Compressive sensing of high speed periodic videos
(a) Coded strobing schematic: Capture periodic phenomena by coding the shutter of a low frame-rate camera during every frame and reconstruct the phenomena at a higher rate by exploiting sparsity of periodic signals.

(b) Observation and signal model: At every pixel, the signal is periodic in time and has sparse Fourier coefficients. Observed values are a linear combination of the Fourier coefficients. The resulting under-determined system of equations are solved by enforcing sparsity of the coefficients.

(c) Results: A mill tool rotating at 50 Hz is captured by the coded strobing camera at 25 fps. The mill-tool is reconstructed at 2000 fps by enforcing sparsity of the Fourier coefficients.

We show that, via temporal modulation, one can observe and capture a high-speed periodic video well beyond the abilities of a low-frame-rate camera. By strobing the exposure with unique sequences within the integration time of each frame, we take coded projections of dynamic events. From a sequence of such frames, we reconstruct a high-speed video of the high-frequency periodic process. Strobing is used in entertainment, medical imaging, and industrial inspection to generate lower beat frequencies. But this is limited to scenes with a detectable single dominant frequency and requires high-intensity lighting. In this paper, we address the problem of sub-Nyquist sampling of periodic signals and show designs to capture and reconstruct such signals. The key result is that for such signals, the Nyquist rate constraint can be imposed on the strobe rate rather than the sensor rate. The technique is based on intentional aliasing of the frequency components of the periodic signal while the reconstruction algorithm exploits recent advances in sparse representations and compressive sensing. We exploit the sparsity of periodic signals in the Fourier domain to develop reconstruction algorithms that are inspired by compressive sensing.

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Coded Strobing Photography: Compressive Sensing of High Speed Periodic Videos. Veeraraghavan, A., Reddy, D., Raskar, R. (2011) IEEE Transactions on Pattern Analysis and Machine Intelligence. Paper. BibTex.

Streaming Compressive Sensing for High-speed Periodic Videos. Asif, M. S., Reddy, D., Boufounos, P., Veeraraghavan, A., (2010) Proceedings of IEEE International Conference on Image Processing. Paper. Videos. BibTex.

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