Image sensors are typically characterized by slow sampling rates, which limit their efficacy in signal reconstruction applications. Their integrative nature though produces image blur when the exposure window is long enough to capture relative motion of the observed object relative to the sensor. Image blur contains more information on the observed dynamics than the typically used centroids, i.e., time averages of the motion within the exposure window. Parameters characterizing the observed motion, such as the signal derivatives at specified sampling instants, can be used for signal reconstruction through the derivative sampling extension of the known sampling theorem. Using slow image based sensors as derivative samplers allows for reconstruction of faster signals, overcoming Nyquist limitations. In this manuscript, we present an algorithm to extract values of a signal and its derivatives from blurred image measurements at specified sampling instants, i.e. the center of the exposure windows, show its application in two signal reconstruction numerical examples and provide a numerical study on the sensitivity of the extracted values to significant problem parameters.
- Dynamic Systems and Control Division
On Derivative Sampling From Image Blur for Reconstruction of Band-Limited Signals
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Tani, J, Mishra, S, & Wen, JT. "On Derivative Sampling From Image Blur for Reconstruction of Band-Limited Signals." Proceedings of the ASME 2014 Dynamic Systems and Control Conference. Volume 3: Industrial Applications; Modeling for Oil and Gas, Control and Validation, Estimation, and Control of Automotive Systems; Multi-Agent and Networked Systems; Control System Design; Physical Human-Robot Interaction; Rehabilitation Robotics; Sensing and Actuation for Control; Biomedical Systems; Time Delay Systems and Stability; Unmanned Ground and Surface Robotics; Vehicle Motion Controls; Vibration Analysis and Isolation; Vibration and Control for Energy Harvesting; Wind Energy. San Antonio, Texas, USA. October 22–24, 2014. V003T45A004. ASME. https://doi.org/10.1115/DSCC2014-6180
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