Detection and classification of vibrating objects in SAR images

The vibratory response of buildings and machines contains key information that can be exploited to infer their operating conditions and to diagnose failures. Furthermore, since vibration signatures observed from the exterior surfaces of structures are intrinsically linked to the type of machinery operating inside of them, the ability to monitor vibrations remotely can enable the detection and identification of the machinery. This dissertation focuses on developing novel techniques for the detection and M-ary classification of vibrating objects in SAR images. The work performed in this dissertation is conducted around three central claims. First, the non-linear transformation that the micro-Doppler return of a vibrating object suffers through SAR sensing does not destroy its information. Second, the instantaneous frequency (IF) of the SAR signal has sufficient information to characterize vibrating objects. Third, it is possible to develop a detection model that encompasses multiple scenarios including both mono-component and multi-component vibrating objects immersed in noise and clutter. In order to cement these claims, two different detection and classification methodologies are investigated. The first methodology is data-driven and utilizes features extracted with the help of the discrete fractional Fourier transform (DFRFT) to feed machine-learning algorithms (MLAs). Specifically, the DFRFT is applied to the IF of the slow-time SAR data, which is reconstructed using techniques of time-frequency analysis. The second methodology is model-based and employs a probabilistic model of the SAR slow-time signal, the Karhunen-Loève transform (KLT), and a likelihood-based decision function. The performance of the two proposed methodologies is characterized using simulated data as well as real SAR data. The suitability of SAR for sensing vibrations is demonstrated by showing that the separability of different classes of vibrating objects is preserved even after non-linear SAR processing Finally, the proposed algorithms are studied when the range-compressed phase-history data is contaminated with noise and clutter. The results show that the proposed methodologies yields reliable results for signal-to-noise ratios (SNRs) and signal-to-clutter ratios (SCRs) greater than -5 dB. This requirement is relaxed to SNRs and SCRs greater than -10 dB when the range-compressed phase-history data is pre-processed with the Hankel rank reduction (HRR) clutter-suppression technique