  Video capture is limited by the trade-off between spatial and temporal
resolution: when capturing videos of high temporal resolution, the spatial
resolution decreases due to bandwidth limitations in the capture system.
Achieving both high spatial and temporal resolution is only possible with
highly specialized and very expensive hardware, and even then the same basic
trade-off remains. The recent introduction of compressive sensing and sparse
reconstruction techniques allows for the capture of single-shot high-speed
video, by coding the temporal information in a single frame, and then
reconstructing the full video sequence from this single coded image and a
trained dictionary of image patches. In this paper, we first analyze this
approach, and find insights that help improve the quality of the reconstructed
videos. We then introduce a novel technique, based on convolutional sparse
coding (CSC), and show how it outperforms the state-of-the-art, patch-based
approach in terms of flexibility and efficiency, due to the convolutional
nature of its filter banks. The key idea for CSC high-speed video acquisition
is extending the basic formulation by imposing an additional constraint in the
temporal dimension, which enforces sparsity of the first-order derivatives over
time.
