图像上的振动频率空间图（频谱图）。将开发新的基于子空间的估计算法，利用FRFT框架获得高分辨率的啁啾率和中心频率估计，这些估计在统计上是一致的和渐近最优的；这些估计反过来转化为由SAR成像系统照射的振动物体的瞬时速度的估计。将开发一个简单的实验室平台来演示所提出的传感概念。基于所提出的方法生成的签名识别结构的反问题也将被研究。在这个项目中，一名本科生将被提名获得NCMR本科生奖学金，我们将努力通过与桑迪亚国家实验室的合作，为我们的学生创造实习机会。研究成果将整合到新墨西哥大学目前的两门课程中：研究生水平的数字信号处理课程和高级水平的选修课程雷达信号处理。

The objective of this project is to introduce a revolutionary approach for synthetic-aperture-radar (SAR) imaging that uniquely combines co-registered vibration sensing with high-resolution imaging. The SAR platform is a natural fit to the problem because (1) it has already been proven as a highly effective imaging technology and (2) it is inherently capable of sensing vibration-induced Doppler shifts in the electromagnetic returns from objects. A powerful signal-processing tool, called the fractional Fourier transform (FRFT), is exploited in this project as a framework to design a novel multi-pulse, multi-chirp SAR imaging strategy that yields a spatial map of vibration frequencies (spectrograms) superimposed on high-resolution SAR imagery. New subspace-based estimation algorithms will be developed that employ the FRFT framework to obtain high-resolution chirp-rate and center-frequency estimates that are statistically consistent and asymptotically optimal; these estimates translate, in turn, into estimates of the instantaneous velocity of the vibrating objects that are illuminated by a SAR imaging system. A simple laboratory platform to demonstrate the proposed sensing concept will be developed. The inverse problem of identifying structures based upon signatures generated by the proposed approach will also be studied. During this project, one undergraduate student will be nominated to receive the NCMR Undergraduate Scholarship and effort will be made through our collaboration with the Sandia National Laboratories to create internship opportunities for our students. Research results will be integrated into two current courses at the University of New Mexico: a graduate-level Digital Signal Processing course and a senior-level elective course titled Radar Signal Processing.