IET RADAR, SONAR AND NAVIGATION 1 Multi-Window Time-Frequency Signature Reconstruction from Undersampled Continuous Wave Radar Measurements for Fall Detection

Fall detection is an area of increasing interest in independence-assisting remote monitoring tech-nologies for the elderly population. Immediate assistance following a fall can lower the risk of medical complications, thus saving lives and reducing the associated health care costs. Therefore, it is important to detect a fall as it happens and promptly mobilize first responders for proper care and attendance to possible injury. Radar offers privacy and non-intrusive monitoring capabilities. Micro-Doppler signatures are typically employed for radar based human motion detections and classifications. Proper time-frequency signal representation is, therefore, required from which important features can be extracted. Missing or noise/interference corrupted data can compromise the integrity of micro-Doppler signatures and subsequently confuse the classifier. In this paper, we restore the time-frequency signatures associated with human motor activities, such as falling, bending over, sitting, and standing, by using a hybrid approach of compressive sensing and multi-window analysis based on Slepian or Hermite functions. Because time-frequency representations of many human gross-motor activities are sparse and share common support in joint-variable domains, the multiple measurement vector approach can be effectively applied for fall classification in both cases of full data or compressed observations. Index Terms Hermite functions, missing samples, multi-window time-frequency representation, multiple measurement vector, Slepian sequences, fall detection