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

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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.