  We present a novel method for the classification and reconstruction of time
dependent, high-dimensional data using sparse measurements, and apply it to the
flow around a cylinder. Assuming the data lies near a low dimensional manifold
(low-rank dynamics) in space and has periodic time dependency with a sparse
number of Fourier modes, we employ compressive sensing for accurately
classifying the dynamical regime. We further show that we can reconstruct the
full spatio-temporal behavior with these limited measurements, extending
previous results of compressive sensing that apply for only a single snapshot
of data. The method can be used for building improved reduced-order models and
designing sampling/measurement strategies that leverage time asynchrony.
